JP2014011577A - Signal processing system and signal processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a signal processing system that reduces the load of compression and restoration processes in compressive sensing.SOLUTION: The signal processing system includes: a random compressive matrix generation section for generating a random compressive matrix having in random positions of rows and columns smaller numbers of nonzero random values than the numbers of rows and columns of a compressive matrix; a compression section for matrix-multiplying every preset frame size of an input digital signal by the random compressive matrix to compress the input digital signal; a random restorative matrix generation section for referring to the random compressive matrix to generate a random restorative matrix equivalent to the random compressive matrix; and a restoration section for performing a restoration process using the random restorative matrix on the signal compressed by the compression section to restore the original digital signal. The restoration process restores the signal by finding an approximate value in solving an L1 optimization problem using a graph representation.

Description

  The present invention relates to a signal processing system and a signal processing method for compressing and decompressing a signal.

  A framework for compressing an input data signal and restoring the result is called compressed sensing. Here, compression is multiplication of a signal and a random compression matrix. A random compression matrix is a matrix having fewer rows than columns, and the elements of the matrix are composed of random variables. When the number of rows is less than the number of columns, compression is possible because the signal output as a result of multiplication of the input data signal and the random compression matrix is less than the input signal.

  In this compression sensing technique, the compressed data is restored to the original signal by using a method such as L1-MINIMATION (L1 minimization) with reference to a random compression matrix (see, for example, Non-Patent Document 1).

E. Candes et al., "An Introduction to Compressive Sampling," IEEE Signal Processing Magazine, pp. 21-30, March, 2008.

  However, the compression processing using the random compression matrix has a problem that the processing time for compression and decompression becomes long because the load of the matrix operation processing is heavy.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide a signal processing system and a signal processing method that can reduce the load of compression and decompression processing in compressed sensing.

  The present invention relates to a random compression matrix generation unit that generates a random compression matrix having non-zero random values less than the number of rows and columns of a compression matrix at random locations of the matrix, and a preset input digital signal. A compression unit that compresses the input digital signal by performing matrix multiplication with the random compression matrix for each frame size, and random restoration that generates a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix A matrix generation unit, and a restoration unit that restores the original digital signal by restoring the signal compressed by the compression unit using the random restoration matrix, and the restoration process is an L1 optimum using a graph representation The signal is restored by obtaining an approximate value for solving the optimization problem.

  The present invention includes a random compression matrix generation unit that generates a random compression matrix having non-zero values that are all ones less than the number of rows and columns of a compression matrix at random locations of the matrix, and an input digital signal A compression unit that compresses the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size, and generates a random decompression matrix equivalent to the random compression matrix with reference to the random compression matrix And a restoration unit that restores the original digital signal by restoring the signal compressed by the compression unit using the random restoration matrix, and the restoration process uses a graph representation. The signal is restored by obtaining an approximate value for solving the L1 optimization problem.

  The present invention includes a random compression matrix generation unit that generates a random compression matrix corresponding to a plurality of interleavers and a plurality of adders, a plurality of interleavers, and a plurality of adders. The digital signals are output in different random patterns, and the signals are switched in order. Each of the plurality of adders is connected to one interleaver, and the sum of the output signals of the interleaver determined in advance is calculated. A compression unit that compresses the input digital signal by outputting, a random restoration matrix generation unit that generates a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix, and the random restoration matrix And a restoration unit for restoring the original digital signal by restoring the signal compressed by the compression unit. The restoration process, and performs restoration of the signal by obtaining an approximate value in solving the L1 optimization problem using graph representation.

  In the present invention, an AD conversion unit that converts an input analog signal into a digital signal, and a digital signal output from the AD conversion unit is divided into compressed sensing frames and converted into a frequency domain signal by performing a fast Fourier transform process. And a fast Fourier transform unit that outputs a signal to the compression unit as the input digital signal.

  The present invention is a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and compresses and senses the digital signal output from the AD converter. A Fast Fourier Transform unit that executes a Fast Fourier Transform process for each frame and outputs a frequency domain signal, and uses a control information received from the central station to reduce the number of non-compressed numbers less than the number of rows and columns of the compression matrix. A random compression matrix generation unit that generates a random compression matrix having a random value of zero at a random location of the matrix, and the random compression matrix and matrix for each preset frame size of the signal output by the fast Fourier transform unit A compression unit that compresses the signal by performing multiplication, transmission of the compressed signal output by the compression unit to the central station, and A first communication unit for receiving control information transmitted by the central station, wherein the central station receives a compressed signal transmitted by the remote station and transmits the control information to the remote station. A control unit that generates the control information to be transmitted to the remote station to generate the random compression matrix, a random recovery matrix generation unit that generates a random recovery matrix using the control information, and the random recovery A restoration unit that restores the original digital signal by restoring the compressed signal received from the remote station using a matrix, and the restoration process is performed when solving an L1 optimization problem using a graph expression. The signal is restored by obtaining an approximate value.

  The present invention is a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and compresses and senses the digital signal output from the AD converter. Using a fast Fourier transform unit that executes a fast Fourier transform process for each frame and outputs a frequency domain signal, and control information received from the central station, the number of rows less than the number of rows and columns of the compression matrix. A random compression matrix generation unit that generates a random compression matrix having non-zero values that are all 1 at random locations in the matrix, and the random compression matrix for each predetermined frame size of the signal output by the fast Fourier transform unit. A compression unit that compresses the signal by performing matrix multiplication with a compression matrix; and transmission of the compressed signal output by the compression unit to the central station; A first communication unit that receives control information transmitted by the central station, and the central station receives a compressed signal transmitted by the remote station and transmits the control information to the remote station. A communication unit; a control unit that generates the control information to be transmitted to the remote station to generate the random compression matrix; a random recovery matrix generation unit that generates a random recovery matrix using the control information; A restoration unit that restores the original digital signal by restoring the compressed signal received from the remote station using a restoration matrix, and the restoration process solves the L1 optimization problem using a graph expression The signal is restored by obtaining an approximate value of.

  The present invention is a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and compresses and senses the digital signal output from the AD converter. A fast Fourier transform unit that performs fast Fourier transform processing for each frame and outputs a frequency domain signal; a random compression matrix generation unit that generates a random compression matrix corresponding to a plurality of interleavers and a plurality of adders; A plurality of interleavers and a plurality of adders, wherein the plurality of interleavers output signals output from the fast Fourier transform unit in different random patterns, and the plurality of adders. Are each connected to one interleaver and output a predetermined number of interleaver output signals. By outputting the sum, a compression unit that compresses the input digital signal, a transmission of the compressed signal output by the compression unit to the central station, and reception of control information transmitted by the central station A communication unit, wherein the central station receives a compressed signal transmitted from the remote station, transmits a control information to the remote station, and generates the random compression matrix for the remote compression matrix. A control unit that generates the control information to be transmitted to a station, a random recovery matrix generation unit that generates a random recovery matrix using the control information, and the compressed signal received from the remote station using the random recovery matrix. A restoration unit that restores the original digital signal by performing a restoration process, wherein the restoration process solves the L1 optimization problem using a graph expression. And performing reconstruction of the signal by obtaining an approximation of the time.

  The present invention is a signal processing method performed by a signal processing system that compresses and decompresses a signal, and includes a random number having a number of non-zero random values less than the number of rows and columns of a compression matrix at random locations in the matrix. A random compression matrix generating step for generating a compression matrix; a compression step for compressing the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal; and the random compression matrix A random restoration matrix generation step for generating a random restoration matrix equivalent to the random compression matrix with reference to FIG. 5 and a restoration process of the signal compressed by the compression step using the random restoration matrix to restore the original digital signal A restoration step, wherein the restoration process is performed when solving an L1 optimization problem using a graph representation. By obtaining the approximate values and performing restoration of the signal.

