CN115097455B - Smooth azimuth sparse reconstruction method for scanning radar - Google Patents

Abstract

The invention discloses a smooth azimuth sparse reconstruction method for a scanning radar, which comprises the steps of firstly constructing an azimuth convolution model, and converting a super-resolution problem into a target sparse reconstruction problem under a regularization frame; then approximating the objective function by using a smoothed L ₀ norm; and finally, solving an optimization function by utilizing the steepest descent and gradient projection algorithm to realize the sparse reconstruction of the target. According to the method, a regularization strategy is introduced, and the antenna measurement matrix close to a good state is used for replacing the antenna measurement matrix in a disease state in an original algorithm, so that errors caused by initial value setting and gradient projection phases are avoided; meanwhile, a hard threshold operator is utilized to prevent the local optimum from being trapped in the steepest descent stage, so that the sparse reconstruction of the target of the real aperture scanning radar based on the L ₀ norm is realized, a sparse imaging result is obtained compared with the traditional method, and the method has a faster operation speed.

Description

A Smoothed Azimuth Sparse Reconstruction Method for Scanning Radar

Technical Field

The present invention belongs to the technical field of radar imaging processing, and is specifically applicable to real aperture scanning radar azimuth super-resolution imaging.

Background Art

Sparse reconstruction is one of the most active research areas in the field of signal processing in recent years and is widely used in many fields such as medical imaging, video processing, seismic inversion, radar imaging, etc. In the field of radar imaging, synthetic aperture radar (SAR), inverse synthetic aperture radar (ISAR), multiple input multiple output (MIMO) radar and ground penetrating radar have achieved high-resolution imaging with the help of sparse reconstruction.

For real aperture scanning radar, its imaging mechanism is to obtain the echo information of the observation area through antenna scanning, and realize the inversion from the echo domain to the target domain through signal processing. In real aperture scanning imaging, the strong scattering targets we are interested in are usually sparse relative to the entire observation scene, so the sparse reconstruction method is also widely used in real aperture scanning radar azimuth super-resolution imaging. In the literature “H.Chen, Y.Li, W.Gao, W.Zhang, H.Sun, L.Guo, and J.Yu, “Bayesian forward-looking superresolution imaging using doppler deconvolution in expanded beam space for high-speed platform,” IEEE Transactions on Geoscience and Remote Sensing, 2021”, a sparse reconstruction method is introduced from the perspective of Bayesian estimation to realize real aperture scanning azimuth super-resolution imaging; in the literature “X.Tuo, Y.Zhang， Y.Huang, and J.Yang, “A fast sparse azimuth super-resolution imaging method of real aperture radar based on iterative reweighted least squares with linear sketching,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol.14, pp.2928–2941, 2021”, a sparse reconstruction method is used from the perspective of regularization to realize real aperture scanning radar azimuth super-resolution imaging. The above method uses the sparse prior of the target to transform the azimuth super-resolution imaging problem into a sparse reconstruction problem, and uses the _L1 norm to characterize the sparse characteristics of the target.

For the sparse representation of the target, the L ₀ norm has stronger sparsity than the L ₁ norm, but directly solving the L ₀ norm minimization is an NP-Hard problem, so most of the current sparse reconstruction algorithms use the L ₁ norm to represent the sparsity of the target. Recently, the paper "H. Mohimani, M. Babaie-Zadeh, and C. Jutten, A fast approach for overcomplete sparse decomposition based on smoothed l0 norm, IEEE Transactions on Signal Processing, vol. 57, no. 1, pp. 289–301, 2009" proposed a smoothed L ₀ norm (SL0) algorithm, which uses a smooth Gaussian function to approximate the L ₀ norm, and then uses the steepest descent and gradient projection to minimize the approximate L ₀ norm. Compared with the traditional sparse reconstruction algorithm based on the L ₁ norm, the smoothed L ₀ norm (SL0) algorithm has the advantages of high accuracy and fast convergence speed.

However, due to the inherent ill-conditioned nature of the antenna measurement matrix, the smoothed _L0 norm (SL0) algorithm introduces a large amount of errors and computational complexity in the initialization and gradient projection stages. At the same time, it is easy to fall into a local loop in the steepest descent stage. Therefore, the traditional smoothed _L0 norm algorithm cannot be directly used in the field of real aperture scanning radar super-resolution imaging.

