Distance super-resolution method optimized by reweighted l1 norm for jointly enveloping and phase

Abstract

The present invention discloses a distance super-resolution method based on joint envelope and phase reweighted l1-norm optimization, including: constructing a distance super-resolution compressive sensing model and its corresponding optimization function; solving the optimization function to obtain an iterative solution function of the target reweighting; using the method of minimizing the reweighted l1-norm to solve the iterative solution function of the target reweighting, and then using the conjugate gradient algorithm to solve the complex equation to obtain the reconstructed super-resolution range image; determining whether the reconstructed super-resolution range image satisfies the first condition, if it satisfies the first condition, obtaining the super-resolution target distance value and the super-resolution range image; if it does not satisfy the first condition, modifying the target reweighting weight coefficient and the iterative solution function of the target reweighting according to the reconstructed super-resolution range image, and obtaining the reconstructed super-resolution range image again according to the modification result until the reconstructed super-resolution range image satisfies the first condition. The present invention can improve the distance resolution ability.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a distance super-resolution method based on the reweighted l1 norm optimization that combines envelope and phase. Background Art

[0002] With the continuous development of advanced technologies such as digital transmission, reception technology, and microwave photonics, radar systems have been continuously improved, and the bandwidth of radars has become larger and larger, resulting in a great improvement in range resolution.

[0003] Although the performance of radars has been continuously improved, the problem of insufficient resolution ability will inevitably occur during the process of processing multiple targets. In the prior art, radar systems usually adopt high range resolution to improve the target resolution ability of radars. Compared with ordinary radar systems, high range resolution radars can detect and identify targets from strong ground clutter backgrounds and achieve high-resolution radar imaging. Among them, improving the range image resolution performance of radars is mainly divided into two categories. One category is to improve the theoretical range resolution of the system by methods such as increasing the effective bandwidth of the system and reducing the noise figure of the receiver. This method not only has too high research costs, increases the amount of sampled data, occupies a large amount of hardware resources, is difficult to implement on hardware, but also is restricted by the actual environment. The other category is to use signal processing algorithms to enhance the super-resolution ability of radars. The above research methods are greatly affected by factors such as sampling frequency, noise model, and signal-to-noise ratio, and the range super-resolution ability is limited. Moreover, in the case of low signal-to-noise ratio, noise suppression processing is not performed, and the range image super-resolution performance is poor in practical applications, and the target phase characteristics after super-resolution are not retained, which greatly affects subsequent radar signal processing.

[0004] Therefore, it is urgent to improve the defects existing in the prior art. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a distance super-resolution method based on the reweighted l1 norm optimization that combines envelope and phase. The technical problems to be solved by the present invention are achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a distance super-resolution method based on the reweighted l1 norm optimization that combines envelope and phase, including:

[0007] Obtain the initial radar range image;

[0008] Perform an inverse Fourier transform on the initial radar range image, and then perform range image aperture expansion to obtain the time-domain spectrum of the expanded initial radar range image and the frequency-domain spectrum of the expanded initial radar range image;

[0009] Obtain the sparse constraint coefficient according to the frequency-domain spectrum of the expanded initial radar range image;

[0010] Construct a distance super-resolution compressive sensing model based on the obtained observation matrix, dictionary matrix, and initial observation signal, and combine the sparse constraint coefficients to construct an optimization function corresponding to the distance super-resolution compression model;

[0011] Obtain the target reweighting coefficient according to the extended frequency-domain spectrum of the initial radar range profile;

[0012] Solve the optimization function according to the target reweighting coefficient and the distance super-resolution compressive sensing model to obtain the iterative solution function of the target reweighting;

[0013] Solve the iterative solution function of the target reweighting using the method of minimizing the reweighted l1 norm, and then use the conjugate gradient algorithm to solve the complex equation to obtain the reconstructed super-resolution range profile;

[0014] Judge whether the reconstructed super-resolution range profile meets the first condition. If it meets the first condition, obtain the super-resolution target distance value and the super-resolution range profile; if it does not meet the first condition, modify the target reweighting coefficient and the iterative solution function of the target reweighting according to the reconstructed super-resolution range profile, and obtain the reconstructed super-resolution range profile again according to the modification result until the reconstructed super-resolution range profile meets the first condition.

[0015] Advantages of the present invention:

[0016] A distance super-resolution method based on the joint envelope and phase reweighted l1 norm optimization provided by the present invention can effectively utilize short observation data, break through the system response bandwidth limitation, and achieve a high-resolution radar range profile far below the Nyquist sampling law; at the same time, the present invention considers the influence of noise on distance super-resolution, reduces the influence of noise on the solution of the compressive sensing method through sparse constraint coefficients, and can perform high-performance distance super-resolution on targets under low signal-to-noise ratios; finally, the present invention effectively retains the phase characteristics at the target after super-resolution, provides support for subsequent radar signal processing while improving the distance resolution ability, and has high application value.