  The present invention relates to a signal processing method performed by a signal processing system that performs signal compression and decompression, in which non-zero values that are all ones less than the number of rows and columns of a compression matrix are assigned to random locations in the matrix. A random compression matrix generating step for generating a random compression matrix, and a compression step for compressing the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal, A random restoration matrix generation step for generating a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix, and a signal compressed by the compression step using the random restoration matrix to restore the original digital A restoration step for restoring the signal, wherein the restoration process solves the L1 optimization problem using a graph representation. And performing reconstruction of the signal by obtaining an approximation of the time.

  The present invention provides a random compression matrix generation step for generating a random compression matrix corresponding to a plurality of interleavers and a plurality of adders, and a signal in which the plurality of interleavers switch the order of input digital signals in different random patterns. And an adder connected to each of the interleavers outputs a sum of output signals of the interleaver in a predetermined number, thereby compressing the input digital signal, and the random step A random restoration matrix generation step for generating a random restoration matrix equivalent to the random compression matrix with reference to the compression matrix, and an original digital signal by restoring the signal compressed by the compression step using the random restoration matrix A restoring step of restoring the graph representation, And performing reconstruction of the signal by obtaining an approximate value in solving the L1 optimization problem had.

  In the present invention, an AD conversion step for converting an input analog signal into a digital signal, and a digital signal output from the AD conversion step are divided into compressed sensing frames and converted into a frequency domain signal by performing a fast Fourier transform process. And a fast Fourier transform step for outputting a signal as the input digital signal to the compression step.

  The present invention is a signal processing method performed by a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and the AD conversion step outputs A fast Fourier transform step that outputs a frequency domain signal by executing a fast Fourier transform process by dividing the digital signal into compressed sensing frames, and the number of rows and columns of the compression matrix using control information received from the central station Random compression matrix generation step for generating a random compression matrix having a smaller number of non-zero random values at random locations of the matrix, and for each preset frame size of the signal output by the fast Fourier transform step, A compression step of compressing the signal by performing matrix multiplication with a random compression matrix; A first communication step for transmitting the compressed signal output by the compression step to the central station, receiving control information transmitted by the central station, and receiving a compressed signal transmitted by the remote station by the central station; And a second communication step for transmitting the control information to the remote station, a control step for generating the control information to be transmitted to the remote station for generating the random compression matrix, and a random step using the control information. A random restoration matrix generating step for generating a restoration matrix; and a restoration step for restoring the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix, The processing is performed by obtaining an approximate value when solving the L1 optimization problem using a graph expression. And performing restoration.

  The present invention is a signal processing method performed by a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and the AD conversion step outputs The digital signal is divided into compressed sensing frames to perform a fast Fourier transform process and output a frequency domain signal, and using control information received from the central station, the number of rows and columns of the compression matrix A random compression matrix generation step for generating a random compression matrix having non-zero values that are all ones less than a number at random locations of the matrix, and a preset frame size of the signal output by the fast Fourier transform step A compression step of compressing the signal by performing matrix multiplication with the random compression matrix A first communication step for transmitting the compressed signal output by the compression step to the central station, receiving control information transmitted by the central station, and a compressed signal transmitted by the remote station by the central station. Using the control information, a second communication step of transmitting the control information to the remote station, a control step of generating the control information to be transmitted to the remote station to generate the random compression matrix, and the control information A random restoration matrix generating step for generating a random restoration matrix, and a restoration step for restoring the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix, The restoration process is performed by obtaining an approximate value when solving the L1 optimization problem using the graph expression. And performing restoration of the signal.

  The present invention is a signal processing method performed by a signal processing system including a remote station and a central station, wherein the remote station converts an input analog signal into a digital signal, and the AD conversion step outputs A fast Fourier transform step in which a digital signal is divided into compressed sensing frames and a fast Fourier transform process is performed to output a frequency domain signal, and a random compression matrix corresponding to a plurality of interleavers and a plurality of adders is generated. A compression matrix generation step and a plurality of interleavers output signals output from the fast Fourier transform step in different random patterns, and a plurality of adders connected to each of the interleavers, Output the sum of output signals of the interleaver for a predetermined number A compression step for compressing the input digital signal; a first communication step for transmitting the compressed signal output by the compression step to the central station; and receiving control information transmitted by the central station; A second communication step in which the central station receives a compressed signal transmitted by the remote station and transmits the control information to the remote station; and the control transmitted to the remote station to generate the random compression matrix. A control step for generating information, a random recovery matrix generation step for generating a random recovery matrix using the control information, and a recovery process for the compressed signal received from the remote station using the random recovery matrix. And restoring the digital signal, wherein the restoration process is a graph representation. And performing reconstruction of the signal by obtaining an approximate value in solving the L1 optimization problem had.

  According to the present invention, it is possible to reduce the load of compression processing in compression sensing. Therefore, the time required for the compression process can be shortened.

It is a figure which shows the structural example of the signal processing system in the 1st Embodiment of this invention. It is a figure which shows typically the example of the random compression matrix in this invention. It is a figure which shows typically the compression and decompression | restoration in this invention. It is a figure which shows the compression in this invention typically. It is a figure which shows typically the graph structure in the decompression | restoration process of this invention. It is a figure which shows typically the example of the partial optimization in the decompression | restoration process of this invention. It is a figure which shows the example of a process sequence which a signal processing system performs. It is a figure which shows typically the example of the random compression matrix in the 2nd Embodiment of this invention. It is a figure which shows typically the example of a structure of the compression sensing part in the 3rd Embodiment of this invention. It is a figure which shows typically the example of a structure of the graph of the decompression | restoration process in the 3rd Embodiment of this invention. It is a figure which shows the structural example of the signal processing system in the 4th Embodiment of this invention. It is a figure which shows the example of a process sequence which the signal processing system in 4th Embodiment performs. It is a figure which shows the example of the system comprised by the remote station in this invention, a central station, and a transmission line. It is a figure which shows the structural example of the signal processing system in the 5th Embodiment of this invention. It is a figure which shows the example of a process sequence which the signal processing system in 5th Embodiment performs.

<First Embodiment>
[Overall configuration of signal processing system]
Hereinafter, a signal processing system according to an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a signal processing system 100 in the present embodiment. The signal processing system 100 shown in this figure includes a compression sensing unit 101, a signal restoration unit 102, a random compression matrix generation unit 103, and a random restoration matrix generation unit 104. The compression sensing unit 101 compresses an input signal using the random compression matrix generated by the random compression matrix generation unit 103, and outputs a compressed signal. The signal restoration unit 102 restores the compressed signal using the random restoration matrix generated by the random restoration matrix generation unit 104, and outputs the restored signal.

  The random compression matrix generation unit 103 generates a random matrix having K and J non-zero random values for each row and each column. Here, K and J are numbers smaller than the number of rows and columns of the random compression matrix, respectively. FIG. 2 shows an example of the random compression matrix when the number of rows and columns of the random compression matrix is 4 and 10, and K and J are 5 and 2. In each row, only 5 components have non-zero values and each column has only 2 components non-zero values. The position of each non-zero value and component having a non-zero value is determined randomly. The random decompression matrix generation unit 104 generates a matrix similar to the random compression matrix generated by the random compression matrix generation unit and sets it as a random decompression matrix.

FIG. 3 is a diagram schematically showing signal processing in the signal processing system 100 shown in FIG. FIG. 3A shows an input signal. As an input signal here, 300 data of (X _{0 to} X ₂₉₉ ) in the time series are extracted and shown. The compressed sensing unit 101 divides the input signal input in time series as described above into units of a compressed sensing frame for each predetermined number of data. In FIG. 3A, an example in which data X _{0 to} X ₂₉₉ is divided into three compressed sensing frames each consisting of 100 data of X _{0 to} X ₉₉ , X _{100 to} X ₁₉₉ and X _{200 to} X _299. Show.

