CN102801428B - Approximation optimization and signal acquisition reconstruction method for 0-1 sparse cyclic matrix - Google Patents
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Abstract
The invention discloses an approximation optimization and signal acquisition reconstruction method for a 0-1 sparse cyclic matrix, belongs to the technical field for the design and optimization of measurement matrix in compressive sensing, and provides a posteriori optimizing method which is easy to implement by hardware and can ensure signal reconstruction effect, wherein the 0-1 sparse cyclic matrix is adopted in the measurement stage, and a Gaussian matrix is adopted in the reconstruction stage. The method comprises the following steps: orthonormalizing the row vector and unitizing the column vector of the measurement matrix obtained by the i-1th iteration by the ith iteration; and optimizing the 0-1 sparse cyclic matrix by taking the maximum value of the absolute value of the correlated coefficient between each row and column vector, the convergence stability of each row vector module and the row and column number of each row and column subjected to Gaussian distribution as the criteria. The posteriori optimization of the measured data and measured matrix is completed by solving a transition matrix and an approximate matrix. The method establishes the foundation for the compressive sensing to be practical from the theoretical study.
Description
Technical field
The invention belongs to compressed sensing technical field, specifically provide a kind of near-optimal and signals collecting reconstructing method of 0-1 rarefaction cycles matrix.
Background technology
In compressed sensing, the Design and optimization of calculation matrix and character are the key factors of bearing signal reconstruct.Random matrix (Gauss, Bernoulli Jacob's equal matrix) though have good signal reconstruction ability and universality, but due to be difficult to hardware implementing people then research character poor, be easy to hard-wired certainty matrix (Teoplitz, circulation, polynomial matrix etc.).Circular matrix in calculation matrix is easy to hardware implementing, and can adopt discrete Fourier transform (DFT) rapid solving; 0-1 sparse matrix is not only easy to hardware implementing but also the little fast operation of required memory space.Therefore, the 0-1 rarefaction cycles matrix (be called for short: rarefaction cycles matrix) both mixed will the design of simplified measurement matrix and hardware implementing greatly.But the ranks irrelevance of sparse matrix is poor, and adopt sparse matrix that each element in measured value can be caused can only to comprise a part of information of signal, each element is no longer in par, and anti-packet loss ability is deteriorated.
In any case current calculation matrix optimal design, invariably all adopt same calculation matrix in measurement and two stages of reconstruct.If adopt in measuring phases and be easy to the hard-wired certainty matrix do not optimized, the quality reconstruction of signal just cannot be ensured in reconstruction stage; If adopt in reconstruction stage and optimize matrix, the easy realization of measuring phases calculation matrix just cannot be ensured.Adopt in measuring phases the certainty matrix that hardware easily realizes, character is poor, reconstruction stage adopt hardware not easily realize, the good Gaussian matrix of character be people expect calculation matrix design and data processing general layout.
Summary of the invention
The present invention is in order to solve the low problem designed with calculation matrix of rarefaction cycles matrix signal re-configurability, and spy provides a kind of near-optimal and signals collecting reconstructing method of 0-1 rarefaction cycles matrix.
The present invention is achieved by following proposal: a kind of near-optimal of 0-1 rarefaction cycles matrix and signals collecting reconstructing method, and the process of described method is:
Step one: generate 0-1 rarefaction cycles matrix
, optimize matrix with season
, wherein
,
.