Summary of the invention

The purpose of the present invention is to address the defects of the background technology, and the present invention proposes a smooth azimuth sparse reconstruction method for scanning radar.

The technical solution of the present invention is: a smooth azimuth sparse reconstruction method for scanning radar, comprising the following steps:

Step 1: Modeling the azimuthal convolution model.

The real aperture scanning radar radiates linear frequency modulation (LFM) signals at a certain pulse repetition frequency (PRF), and uses antenna scanning to detect the observation area. Based on the scanning imaging process, the azimuth echo signal is constructed as the convolution of the antenna function and the target scattering coefficient, and considering additive Gaussian white noise, the azimuth signal model is expressed as:

y＝Hx+n (1)

in, Represents the received echo matrix, with a dimension of N×1. represents the i-th element of the echo matrix, N is the number of azimuth sampling points, Ω is the imaging area, ω is the scanning speed, PRF is the pulse repetition frequency, and similarly is the target scattering coefficient matrix, with dimension N×1, where T represents the matrix transpose operation; The noise matrix satisfies the Gaussian distribution and has a dimension of N×1. H is the antenna measurement matrix composed of antenna pattern sampling and has a dimension of N×N:

in, is the antenna pattern sampling vector, and its number of sampling points is S, θ is the antenna main lobe width;

Step 2: Objective function construction and transformation,

In the sparse regularization framework, using the _L0 norm, the following objective function is constructed:

Among them, || || ₂ represents the 2-norm of the vector; || || ₀ represents the 0-norm of the vector.

Since the L ₀ norm minimization problem of a vector is discontinuous, it is difficult to solve it by direct minimization. The smooth L ₀ norm uses a series of continuous functions to approximate the discontinuous L ₀ norm, and approximates the minimization of the L ₀ norm by minimizing the continuous function. The L ₀ norm can be approximated as a continuous function of the following formula:

in, represents the sum of N Gaussian functions with varying shape parameters, _xi represents the i-th element of vector x; σ represents the shape parameter of the Gaussian function. When σ→0, the Gaussian function will approach the _L0 norm, so the smoothed _L0 norm will use a decreasing sequence of σ values to continuously approximate the _L0 norm.

Step 3: Initialize parameters and results.

Set the following parameters: regularization parameter λ, attenuation coefficient ρ (0＜ρ＜1), number of inner loops L, and iteration step size μ.

Using the regularization strategy, the target scattering coefficient is initialized as:

Where I represents the N×N identity matrix;

At the same time, the initial value of the decreasing sequence of σ is determined by the following formula:

The threshold operator threshold is determined by the following formula:

Step 4: Steepest descent phase,

Update the target scatter coefficient to:

in,

Step 5: Gradient projection stage,

The target scattering coefficient in step 4 is further updated through gradient projection using the regularization strategy as follows:

Step 6: Hard threshold correction,

In the process of searching for the optimal value by the steepest descent, the search path will be jagged and prone to falling into the local minimum. The hard threshold operation is used to further correct the result, which is defined as:

Here, δ is the threshold value.

By using the hard threshold operator, when When an element is less than the set threshold δ, the element is set to 0. Use hard threshold operation to prevent falling into the local minimum and improve the convergence speed.

Step 7: Update the σ value.

Repeat steps 4, 5, and 6 for L cycles. After the inner loop is completed, update the σ value to the following formula:

σ＝ρσ (11)

Where ρ represents the attenuation coefficient, 0＜ρ＜1;

Then continue the inner loop (including: L times of step 4, step 5, step 6) and step 7 until σ reaches a preset threshold.

Beneficial effects of the present invention: The method of the present invention first constructs an azimuth convolution model, and transforms the super-resolution problem into a target sparse reconstruction problem under a regularization framework; then the smooth _L0 norm is used to approximate the target function; finally, the optimization function is solved by the steepest descent and gradient projection algorithms to achieve target sparse reconstruction. The method of the present invention introduces a regularization strategy to replace the ill-conditioned antenna measurement matrix in the original algorithm with a nearly well-conditioned antenna measurement matrix, thereby avoiding errors introduced in the initial value setting and gradient projection stages; at the same time, a hard threshold operator is used to prevent falling into a local optimum in the steepest descent stage, thereby achieving sparse reconstruction of real aperture scanning radar targets based on the _L0 norm, obtaining sparser imaging results than traditional methods, and having a faster computing speed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a smoothed azimuth sparse reconstruction method for scanning radar according to the present invention.