Then, as shown as a transition from FIG. 3A to FIG. 3B, the compressed sensing unit 101 performs compression processing on the compressed sensing frame composed of the data X _{0 to} X ₉₉ to obtain 40 data. A compressed frame composed of T _{0 to} T ₃₉ is generated. Similarly, the compressed sensing unit 101 performs compression processing on the compressed sensing frame composed of data X _{100 to} X ₁₉₉ to generate a compressed frame composed of 40 pieces of data T _{40 to} T ₇₉ . Similarly, the compressed sensing unit 101 performs compression processing on the compressed sensing frame composed of the data X _{200 to} X ₂₉₉ to generate a compressed frame composed of 40 pieces of data T _{80 to} T ₁₁₉ . The compressed frames (T _{0 to} T ₃₉ ), (T _{40 to} T ₇₉ ), and (T _{80 to} T ₁₁₉ ) thus obtained are output as compressed signals.

  As described above, the compressed sensing unit 101 compresses each compressed sensing frame including N pieces of data so that M (M <N) pieces of data are obtained. In the example of FIG. 4, since N = 100 and M = 40, the compression rate is 40%.

Next, the signal restoration unit 102 inputs compressed frames (T _{0 to} T ₃₉ ), (T _{40 to} T ₇₉ ), and (T _{80 to} T ₁₁₉ ) as compressed signals, and restores each compressed frame as a target. Execute the process. That is, the signal restoration unit 102 performs a restoration process on the compressed frame including the data T _{0 to} T ₃₉ and restores the data to X _{0 to} X ₉₉ . Similarly, the signal restoration unit 102 performs a restoration process on the compressed frame including the data T _{40 to} T ₇₉ to restore the data of X _{100 to} X ₁₉₉ . Similarly, the signal restoration unit 102 performs a restoration process on the compressed frame including the data T _{80 to} T ₁₁₉ and restores the data to X _{200 to} X ₂₉₉ . The data X _{0 to} X ₂₉₉ restored in this way becomes a restoration signal. In this figure, the case where the compression rate is 40% is shown, but the compression rate is merely an example, and other compression rates may be adopted.

[Configuration of signal restoration unit]
Hereinafter, an input signal corresponding to one compressed sensing frame (N), a random compression matrix, a signal after compression, and a signal after signal restoration are referred to as X0, H, Y, and X, respectively. . In the first embodiment, since the random decompression matrix is the same as the random compression matrix, the random decompression matrix is also referred to as H, like the random compression matrix. The sizes of the X0, H, Y, and X matrices are N × 1, M × N, M × 1, and N × 1, respectively. X0, H, and Y are expressed as Y = H × X0 because the compressed signal Y is obtained by multiplying the random compression matrix H by the input signal X0.

の関係式で表現される。ここで、∂ｕは、Ｈのｕ行目の非ゼロ成分に対する列添字の集合を表す。例えば、図２に示すランダム圧縮行列の例において、ランダム圧縮行列の１行目の非ゼロ成分に対する列添字の集合は、｛１、４、６、７、９｝であるため、∂１は｛１、４、６、７、９｝である。同様に、∂２は、｛２、３、４、８、１０｝である。 Hereinafter, the u-th and i-th components of H are referred to as H _ui . The component in the i-th row of X0 is referred to as X0 _i . Also, the u-th component of Y is referred to as _{Y u.} X0 _i and _{H ui} and _{Y u} is,

It is expressed by the relational expression. Here, ∂u represents a set of column subscripts for the non-zero component of the u-th row of H. For example, in the example of the random compression matrix shown in FIG. 2, the set of column subscripts for the non-zero component in the first row of the random compression matrix is {1, 4, 6, 7, 9}, so that ∂1 is { 1, 4, 6, 7, 9}. Similarly, ∂2 is {2, 3, 4, 8, 10}.

  Hereinafter, similarly, a set of row subscripts for the non-zero component of the i-th column of H is denoted as ∂i. For example, in the column of the random compression matrix shown in FIG. 2, since the set of row subscripts for the non-zero component in the first column of the random compression matrix is {1, 3}, ∂1 is {1, 3} . Similarly, ∂2 is {2, 3}.

ここで、ＸのＬ１ノルムとは、

であり、Ｘの各成分の絶対値の総和を表す。 L1-MINIMIZATION (L1 minimization) is a process of searching for X that minimizes the L1 norm of X while satisfying the constraint condition of H × X = Y as a policy for signal restoration when H and Y are given. It is expressed as (Equation 1).

Here, the L1 norm of X is

And represents the sum of absolute values of each component of X.

ここで、λは、λ＞０を満たす。 It is known that (Equation 1) is the same as the optimization problem of X represented by the following (Equation 2) without constraint conditions.

Here, λ satisfies λ> 0.

ここで、Ｚは、（式２）と（式３）を同様にするＹとＸの変数である。 Furthermore, (Equation 2) becomes the same as the optimization problem of Z and X in (Equation 3) by solving that λ approaches +0.

Here, Z is a variable of Y and X that makes (Equation 2) and (Equation 3) similar.

  In the restoration process of the signal restoration unit 102, X obtained as a solution to the optimization problem expressed by (Equation 3) is regarded as an approximate value of the input signal X0, and the restoration process of the input signal X0 is performed.

ここで、

は、Ｘに単独に依存し、

は、Ｚに単独に依存する。 In preparation for obtaining a solution to the optimization problem of (Expression 3), the objective function of the optimization problem of (Expression 3) is referred to as Ω (X, Z) and is expressed as (Expression 4).

here,

Depends solely on X,

Depends solely on Z.

A graph representation of the objective function Ω (X, Z) represented by (Expression 4) is introduced. FIG. 5 shows an example of a graphical representation of the objective function Ω (X, Z). In FIG. 5, the display of “◯” represents a term λ | X _i | that is independently dependent on X _i in each component X _i and the objective function (Equation 4) of the signal. The display of "□", Section depends solely with respect to _{Z u} in the variables _{Z u} and objective function (Equation 4) - ^_(1/2) representing a _{Z u 2 + Z u Y u} . The connection between the display of “◯” and the display of “□” means the interaction term H _ui Z _u X _i .

  The restoration process of the signal restoration unit 102 is to find a solution to the optimization problem expressed by (Equation 3). However, the optimization problem of (Equation 3) needs to simultaneously optimize multiple variables. The signal processing is complicated and the load on the signal processing is large. Hereinafter, in order to reduce the processing load of the optimization problem of (Equation 3), the objective function expressed by (Equation 4) is approximated to a bundle of independent objective functions for each variable, and Find the optimization problem independently.

ここで、Ｘ＼Ｘ_ｉは集合Ｘから要素Ｘ_ｉを取り除いてできる集合を表し、また、Ｚ＼Ｚ_ｕは集合Ｚから要素Ｚ_ｕを取り除いてできる集合を表す。例えば、集合Ｘが｛Ｘ_１，Ｘ_２，Ｘ_３，Ｘ_４，Ｘ_５｝の場合、Ｘ＼Ｘ_２は、集合ＸからＸ_２を取り除いた｛Ｘ_１，Ｘ_３，Ｘ_４，Ｘ_５｝である。 Among the Omega (X, Z) (Equation 4), called the objective function that depends only on _{X i} Omega _i and _{(X i),} expressed in (Equation 5). Similarly, referred to as in the Omega (X, Z) (Equation 4), the objective function that depends only on _{Z u Ω u (Z u)} , represented in (Equation 6).

Here, X\X _i represents a set that can remove the element _{X i} from the set X, also, Z\Z _u denotes the set that can remove the element _{Z u} from the set Z. For example, if the set X is _{{X 1, X 2, X} 3, X 4, X 5}, X\X 2 is to remove _{X 2} from the set X _{{X 1,} X _3, X 4, _{X 5} }.

And X _i only depends Omega _{i (X i), Z u} only Omega dependent _u a _{(Z u),} respectively, referred to as marginal cost marginal cost (MARGINAL COST) and _{Z u} of _{X i.} Given X _i marginal cost Omega _i of _{(X i)} is the restored value of _{X i} is, Omega _i a _{(X i)} determined by optimizing the _{X i.} This is technically and computationally easier than optimizing Ω (X, Z) of the multivariable objective function (Equation 4).