initial row vector be comprise (
) individual random distribution 1 0-1 loose line vector, each row vector is all that each element of previous row vector moves to right successively
(
and meet
) result of position.Represent
complementation,
,
,
with
it is all natural number;
Step 2: inspection
in whether have identical row or column, if return perform step one, otherwise setting iterations
iinitial value be 0,
, setting iteration error
;
Step 3: calculate with Ha Erke-Bei La (Jarque-Bera) inspection
the line number of each row and each row Gaussian distributed
and columns
; Calculate
coefficient correlation between each column vector, takes out the maximum of its absolute value
; Calculate the coefficient correlation between each row vector, take out the maximum of its absolute value
; Calculate
the mould of each row vector, takes out its maximum
and minimum value
;
Step 4: orthonormal
each row vector, then unitization each column vector, makes
i=
i+ 1, just can be optimized matrix
.Calculate transition matrix simultaneously
, approximate matrix
, and make
;
Step 5: judgement optimization matrix
with
with
with
with
with
, if perform step 6, otherwise return execution step 3;
Step 6: obtain optimization matrix
, transition matrix
and approximate matrix
;
Step 7: by rarefaction cycles matrix with the conventional method image data shown in the constraint equation in following formula:
Step 8: the measurement data that conventional method collects is optimized by transition matrix:
Step 9: the signal reconstruction algorithm reconstruction signal by traditional:
。
The present invention is with right
the iterative cycles computing of the orthonormal of each row vector and the unitization of each column vector achieves the optimization of 0-1 rarefaction cycles matrix.Then by measurement data that transition matrix near-optimal conventional method collects
and calculation matrix
.Optimization matrix and approximate matrix had both had the universality of Gaussian matrix, turn improved signal reconstruction ability.Method of the present invention not only simplifies hardware designs and the realization of calculation matrix, and improve signal reconstruction effect, have a wide range of applications in the field such as image procossing, video analysis, radar remote sensing, communication code, digital audio of compressed sensing.
Accompanying drawing explanation
Fig. 1 is a kind of near-optimal of 0-1 rarefaction cycles matrix described in embodiment one and the flow chart of signals collecting reconstructing method; Fig. 2 be application embodiment to 128 × 256 the optimization matrix that obtains of rarefaction cycles matrix disposal and the row module maximum of approximate matrix and the graph of a relation of iterations; Fig. 3 be application embodiment to 128 × 256 the optimization matrix that obtains of rarefaction cycles matrix disposal and the ranks coefficient correlation of approximate matrix and the graph of a relation of iterations; Fig. 4 is application embodiment optimization to the optimization matrix that obtains of rarefaction cycles matrix disposal of 128 × 256 and the graph of a relation meeting ranks number that Ha Erke-Bei La (Jarque-Bera) checks and iterations of approximate matrix; Fig. 5 be application embodiment to 128 × 256 the reconstruct probability of optimization matrix, approximate matrix and rarefaction cycles matrix that obtains of rarefaction cycles matrix disposal and the graph of a relation of degree of rarefication.
Embodiment
Embodiment one: illustrate present embodiment according to Figure of description 1.The near-optimal of 0-1 rarefaction cycles matrix and a signals collecting reconstructing method, the process of described method is:
Step one: generate 0-1 rarefaction cycles matrix
, optimize matrix with season
, wherein
,
.
initial row vector be comprise
(
) individual random distribution 1 0-1 loose line vector, each row vector is all that each element of previous row vector moves to right successively
(
and meet
) result of position.
represent
complementation,
,
,
with
it is all natural number;
Step 2: inspection
in whether have identical row or column, if return perform step one, otherwise setting iterations
iinitial value be 0,
, setting iteration error
;
Step 3: calculate with Ha Erke-Bei La (Jarque-Bera) inspection
the line number of each row and each row Gaussian distributed
and columns
; Calculate
coefficient correlation between each column vector, takes out the maximum of its absolute value
; Calculate the coefficient correlation between each row vector, take out the maximum of its absolute value
; Calculate
the mould of each row vector, takes out its maximum
and minimum value
;
Step 4: orthonormal
each row vector, then unitization each column vector, makes
i=
i+ 1, just can be optimized matrix
.Calculate transition matrix simultaneously
, approximate matrix
, and make
;
Step 5: judgement optimization matrix
with
with
with
with
with
, if perform step 6, otherwise return execution step 3;
Step 6: obtain optimization matrix
, transition matrix
and approximate matrix
;
Step 7: by rarefaction cycles matrix with the conventional method image data shown in the constraint equation in following formula:
Step 8: the measurement data that conventional method collects is optimized by transition matrix:
Step 9: the signal reconstruction algorithm reconstruction signal by traditional:
。
Embodiment two: this embodiment is further illustrating a kind of Gaussian matrix optimization method based on compressed sensing described in embodiment one, sets iteration error in step 2
err1 is
,
err2 are
,
err3 are
.
Embodiment three: this embodiment is to a kind of near-optimal of 0-1 rarefaction cycles matrix described in embodiment one and further illustrating of signals collecting reconstructing method, the orthonormal described in step 4
each row vector, then the detailed process of unitization each column vector is: first right
each row vector orthogonalization, then unitization each row vector, last unitization each column vector.