FIG. 2 is a diagram of a geometric model of an airborne radar forward-looking imaging according to an embodiment of the present invention.

FIG. 3 is an image of f _σ (x) with three different σ values according to an embodiment of the present invention.

FIG. 4 is an original scene diagram of point target simulation according to an embodiment of the present invention.

FIG. 5 is a super-resolution imaging result of an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention is mainly verified by simulation experiment, and all steps and conclusions are verified to be correct on Matlab 2019. The method of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

The process of the smoothed azimuth sparse reconstruction method for scanning radar of the present invention is shown in FIG1 , and the specific implementation steps are as follows:

Step 1: Establishment of azimuth echo convolution model

The airborne radar forward-looking imaging geometric model shown in Figure 2 is adopted, and the radar simulation system parameters shown in Table 1 are selected.

Table 1

The signal-to-noise ratio is set to SNR = 20 dB. Assume that the airborne radar platform flies at a constant speed v = 20 m/s along the y-axis, and the radar antenna scans the forward-looking area at ω = 30°/s. The flight altitude of the platform is H = 1000 m, and the initial slant range between the platform and the target P is R ₀ = 3000 m. At time t, the distance history R(t) between the platform and the target is expressed as

Wherein, θ and β represent the azimuth and elevation angles respectively.

The radar obtains the original echo data by transmitting a linear frequency modulation signal. After the original echo is subjected to range pulse compression and range movement correction, the echo signal can be expressed as:

In formula (13), τ and t represent the range and azimuth time variables, respectively; σ(x, y) and h(·) represent the target backscatter coefficient and antenna pattern response function, respectively; sinc(·) represents the pulse compression response function; Φ is the observation area of interest; B = 40 MHz is the bandwidth; λ = 0.01 m is the wavelength; ω = 30°/s is the beam scanning speed; c = 3 × 10 ⁸ m/s is the electromagnetic wave propagation speed; R ₀ = 3000 m is the initial slant range between the platform and the target; and R(t) is the distance history between the platform and the target.

From the above derivation, it can be seen that based on the scanning imaging process, the azimuth echo signal can be constructed as the convolution of the antenna function and the target scattering coefficient, and considering the additive Gaussian white noise, after the azimuth signal is discretized, the azimuth signal model can be expressed as:

y＝Hx+n (14)

in, is the received echo vector, is the vector of target scattering coefficient distribution, is the noise vector. N=667 represents the number of azimuth sampling points, which can be calculated from the scanning speed, scanning range and PRF in Table 1. H represents the N×N antenna measurement matrix composed of antenna pattern profiles.

Step 2: Objective function construction and transformation

In the sparse regularization framework, using the _L0 norm, the following objective function can be constructed:

By minimizing the continuous function, the _L0 norm can be approximated as the following continuous function:

in, represents the sum of N Gaussian functions with varying shape parameters, σ represents the shape parameter of the Gaussian function. As shown in Figure 3, when σ→0, the Gaussian function approaches the _L0 norm.

Step 3: Initialize parameters and results

Set the following parameters: In this simulation, the regularization parameter λ=2, the attenuation coefficient ρ=0.5, the number of inner loops L=5, and the iteration step μ=2.

Using the regularization strategy, the target scattering coefficient is initialized as:

Wherein, I represents the N×N identity matrix.

At the same time, the initial value of the decreasing sequence of σ is determined by the following formula:

The threshold operator threshold is determined by the following formula:

Step 4: Steepest Descent

Update the target scatter coefficient to:

in, μ=2 is the iteration step size.

Step 5: Gradient projection stage

The target scattering coefficient in step 4 is further updated through gradient projection using the regularization strategy as follows:

Among them, the regularization parameter λ=2.

Step 6: Hard Threshold Correction

The result is further modified by hard threshold operation, which is defined as:

in, is a variable, is the threshold value.