のみである。このことに着目し、Ｘ_ｉに関する項を取り除いて得られる目的関数をΩ_＼ｉ（Ｘ＼Ｘｉ，Ｚ）と定義する。Ω_＼ｉ（Ｘ＼Ｘｉ，Ｚ）は下記の（式７）のように表される。

Here, another auxiliary objective function is introduced. In Ω (X, Z) of (Equation 4), the term related to X _i is

Only. Focusing on this, the objective function obtained by removing the term relating to X _i is defined as Ω _{\ i} (X _\ Xi, Z). Ω _{\ i} (X _\ Xi, Z) is expressed as in the following (formula 7).

Similarly, defined as the Omega (X, Z) (Equation 4), the objective function obtained by removing the section on _{Z u Ω \u (X, Z\Z} u). Ω _{\ u} (X, Z \ Z _u ) is expressed as in the following (formula 8).

Referred as defined in (Equation 7) and (Equation _{8), Ω \i (X\Xi,} Z) and _Ω \u (X, Z\Z _u) and the cavity cost (CAVITY COST).

The relationship of (Expression 9) is established between Ω _i (X _i ) of (Expression 5) and Ω _{\ i} (X _\ Xi, Z) of (Expression 7).

Similarly, the relationship of (Expression 10) is established between Ω _u (Z _u ) in (Expression 6) and Ω \ _u (X, Z _\ Z _u ) in (Expression 8).

Here, when the restoration process of the signal restoration unit 102 obtains the solution to the optimization problem expressed by (Equation 3), when the graph of FIG. There is no possibility that parts that are locally separated by removing are connected by other parts. Therefore, the optimization process can be performed independently between the parts separated by removing any node. FIG. 6 shows an example of four independent optimization processes that are locally separated by removing X _i . In Figure 6, by removing the X _i, divided into 4 portions graph of FIG. 5 are not connected. The final solution is obtained by comparing only the four results obtained after the optimization of these four parts independently.

Next, a description will be given of a method of performing the optimization process independently between the divided parts by removing an arbitrary node. First, the marginal cost of Z _u in the cavity cost Ω _{\ i} (X _\ Xi, Z) obtained by removing the term related to X _i is referred to as Ω _{u \ i} (Z _u ) and defined as (Equation 11) To do.

Similarly, cavity cost obtained by removing the section on _{Z u Ω \u (X, Z\Z} u) in the marginal cost of _{X i} called Omega _{I\u (X i),} as represented by equation (12) Defined in

_Then, Ω u\i _{(Z u)} and Omega _I\u the _{(X i)} is referred to as a cavity marginal (CAVITY MARGINAL).

And X _i marginal cost Omega _i of _{(X i),} a cavity cost _Ω \i _(X\X i, Z) of _{X i} and, _Ω \i _(X\X i, Z) in the cavity marginal of _{Z u} Omega The relationship of _{u \ i} (Z _u ) is as shown in (Equation 13).

Similarly, _{Z u} marginal cost Omega _u and _{(Z u),} cavity cost _Ω \u (X, Z\Z _u) of _{Z u} and, _Ω \u (X, Z\Z _u) in, the _{X i} The relationship of the cavity marginal Ω _{i \ u} (X _i ) is as shown in (Expression 14).

ここで、∂ｉ＼ｕは、上記ランダム圧縮行列Ｈのｉ列目の非ゼロ成分に対する行添字の集合である∂ｉから、ｕ行目の行添字を取り除いた行添字の集合である。例えば、図２に表すランダム圧縮行列Ｈにおいて、３列目の非ゼロ成分に対する行添字の集合を表す∂３は、｛２，４｝であり、この集合から２行目の行添字を取り除いた行添字の集合∂３＼２は、｛４｝になる。また、Ｚ_ｖは、集合∂ｉ＼ｕの行添字に関するＺの変数である。例えば、上記の集合∂３＼２の｛４｝の場合、Ｚ_ｖはＺ_４である。なお、Ｈ_ｖｉは、上記ランダム圧縮行列Ｈのｖ行目とｉ列目の成分を表す。図２に示すランダム圧縮行列Ｈにおいて、上記の集合∂３＼２の｛４｝の場合、Ｈ_４３は、４行目の３列目の成分である１．４である。そして、Ω_ｖ＼ｉ（Ｚ_ｖ）は、Ｘ_ｉに関する項を取り除いて得られるキャビティコストΩ_＼ｉ（Ｘ＼Ｘ_ｉ，Ｚ）における、Ｚ_ｖのマージナルコストである。 By the way, when the graph of FIG. 5 does not include a loop and has a tree structure, the relational expression of (Expression 15) is established for the cavity marginal.

Here, ∂i \ u is a set of row subscripts obtained by removing the row subscript of the u-th row from ∂i, which is a set of row subscripts for the non-zero component of the i-th column of the random compression matrix H. For example, in the random compression matrix H shown in FIG. 2, ∂3 representing the set of row subscripts for the non-zero component of the third column is {2, 4}, and the row subscript of the second row is removed from this set. The set of line subscripts ∂3 \ 2 becomes {4}. In addition, _{Z v} is a Z variable of on-line index of the set ∂i\u. For example, in the case of {4} above the set ∂3\2, _{Z v} is _{Z 4.} H _vi represents the components of the v-th row and the i-th column of the random compression matrix H. In random compressed matrix H shown in FIG. 2, in the case of {4} above the set _{∂3\2, H 43} is 1.4 which is a component of the third column of the fourth row. Ω _{v \ i} (Z _v ) is the marginal cost of Z _v in the cavity cost Ω \ _i (X _\ X _i , Z) obtained by removing the term related to X _i .

ここで、∂ｕ＼ｉは、上記ランダム圧縮行列Ｈのｕ行目の非ゼロ成分に対する列添字の集合である∂ｕから、ｉ列目の列添字を取り除いた列添字の集合である。Ｘ_ｌは、集合∂ｕ＼ｉの列添字に関するＸの変数である。Ｈ_ｕｌは、上記ランダム圧縮行列Ｈのｕ行目とｌ列目の成分を表す。Ω_ｌ＼ｕ（Ｘ_ｌ）は、Ｚ_ｕに関する項を取り除いて得られるキャビティコストΩ_＼ｕ（Ｘ，Ｚ＼Ｚ_ｕ）における、Ｘ_ｌのマージナルコストである。 Similarly, when the graph of FIG. 5 has a tree structure that does not include a loop, the relational expression of (Expression 16) holds for the cavity marginal.

Here, ∂u \ i is a set of column subscripts obtained by removing the column subscript of the i-th column from ∂u, which is a set of column subscripts for the non-zero component of the u-th row of the random compression matrix H. X _l is a variable of X related to the column index of the set ∂u \ i. H _ul represents components of the u-th row and the l-th column of the random compression matrix H. _Ω l\u _{(X l)} are cavities cost obtained by removing the section on _{Z u Ω \u (X, Z\Z} u) in a marginal cost of _{X l.}

As long obtained cavity marginal _Ω u\i _{(Z u)} of equation (16), marginal cost Omega _{i (X i)} of the _{X i} defined in (Equation 5) is obtained by the equation (17).

Similarly, after calculating the cavity marginal Ω _{u \ i} (Z _u ) of (Equation 16) for each component of X _i (i = 1, 2, 3,..., N), (Equation 17) Each component of X _i can be obtained from Ω _i (X _i ).