Embodiment four: illustrate present embodiment below in conjunction with Fig. 2-Fig. 5.Present embodiment adopts the gaussian signal of different degree of rarefication to be applied to respectively to optimize matrix, approximate matrix and rarefaction cycles matrix, compares the reconstruct probability after its each 500 experiments.Be with in Fig. 2 "
" what mark is maximum curve; Band "
" what mark is minimum value curve; Band "
" what mark is reference line.Be with in Fig. 3-Fig. 4 "
" what mark is row curves; Band "
" what mark is row curve.(a) representing optimized matrix in Fig. 2-Fig. 4; B () represents approximate matrix.Be with in Fig. 5 "
,
,
" curve that marks is adopt the reconstruct probability curve optimizing matrix, approximate matrix and rarefaction cycles matrix respectively.
Experimental result as Figure 2-Figure 5.As seen from Figure 2, the extreme difference of the optimization matrix in rarefaction cycles matrix optimizing iterative process and each row vector mould of approximate matrix corresponding with it constantly diminishes convergence; As seen from Figure 3, the maximum optimizing matrix and approximate matrix each ranks coefficient correlation absolute value constantly diminishes convergence; As seen from Figure 4, the ranks number optimizing matrix and approximate matrix each ranks Gaussian distributed corresponding with it in rarefaction cycles matrix optimizing iterative process becomes rapidly many in the iteration later stage, nearly all Gaussian distributed; As seen from Figure 5, optimize matrix closely similar with the reconstruct probability curve of approximate matrix, be positioned at the right side of the curve of rarefaction cycles matrix completely.
Claims (1)
1. the near-optimal of 0-1 rarefaction cycles matrix and a signals collecting reconstructing method, is characterized in that: the process of described method is:
Step one: generate 0-1 rarefaction cycles matrix
, optimize matrix with season
, wherein
,
,
initial row vector be comprise
(
) individual random distribution 1 0-1 loose line vector, each row vector is all that each element of previous row vector moves to right successively
(
and meet
) result of position,
represent
complementation,
,
,
with
it is all natural number;
Step 2: inspection
in whether have identical row or column, if return perform step one, otherwise setting iterations
iinitial value be 0,
, setting iteration error
;
Step 3: calculate with Ha Erke-Bei La (Jarque-Bera) inspection
the line number of each row and each row Gaussian distributed
and columns
; Calculate
coefficient correlation between each column vector, takes out the maximum of its absolute value
; Calculate the coefficient correlation between each row vector, take out the maximum of its absolute value
; Calculate
the mould of each row vector, takes out its maximum
and minimum value
;
Step 4: orthonormal
each row vector, then unitization each column vector, makes
i=
i+ 1, just can be optimized matrix
; Calculate transition matrix simultaneously
, approximate matrix
, and make
;
Step 5: judgement optimization matrix
with
with
with
with
with
, if perform step 6, otherwise return execution step 3;
Step 6: obtain optimization matrix
, transition matrix
and approximate matrix
;
Step 7: by rarefaction cycles matrix with the conventional method image data shown in the constraint equation in following formula:
Step 8: the measurement data that conventional method collects is optimized by transition matrix:
Step 9: the signal reconstruction algorithm reconstruction signal by traditional:
。
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| CN103017738B (en) * | 2012-12-18 | 2015-01-07 | 程涛 | Remote-sensing image efficient acquisition and incremental updating method based on two-dimensional compressed sensing |
| CN104104389B (en) * | 2013-04-09 | 2017-08-18 | 华为技术有限公司 | A kind of signal reconstruction method and apparatus |
| CN103888145B (en) * | 2014-03-28 | 2017-03-15 | 电子科技大学 | A kind of method of reconstruction signal |
| CN104270156B (en) * | 2014-06-12 | 2017-05-31 | 湘潭大学 | Reduction compensation mechanism calculation matrix building method is followed the trail of in compressed sensing |
| CN104242948A (en) * | 2014-08-26 | 2014-12-24 | 重庆邮电大学 | Toeplitz structure measurement matrix construction method based on singular value decomposition |
| CN105790769B (en) * | 2016-02-19 | 2019-04-12 | 哈尔滨工业大学 | Random demodulation method based on discrete ellipsoid sequence |
| TWI617925B (en) * | 2016-10-26 | 2018-03-11 | 聯發科技股份有限公司 | Measurement matrix generating system based on scrambling and method thereof |
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