By using the hard threshold operator, when When an element is less than the set threshold δ, the element is set to 0. Use hard threshold operation to prevent falling into the local minimum and improve the convergence speed.

Step 7: Update σ value

Repeat steps 4, 5, and 6, and the number of inner loops is L = 5. After the inner loop is completed, the σ value is updated to the following formula:

σ＝ρσ (23)

Here, ρ=0.5 represents the attenuation coefficient.

Then continue the inner loop (including: L times of step 4, step 5, step 6) and step 7 until σ≤0.01.

As for the simulation test results, Figure 5(a) is the real beam imaging result. It can be seen that the two targets are indistinguishable. Figures 5(b) and 5(c) are the deconvolution imaging results based on the sparse regularization method and the IAA method, respectively. Figure 5(d) is the deconvolution imaging result obtained based on the MSL0 method proposed in the present invention. It can be seen from observation that the sparse regularization method and the IAA method can distinguish the two targets to a certain extent, but their super-resolution performance is weaker than the method proposed in Figure 5(d). In addition, the running time of the three algorithms was tested, as shown in Table 2.

Table 2

The calculation time of the MLS0 method proposed in the present invention is much shorter than that of the sparse regularization method and the IAA method, which also proves the advantage of the MLS0 method in terms of computational efficiency. In summary, for sparse targets, the method of the present invention has better super-resolution performance and faster running speed than traditional methods.

Claims (1)

1. A smooth azimuth sparse reconstruction method for a scanning radar comprises the following steps:

Step one: modeling a convolution model of an azimuth,

The real aperture scanning radar radiates a linear frequency modulation signal at a certain pulse repetition frequency, an antenna is used for scanning and detecting an observation area, based on the scanning imaging process, an azimuth echo signal is constructed as convolution of an antenna function and a target scattering coefficient, and additive Gaussian white noise is considered, and an azimuth signal model is expressed as follows:

y＝Hx+n (1)

wherein, Representing the received echo matrix, with dimensions N x 1,Representing the i-th element of the echo matrix, N being the number of azimuth sampling points,Omega is imaging region, omega is scan speed, PRF is pulse repetition frequency, and the same holdsThe method is a target scattering coefficient matrix, the dimension is Nx1, and T represents matrix transposition operation; The noise matrix meeting Gaussian distribution has dimension of N multiplied by 1; h is an antenna measurement matrix consisting of antenna pattern samples, with dimensions n×n:

wherein, Is an antenna pattern sampling vector, the number of sampling points is S,Θ is the antenna main lobe width;

Step two: the construction and conversion of the objective function are carried out,

Under the sparse regularization framework, the following objective function is constructed by using the L ₀ norm:

Wherein, the term ₂ represents the 2-norm of the vector; the term ₀ represents the 0-norm of the vector;

The L ₀ norm approximates a continuous function of:

wherein, A gaussian function summation representing the constant change of N shape parameters,X _i represents the ith element of vector x; sigma represents a shape parameter of a gaussian function;

step three: the parameters and the results are initialized and the results are displayed,

The following parameters were set: regularization parameter lambda, attenuation coefficient rho (0 < rho < 1), internal circulation times L and iteration step length mu;

using a regularization strategy, the target scattering coefficient is initialized to:

wherein I represents an n×n identity matrix;

meanwhile, the initial value of the decreasing sequence of σ is determined by:

the threshold operator threshold is determined by:

Step four: in the stage of the steepest descent of the vehicle,

Updating the target scattering coefficient as follows:

wherein,

Step five: in the stage of gradient projection,

Updating the target scattering coefficient in the fourth step into the following formula by utilizing a regularization strategy:

Step six: the hard threshold value is corrected and,

The result is further modified by hard thresholding, defined as:

wherein δ is a threshold;

Step seven: the value of sigma is updated and,

Repeating the calculation step four, the step five and the step six, wherein the circulation times are L, and after the internal circulation is finished, updating the sigma value into the following formula:

σ＝ρσ (11)

wherein ρ represents an attenuation coefficient, 0 < ρ < 1;

The inner loop then continues, including: l times of step four, step five, step six, and step seven until sigma reaches a preset threshold.