ここで、Ｆ_ｉ→ｕは、（式１５）を（式１８）に近似するため追加した項である。さらに、（式１８）を（式１９）のように簡易化することができる。

ここで、Ｘ_ｉ→ｕは、（式１８）を解いた結果であり、下記（式２０）の最適化問題の解である。

また、（式１６）のΩ_ｕ＼ｉ（Ｚ_ｕ）は、（式２１）のように近似することができる。

ここで、Ｄ_ｉ→ｕは、（式１６）のΩ_ｕ＼ｉ（Ｚ_ｕ）を（式２１）に近似するため追加した項である。 The amount of calculation required to update the relationship between the cavity marginals (Equation 15) and (Equation 16) is proportional to the total number of nodes N, but is technically difficult to implement because it is a functional equation. Therefore, in order to simplify the implementation, (Equation 15) is approximated to the relational expression of (Equation 18).

Here, F _{i → u} is a term added to approximate (Equation 15) to (Equation 18). Furthermore, (Expression 18) can be simplified as (Expression 19).

Here, X _{i → u} is the result of solving (Equation 18), and is the solution of the optimization problem of (Equation 20) below.

Further, Ω _{u \ i} (Z _u ) in (Expression 16) can be approximated as in (Expression 21).

Here, D _{i → u} is a term added to approximate Ω _{u \ i} (Z _u ) of (Expression 16) to (Expression 21).

ここで、（式２４）のｓｇｎ（・）は符号関数であり、ｓｇｎ（・）の中の値の符号を表す。例えば、Ｆ_ｉ→ｕが３の場合、ｓｇｎ（Ｆ_ｉ→ｕ）は、＋１になり、Ｆ_ｉ→ｕが、−２の場合、ｓｇｎ（Ｆ_ｉ→ｕ）は、−１になる。また、Θ（・）は、段階関数（ＵＮＩＴ ＳＴＥＰ ＦＵＮＣＴＩＯＮ）であり、Θ（・）の中の値が正の値である場合、負の値である場合、０の場合、それぞれ＋１、０、０．５を出力する。 The cavity marginal _Ω i\u _{(X i)} and _Ω u\i _{(Z u)} and relationship to be satisfied by F _{i → u} and D _{i → u} is from (Equation 22) to (Equation 24).

Here, sgn (•) in (Equation 24) is a sign function, and represents the sign of the value in sgn (•). For example, when F _{i → u} is 3, sgn (F _{i → u} ) is +1, and when F _{i → u} is −2, sgn (F _{i → u} ) is −1. Further, Θ (·) is a step function (UNIT STEP FUNCTION), and when the value in Θ (·) is a positive value, a negative value, or 0, +1, 0, 0.5 is output.

  Hereinafter,: = means that the calculation result of the formula on the right side of: = is input to the variable on the left side of: =. For example, when the initial value of a certain variable A is 3, A: = A + 1 means that the value of A + 1 on the right is substituted into the variable A on the left. In this case, since the initial value of A is 3, the result 4 of A + 1 is substituted into the variable A on the left side of the equation, and A becomes 4.

同様に、Ｘ_ｉの成分毎に、（式２１）から（式２２）までの計算を行うことにより、復元信号Ｘが得られる。 The restoration signal X _i is obtained by (Expression 25) and (Expression 26) after each parameter is determined by (Expression 22), (Expression 23), and (Expression 24).

Similarly, for each component of X _i, by performing the calculation of the equation (21) to (Equation 22), recovered signal X is obtained.

に表す。 From here, the mechanism for setting λ to +0 in (Equation 3) will be described. Hereinafter, in (Equation 26), a component in which F _i exceeds λ, that is, a component in which Θ (| F _i | −λ) outputs +1 is referred to as a survival component. In addition, the number of components exceeding λ,

Expressed in

とＭを比較し、

がＭより多ければ、λを増大させ、逆に、

がＭより小さければ、λを減少させることが必要である。上記のことを考慮し、λを（式２７）のように更新する。

この制御の下では，更新時の生き残り成分数が、圧縮後のデータの数Ｍを下回っている場合、λは減少していくため復元が成功に向かうにつれて、λを＋０に近づけることができる。 In order for the restoration to be successful, the number of surviving components must not exceed the number of compressed data M. If λ is too small, the number of surviving components is greater than M, and if λ is too large, the number of surviving components is conversely smaller than M. Therefore, to set an appropriate value for λ, the number of surviving components

And M,

If is greater than M, increase λ, and conversely

If is less than M, it is necessary to reduce λ. Considering the above, λ is updated as in (Equation 27).

Under this control, when the number of surviving components at the time of update is less than the number M of data after compression, λ decreases, so λ can be brought closer to +0 as restoration is successful.

A reconstructed signal is obtained by updating λ according to (Expression 27) and repeating (Expression 22) to (Expression 26).

  As described above, in the present embodiment, a restoration method in which the amount of calculation required for each iteration of the compression sensing signal restoration process only needs to be proportional to the total number N of nodes, and a method for simplifying the implementation are described in this embodiment. Greatly reduces the processing load. Thereby, the compression processing time is also effectively shortened.

[Example of processing procedure]
The flowchart of FIG. 10 is a flowchart showing a processing procedure executed by the signal processing system 100 shown in FIG. Each process shown in this figure is appropriately executed by any of the parts shown in FIG. First, the random compression matrix generation unit 103 generates a random compression matrix as described with reference to FIG. 1, and the compression sensing unit 101 executes compression of the input signal using this random compression matrix, and the result is signaled. The data is output to the restoration unit 102 (step S11). Then, the signal restoration unit 102 performs signal restoration processing using the random restoration matrix generated by the random restoration matrix generation unit 104 (step S12), and outputs the restored signal (step S13).

<Second Embodiment>
[Overall configuration of signal processing system]
The overall configuration of the signal processing system 100 in the second embodiment is the same as that of the first embodiment. However, the random compression matrix generated by the random compression matrix generation unit 103 has all the non-zero values being 1. FIG. 8 shows an example in which all non-zero values are 1 in the example of FIG. Hereinafter, the matrix shown in FIG. 8 is referred to as a binary random compression matrix.

  The compression process in the second embodiment is the same as that in the first embodiment. However, the signal restoration processing can improve the efficiency as described below by utilizing the fact that the random compression matrix is a binary random compression matrix.

[Signal reconstruction processing for binary random compression matrix]
When the random compression matrix is a binary random compression matrix, in order to improve the efficiency in the decompression process, (Expression 24) is changed to (Expression 28) using an arbitrary constant Δ, and then Δ is optimized. To improve the performance of the restoration process.

ここで、Ｊは、ランダム圧縮行Ｈの各列のあたりの非ゼロ値の個数である。 The optimum Δ depends on the nature of the random compression matrix H. In the following, a method for obtaining the optimal Δ when the random compression matrix is a binary random compression matrix will be described. In this case, the above (Expression 22) to (Expression 26) can be simplified by using the fact that all non-zero elements of H are 1 and can be expressed as (Expression 29) to (Expression 33), respectively. .

Here, J is the number of non-zero values per column of the random compressed row H.

ここで、ρは、圧縮前の元信号Ｘ０の非ゼロ要素の割合である。例えば、Ｘ０が｛０，０，０，１，２，０，１｝である場合、非ゼロ要素の割合は３／７であるため、ρ＝３／７になる。 [Acceleration of convergence when the value of the non-zero element is 1]
In order to improve the convergence of the variable X _{i → u} and improve the performance of the restoration process, a method of linearizing the variable X _{i → u} and minimizing the difference is considered. In preparation, the variable X _{i → u} is linearized with respect to δX _{i → u} around the fixed point X0 _i as X _{i → u} = X0 _i + δX _{i → u} . Here, X0 _i is a component of the i-th row of the original signal X0 before compression. In other words, if the restoration process is perfect, X _i should be the same as X0 _i as a result after the restoration process, but the deviation of the restoration process is expressed as δX _{i → u,} and X _i is around X0 _i By considering the probability distribution by the random variable δX _{i → u} and minimizing the variation, the performance of the restoration process is improved. Therefore, it is regarded as a random variable independent probability distribution of [delta] X _{i → u,} when denoted the mean and variance of the _{M 1} and _{M 2,} respectively, _{M 1} and _{M 2} are from (Equation 26), respectively (equation 34) (Expression 35).

Here, ρ is a ratio of non-zero elements of the original signal X0 before compression. For example, when X0 is {0, 0, 0, 1, 2, 0, 1}, the ratio of non-zero elements is 3/7, so ρ = 3/7.

By setting the above-mentioned arbitrary constant Δ so that M ₁ and M ₂ in (Expression 34) and (Expression 35) converge to zero quickly, the convergence of the variable X _{i → u} is improved, and the restoration process is performed. Performance can be improved.

より、変数Ｘ_ｉ→ｕについては、（式３６）が成り立つことが要請される。

（式３６）が満たされる場合、（式３７）が成り立ち、結果的にＭ_ｌはゼロとなる。
（式３７）δＸ_ｉ→ｕ＝０
ここで、（式３６）を各更新時に成立させるため、（式３７）が各更新時に要請される。

Ｄ_ｕ→ｉの更新式である（式２９）に続いて、（式３９）の処理を行うことで、（式３７）を満足させることができ、Ｍ_ｌはゼロになる。

The average value M _l of the variable δX _{i → u} can be deleted at each update, not by setting Δ.
In other words, the compression result constraint

Therefore, for the variable X _{i → u} , (Equation 36) is required to hold.

When (Expression 36) is satisfied, (Expression 37) is satisfied, and as a result, M _l becomes zero.
(Expression 37) δX _{i → u} = 0
Here, in order to establish (Equation 36) at each update, (Equation 37) is requested at each update.

Subsequent to (Expression 29) which is an update expression of _{Du → i} , (Expression 39) can be satisfied by performing the process of (Expression 39), and M _l becomes zero.

を、Δに関して最小化する。結果的に、Δ_＊＝ρ（Ｋ−１）が、最適値として得られる。 ここで、Δ_＊は、

を最小化するときのΔの値である。ただし、圧縮前の元信号の非ゼロ要素の密度ρを事前に知ることはできないため、次善の策として、圧縮後のデータの数Ｍで復元できる非ゼロ密度の最大値であるα＝Ｍ／Ｎをρの代わりに用いる。つまり、下記の（式４０）のΔ_＊の値をΔの値として設定する。
（式４０）Δ_＊＝α（Ｋ−１） In order to accelerate the convergence of the variance value M ₂ of the variable δX _{i → u} , the rate of change

Is minimized with respect to Δ. As a result, Δ _* = ρ (K−1) is obtained as the optimum value. Where Δ _* is

Is the value of Δ when minimizing. However, since the density ρ of the non-zero element of the original signal before compression cannot be known in advance, as the next best measure, α = M which is the maximum value of non-zero density that can be restored with the number M of data after compression. / N is used instead of ρ. That is, the value of Δ _{* in} (Equation 40) below is set as the value of Δ.
(Formula 40) Δ _* = α (K−1)

なお、閾値の更新波（式４４）にしたがって行う。

It is possible to perform signal restoration processing by setting the initial value of X _{i → u} to 0 and repeating the following operation. First, the parameter is updated by calculation of (Equation 41) to (Equation 43).

It is performed according to the threshold update wave (formula 44).

  A reconstructed signal is obtained by repeating the operations of (Equation 41) to (Equation 44).

[Example of processing procedure]
The procedure example of the second embodiment is the same as the example of the first embodiment.

  Thus, in the compression sensing signal restoration processing, when the random compression matrix is a binary random compression matrix, a restoration method in which the amount of calculation required for each iteration is only proportional to the total number N of nodes, and In this embodiment, the processing load of the method for simplifying the mounting is greatly reduced. Thereby, the compression processing time is also effectively shortened.

<Third Embodiment>
[Overall configuration of signal processing system]
The overall configuration of the signal processing system 100 in the third embodiment is the same as that of the first embodiment and the second embodiment. However, the combination of the random components of the random compression matrix is generated by using an interleaver that rearranges the signal components at random, so that it can be easily implemented on a device having a low calculation function.

The compressed sensing unit 101 includes a plurality of interleavers and adders. FIG. 9 shows an example of a compressed sensing unit including a plurality of interleavers and adders. The original signal X0 before N-dimensional compression is input to J interleavers (a device that rearranges the positions of the components of X0 randomly). Each interleaver forms part of independent J modules. Here, the output result of the n-th interleaver of the i-th component of X0 is expressed as π ⁿ (i). Further, it denoted the inverse function of π ⁿ (i) and ^{(π n) -1 (i)} . For example, if the input signal {1, 2, 3, 4, 5} is input to the third interleaver and the signal {5, 1, 2, 3, 4} is output, the input signal to the third interleaver Since 1 which was the first component of the original signal has changed to 5, π ³ (1) = 5. Similarly, π ³ (2) = 1, π ³ (3) = 2, π ³ (4) = 3, and π ³ (5) = 4. Since (π ⁿ ) ⁻¹ (i) is an inverse function of π ⁿ (i), π ³ (1) = 5 to (π ³ ) ⁻¹ (5) = 4 holds. Similarly, (π ³ ) ^-1 (1) = 2, (π ³ ) ^-1 (2) = 3, (π ³ ) ^-1 (3) = 4, (π ³ ) ^-1 (4) = 5 become. Incidentally, among the output of the n-th interleaver, the i-th component is denoted as X0 _i ^n. For example, in the above example, X0 ₁ ³ = 5, X0 ₂ ³ = 1, X0 ₃ ³ = 2, X0 ₄ ³ = 3, and X0 ₅ ³ = 4.

Each adder outputs K sums from the front with respect to the original signal input via the interleaver. X0 _i ⁿ which is the i-th component of the original signal on which the n-th interleaver is operated is expressed as (Equation 47).

この計算は、加算器のごとに独立に行うことができるため、処理速度を速くすることが可能である。 Therefore, the t-th output data of the n-th adder is as shown in (Equation 48).

Since this calculation can be performed independently for each adder, the processing speed can be increased.

  When the compressed sensing unit 101 includes a plurality of interleavers and adders, a parameter update and signal restoration method in the signal restoration unit 102 is shown in FIG. In this case, since each signal component is included in only one data among the measurement values in each adder, when represented in a graph, each adder is parallel to each component of the signal, and one “□” "Plays the role of a display node. Further, since the same signal vector (original signal before compression) is input to each adder, the entire signal vector is collectively expressed as a node indicated by “◯”.

In FIG. 10, when the signal estimation value of each nth adder is expressed as X _{i → n} and the influence from each nth adder is expressed as D _{n → i} , The parameter update formulas up to formula 51) are obtained. In addition, the following signals (Equation 52) and (Equation 52) are restored.

ここで、

が、加算器毎に成立するため、平均の計算は、加算器毎に行う。

なお、閾値の更新式は、（式５４）である。

∂t is a set of signal subscripts constituting the t-th compressed data of each adder, and ∂t = {K (t−1), K (t−1) +1,. . . , Kt}.

here,

However, since it is established for each adder, the average calculation is performed for each adder.

The threshold update formula is (Formula 54).

[Example of processing procedure]
The treatment procedure example of the third embodiment is the same as the example of the first embodiment.

  As described above, the compressed sensing unit 101 composed of a plurality of interleavers and adders and the above-described restoration processing method can be easily mounted on a device having a low calculation function.

<Fourth Embodiment>
[Overall configuration of signal processing system]
FIG. 11 is a block diagram showing the overall configuration of the signal processing system 200 in the present embodiment. The signal processing system 200 shown in this figure includes an AD conversion unit 201, an FFT processing unit 202, a compression sensing unit 101, a signal restoration unit 102, a random compression matrix generation unit 103, and a random restoration matrix generation unit 104.

  The AD conversion unit 201 receives an input analog signal, performs AD conversion, and outputs a digital signal. The FFT processing unit 202 divides the signal output from the AD conversion unit 201 for each frame of compressed sensing, performs FFT processing, and outputs the result. The compressed sensing unit 101, the signal restoration unit 102, the random compression matrix generation unit 103, and the random restoration matrix generation unit 104 are the same as those in the first to third embodiments.

[Example of processing procedure]
FIG. 12 is a flowchart showing a processing procedure executed by the signal processing system 200 shown in FIG. Each process shown in this figure is appropriately executed by any of the parts shown in FIG. First, the AD conversion unit 201 converts an input analog signal into a digital signal (step S21). Then, the FFT processing unit 202 performs an FFT process on the signal output from the AD conversion unit 201 for each compressed sensing frame, and outputs the result to the compressed sensing unit 101 (step S22). The random compression matrix generation unit 103 generates a random compression matrix as described with reference to FIG. 1, and the compression sensing unit 101 performs compression of the input signal using the random compression matrix, and the result is a signal restoration unit. It outputs to 102 (step S23). Then, the signal restoration unit 102 performs signal restoration processing using the random restoration matrix generated by the random restoration matrix generation unit 104 (step S24), and outputs the restored signal (step S25).

<Fifth Embodiment>
[Overall configuration of communication system]
FIG. 13 is a block diagram illustrating an example of the overall configuration of a communication processing system 600 to which the signal processing system configuration is applied. A communication processing system 600 shown in this figure includes a remote station 300 and a central station 400. There are a plurality of remote stations 300 with respect to the central station 400, and each remote station 300 is connected to the central station 400 via the transmission path 500 so as to be communicable. Note that the transmission line 500 is not particularly limited. Further, the transmission path 500 may be wired or wireless.

  The remote station 300 transmits an analog signal such as an audio signal to the central station 400, for example. At this time, the remote station 300 converts the analog signal into a digital signal and then compresses it. Then, the remote station 300 transmits the compressed signal to the central station 400 via the transmission path 500. By compressing the signal to be transmitted in this manner, a finite band of the transmission line 500 can be used effectively. The central office 400 restores the transmitted compressed signal and uses it for a predetermined purpose.

[Configuration of Remote Station and Central Station of Fifth Embodiment]
FIG. 14 shows a configuration example when the signal processing system 200 shown in FIG. 11 is applied to the remote station 300 and the central station 400. In this figure, the same parts as those in FIG.

  The remote station 300 includes an AD conversion unit 301, an FFT processing unit 302, a compression sensing unit 101, a random compression matrix generation unit 103, and a communication unit 303. The AD conversion unit 301 receives an analog signal input from the outside of the remote station 300, performs AD conversion, and outputs a digital signal. The FFT processing unit 302 divides the signal output from the AD conversion unit 301 for each frame of compressed sensing, performs FFT processing, and outputs the result.

  The communication unit 303 transmits the compressed signal output from the compression sensing unit 101 to the central station 400 via the transmission line 500. The communication unit 303 receives various control signals output from the control unit 402 of the central office 400 via the transmission line 500.

  The central office 400 includes a signal restoration unit 102, a random restoration matrix generation unit 104, a control unit 402, and a communication unit 401. The signal restoration unit 102 receives the compressed signal transmitted via the transmission line 500. Then, restoration is performed using the compressed signal and the random restoration matrix generated by the random restoration matrix generation unit 104, and a restoration signal is output.

  The control unit 402 notifies the size of the compressed sensing frame to the AD conversion unit 301 of the remote station 300. The AD conversion unit 301 outputs a digital signal after AD conversion in units of compressed sensing frames with the notified size. In addition, the control unit 402 notifies the random compression matrix generation unit 103 of the remote station 300 of the size of the compressed sensing frame, the number of rows and the number of columns of the random compression matrix via the transmission path 500. The random compression matrix generation unit 103 generates a random compression matrix according to the notified information.

  In addition, the control unit 402 notifies the random restoration matrix generation unit 104 in the same central station 400 of the size of the compressed sensing frame and the number of rows and columns of the random restoration matrix. The random restoration matrix generation unit 104 generates a random restoration matrix according to the notified information. The communication unit 401 receives the compressed signal transmitted from the remote station 300. The communication unit 401 transmits a control signal output from the control unit 402 for each notification to the remote station 300 via the transmission line 500.

[Example of processing procedure]
FIG. 15 is a flowchart illustrating a processing procedure executed by the communication processing system 600. Each process shown in this figure is executed appropriately by any of the parts shown in FIG. First, the remote station 300 sets parameters based on control information such as the size of a compressed frame received from the control unit 402 of the central station 400 via the transmission path 500 (step S31). Then, the AD conversion unit 301 converts the input analog into a digital signal (step S32). Then, the FFT processing unit 302 performs FFT processing on the signal output from the AD conversion unit 301 for each compressed sensing frame, and outputs the result to the compressed sensing unit 101 (step S33). The random compression matrix generation unit 103 generates a random compression matrix as described with reference to FIG. 1, and the compression sensing unit 101 executes compression of the input signal using the random compression matrix, and the result is transmitted to the communication unit 303. (Step S34).

  Then, the communication unit 303 transmits the compressed data to the central station 400 via the transmission line 500 (step S35), and the communication unit 401 of the central station 400 receives this data (step S36). Subsequently, the signal restoration unit 102 performs signal restoration processing using the random restoration matrix generated by the random restoration matrix generation unit 104 (step S37). The control unit 402 determines update of the parameter based on the restored signal, and when updating, transmits the updated parameter to the remote station 300 via the transmission line 500 (step S38). The signal restoration unit 102 outputs the restored signal (step S39).

  It should be noted that a program for realizing the functions of the parts shown in each figure is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into a computer system and executed for compression and decompression. Processing may be performed. Here, the “computer system” includes an OS and hardware such as peripheral devices. The “computer system” includes a WWW system having a homepage providing environment (or display environment). The “computer-readable recording medium” refers to a storage device such as a flexible medium, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Further, the “computer-readable recording medium” refers to a volatile memory (RAM) in a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. In addition, those holding programs for a certain period of time are also included.

  The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, what is called a difference file (difference program) may be sufficient.

  As mentioned above, although embodiment of this invention has been described with reference to drawings, the said embodiment is only the illustration of this invention, and it is clear that this invention is not limited to the said embodiment. is there. Accordingly, additions, omissions, substitutions, and other changes of the components may be made without departing from the technical idea and scope of the present invention.

  It can be applied to applications where it is essential to reduce the load of compression and decompression processing in compression sensing.

  DESCRIPTION OF SYMBOLS 100 ... Signal processing system, 101 ... Compression sensing part, 102 ... Signal decompression | restoration part, 103 ... Random compression matrix production | generation part, 104 ... Random decompression matrix production | generation part, 200 ... Signal processing system, 300 ... Remote station, 301 ... AD conversion part , 302 ... FFT processing unit, 303 ... communication unit, 400 ... central office, 401 ... communication unit, 402 ... control unit, 600 ... communication processing system

Claims (14)

A random compression matrix generator that generates a random compression matrix having non-zero random values less than the number of rows and columns of the compression matrix at random locations in the matrix;
A compression unit that compresses the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal;
A random restoration matrix generation unit that generates a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration unit that restores the original digital signal by restoring the signal compressed by the compression unit using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A random compression matrix generation unit for generating a random compression matrix having non-zero values that are all ones less than the number of rows and columns of the compression matrix at random locations of the matrix;
A compression unit that compresses the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal;
A random restoration matrix generation unit that generates a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration unit that restores the original digital signal by restoring the signal compressed by the compression unit using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A random compression matrix generation unit that generates a random compression matrix corresponding to a plurality of interleavers and a plurality of adders;
A plurality of interleavers and a plurality of adders are configured, the plurality of interleavers output signals in which the order of input digital signals is switched with different random patterns, and the plurality of adders each have one interleaver. A compression unit that is connected to a Lever and compresses the input digital signal by outputting a sum of a predetermined number of output signals of the interleaver;
A random restoration matrix generation unit that generates a random restoration matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration unit that restores the original digital signal by restoring the signal compressed by the compression unit using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. An AD converter for converting an input analog signal into a digital signal;
A fast Fourier transform for dividing the digital signal output from the AD converter into compressed sensing frames and executing a fast Fourier transform process to convert the signal into a frequency domain signal as the input digital signal to the compressing unit The signal processing system according to claim 1, further comprising: a unit. A signal processing system comprising a remote station and a central station,
The remote station is
An AD converter for converting an input analog signal into a digital signal;
A fast Fourier transform unit that divides the digital signal output by the AD converter for each compressed sensing frame and executes a fast Fourier transform process to output a frequency domain signal;
A random compression matrix generation unit for generating a random compression matrix having random numbers of non-zero random values less than the number of rows and columns of the compression matrix using the control information received from the central station; and
A compression unit that compresses the signal by performing matrix multiplication with the random compression matrix for each preset frame size of the signal output by the fast Fourier transform unit;
A first communication unit that transmits the compressed signal output by the compression unit to the central station and receives control information transmitted by the central station;
The central office is
Receiving a compressed signal transmitted by the remote station, and a second communication unit for transmitting the control information to the remote station;
A control unit for generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation unit that generates a random restoration matrix using the control information;
A restoration unit that restores the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing system comprising a remote station and a central station,
The remote station is
An AD converter for converting an input analog signal into a digital signal;
A fast Fourier transform unit that divides the digital signal output by the AD converter for each compressed sensing frame and executes a fast Fourier transform process to output a frequency domain signal;
Random compression matrix that generates a random compression matrix having non-zero values that are all ones less than the number of rows and columns of the compression matrix at random locations using the control information received from the central office A generator,
A compression unit that compresses the signal by performing matrix multiplication with the random compression matrix for each preset frame size of the signal output by the fast Fourier transform unit;
A first communication unit that transmits the compressed signal output by the compression unit to the central station and receives control information transmitted by the central station;
The central office is
Receiving a compressed signal transmitted by the remote station, and a second communication unit for transmitting the control information to the remote station;
A control unit for generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation unit that generates a random restoration matrix using the control information;
A restoration unit that restores the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing system comprising a remote station and a central station,
The remote station is
An AD converter for converting an input analog signal into a digital signal;
A fast Fourier transform unit that divides the digital signal output by the AD converter for each compressed sensing frame and executes a fast Fourier transform process to output a frequency domain signal;
A random compression matrix generation unit that generates a random compression matrix corresponding to a plurality of interleavers and a plurality of adders;
The interleaver includes a plurality of interleavers and a plurality of adders, and the plurality of interleavers output signals output by the fast Fourier transform unit in different random patterns, and the plurality of adders A compression unit that is connected to each interleaver and compresses the input digital signal by outputting a sum of output signals of the predetermined number of interleavers;
A first communication unit that transmits the compressed signal output by the compression unit to the central station and receives control information transmitted by the central station;
The central office is
Receiving a compressed signal transmitted by the remote station, and a second communication unit for transmitting the control information to the remote station;
A control unit for generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation unit that generates a random restoration matrix using the control information;
A restoration unit that restores the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration system is characterized in that the restoration process restores the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing method performed by a signal processing system that compresses and decompresses signals,
A random compression matrix generation step for generating a random compression matrix having non-zero random values less than the number of rows and columns of the compression matrix at random locations in the matrix;
A compression step of compressing the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal;
A random decompression matrix generating step for generating a random decompression matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration step of restoring the original digital signal by restoring the signal compressed by the compression step using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing method performed by a signal processing system that compresses and decompresses signals,
A random compression matrix generation step for generating a random compression matrix having non-zero values that are all ones less than the number of rows and columns of the compression matrix at random locations in the matrix;
A compression step of compressing the input digital signal by performing matrix multiplication with the random compression matrix for each preset frame size of the input digital signal;
A random decompression matrix generating step for generating a random decompression matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration step of restoring the original digital signal by restoring the signal compressed by the compression step using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A random compression matrix generation step for generating a random compression matrix corresponding to a plurality of interleavers and a plurality of adders;
The plurality of interleavers output signals whose input digital signals are switched in order with different random patterns, and an adder connected to each of the interleavers outputs a predetermined number of output signals of the interleaver A compression step of compressing the input digital signal by outputting the sum of
A random decompression matrix generating step for generating a random decompression matrix equivalent to the random compression matrix with reference to the random compression matrix;
A restoration step of restoring the original digital signal by restoring the signal compressed by the compression step using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. An AD conversion step for converting an input analog signal into a digital signal;
A fast Fourier transform for dividing the digital signal output in the AD conversion step into compressed sensing frames and performing a fast Fourier transform process to convert the signal into a frequency domain signal as the input digital signal to the compression step The signal processing method according to claim 8, further comprising: a step. A signal processing method performed by a signal processing system including a remote station and a central station,
The remote station is
An AD conversion step for converting an input analog signal into a digital signal;
A fast Fourier transform step in which the digital signal output by the AD conversion step is divided into compressed sensing frames to perform a fast Fourier transform process to output a frequency domain signal;
Random compression matrix generation step of generating a random compression matrix having random numbers of non-zero random values less than the number of rows and columns of the compression matrix using the control information received from the central station,
A compression step of compressing the signal by performing matrix multiplication with the random compression matrix for each preset frame size of the signal output by the fast Fourier transform step;
A first communication step for transmitting the compressed signal output by the compression step to the central station and receiving control information transmitted by the central station;
The central office is
A second communication step of receiving a compressed signal transmitted by the remote station and transmitting the control information to the remote station;
A control step of generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation step of generating a random restoration matrix using the control information;
Restoring the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing method performed by a signal processing system including a remote station and a central station,
The remote station is
An AD conversion step for converting an input analog signal into a digital signal;
A fast Fourier transform step in which the digital signal output by the AD conversion step is divided into compressed sensing frames to perform a fast Fourier transform process to output a frequency domain signal;
Random compression matrix that generates a random compression matrix having non-zero values that are all ones less than the number of rows and columns of the compression matrix at random locations using the control information received from the central office Generation step;
A compression step of compressing the signal by performing matrix multiplication with the random compression matrix for each preset frame size of the signal output by the fast Fourier transform step;
A first communication step for transmitting the compressed signal output by the compression step to the central station and receiving control information transmitted by the central station;
The central office is
A second communication step of receiving a compressed signal transmitted by the remote station and transmitting the control information to the remote station;
A control step of generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation step of generating a random restoration matrix using the control information;
Restoring the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression. A signal processing method performed by a signal processing system including a remote station and a central station,
The remote station is
An AD conversion step for converting an input analog signal into a digital signal;
A fast Fourier transform step in which the digital signal output by the AD conversion step is divided into compressed sensing frames to perform a fast Fourier transform process to output a frequency domain signal;
A random compression matrix generation step for generating a random compression matrix corresponding to a plurality of interleavers and a plurality of adders;
A plurality of interleavers output signals output by the fast Fourier transform step in different random patterns, and a plurality of adders connected to each of the interleavers determine a predetermined number. A compression step of compressing the input digital signal by outputting the sum of the output signals of the interleaver;
A first communication step for transmitting the compressed signal output by the compression step to the central station and receiving control information transmitted by the central station;
The central office is
A second communication step of receiving a compressed signal transmitted by the remote station and transmitting the control information to the remote station;
A control step of generating the control information to be transmitted to the remote station for generation of the random compression matrix;
A random restoration matrix generation step of generating a random restoration matrix using the control information;
Restoring the original digital signal by restoring the compressed signal received from the remote station using the random restoration matrix;
The signal restoration method is characterized in that the restoration processing comprises restoring the signal by obtaining an approximate value when solving an L1 optimization problem using a graph expression.

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