[0017] The following will further elaborate on the present invention in conjunction with the accompanying drawings and embodiments. Description of the Drawings

[0018] Figure 1 is a flowchart of a distance super-resolution method based on the joint envelope and phase reweighted l1 norm optimization provided by an embodiment of the present invention;

[0019] Figure 2 is another flowchart of a distance super-resolution method based on the joint envelope and phase reweighted l1 norm optimization provided by an embodiment of the present invention;

[0020] Figure 3(a) is a schematic diagram of a radar one-dimensional range profile obtained under the condition of four times bandwidth provided by an embodiment of the present invention;

[0021] Figure 3(b) is a schematic diagram of an initial range profile of a radar provided by an embodiment of the present invention;

[0022] Figure 3(c) is a schematic diagram after super-resolution provided by an embodiment of the present invention;

[0023] Figure 3(d) is a comparison diagram of an ideal 4-fold resolution under large bandwidth conditions and a 4-fold super-resolution image obtained under small bandwidth conditions provided by an embodiment of the present invention;

[0024] Figure 4(a) is a schematic diagram of a radar two-dimensional spectrum obtained under the condition of four times bandwidth provided by an embodiment of the present invention;

[0025] Figure 4(b) is a schematic diagram of a radar one-dimensional range profile at the target obtained under the condition of four times bandwidth provided by an embodiment of the present invention;

[0026] Figure 4(c) is a schematic diagram of a radar two-dimensional spectrum provided by an embodiment of the present invention;

[0027] Figure 4(d) is a schematic diagram of an initial range profile of a radar at the target provided by an embodiment of the present invention;

[0028] Figure 4(e) is another schematic diagram after super-resolution provided by an embodiment of the present invention;

[0029] Figure 4(f) is a comparison schematic diagram of an ideal 4-fold resolution under large bandwidth conditions and a 4-fold super-resolution image obtained under small bandwidth conditions provided by an embodiment of the present invention;

[0030] Figure 5(a) is a comparison schematic diagram of sparse reconstruction and an ideal 4-fold resolution range profile at 20 dB provided by an embodiment of the present invention;

[0031] Figure 5(b) is a comparison schematic diagram of Burg extrapolation and an ideal 4-fold resolution range profile at 20 dB provided by an embodiment of the present invention;

[0032] Figure 5(c) is a comparison schematic diagram of time-domain interpolation and padding with zeros and an ideal 4-fold resolution range profile at 20 dB provided by an embodiment of the present invention;

[0033] Figure 5(d) is a comparison schematic diagram of sparse reconstruction and an ideal 4-fold resolution range profile at 10 dB provided by an embodiment of the present invention;

[0034] Figure 5(e) is a comparison schematic diagram of Burg extrapolation and an ideal 4-fold resolution range profile at 10 dB provided by an embodiment of the present invention;

[0035] Figure 5(f) is a comparison diagram between zero-padding by time-domain interpolation at 10 dB and the ideal 4-fold resolution range image provided by an embodiment of the present invention;

[0036] Figure 5(g) is a comparison diagram between sparse reconstruction at 5 dB and the ideal 4-fold resolution range image provided by an embodiment of the present invention;

[0037] Figure 5(h) is a comparison diagram between Burg extrapolation at 5 dB and the ideal 4-fold resolution range image provided by an embodiment of the present invention;

[0038] Figure 5(i) is a comparison diagram between zero-padding by time-domain interpolation at 5 dB and the ideal 4-fold resolution range image provided by an embodiment of the present invention. Detailed implementation manners

[0039] The following further describes the present invention in detail with reference to specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0040] A distance super-resolution method based on reweighted l1-norm optimization that combines envelope and phase is provided by the present invention to address the defects in the prior art, including poor distance super-resolution performance at low signal-to-noise ratios, non-preservation of phase information after distance super-resolution, which affects subsequent radar signal processing performance, and large amounts of data and high hardware resource consumption in processing ultra-wideband radar signals.

[0041] Please refer to Figure 1 and Figure 2 as shown, Figure 1 is a flowchart of a distance super-resolution method based on reweighted l1-norm optimization that combines envelope and phase provided by an embodiment of the present invention, Figure 2 is another flowchart of a distance super-resolution method based on reweighted l1-norm optimization that combines envelope and phase provided by an embodiment of the present invention. A distance super-resolution method based on reweighted l1-norm optimization that combines envelope and phase provided by the present invention includes:

[0042] S101. Obtain the initial radar range image.

[0043] Specifically, in this embodiment, according to the data of the radar system, the initial radar range image is obtained; when using single-snapshot data for distance super-resolution, the initial radar range image is directly obtained according to the single-snapshot data When using multi-snapshot data for distance super-resolution, the initial radar range image is obtained by accumulating the multi-snapshot data Among them, both single-snapshot data and multi-snapshot data are radar snapshot data, that is, the data of the radar system; in addition, the radar system data also includes the carrier frequency f c of the radar, wavelength λ, and pulse width T PAnd the signal bandwidth B, the radar ranging range ΔR in the application scenario, the number of radar snapshots, the number of single snapshots, or M snapshots.

[0044] S102. Perform an inverse Fourier transform on the initial radar range image, and then perform range image aperture expansion to obtain the time-domain spectrum of the expanded initial radar range image and the frequency-domain spectrum of the expanded initial radar range image.

[0045] Specifically, the time-domain spectrum of the expanded initial radar range image and the frequency-domain spectrum of the expanded initial radar range image are obtained through the following steps.

[0046] S1021. Perform an inverse Fourier transform on the initial radar range image to obtain the time-domain spectrum of the initial radar range image.

[0047] S1022. Determine the number of sampling points N after super-resolution according to the super-resolution multiple required by the radar scene target, and perform range image aperture expansion by padding zeros or spectral extrapolation on the initial radar range image to obtain the time-domain spectrum S of the expanded initial radar range image te and the frequency-domain spectrum S of the expanded initial radar range image fe ; where the number of expanded points is the same as the number of super-resolution sampling points.

[0048] It should be noted that the range super-resolution aperture expansion is to prepare for subsequent range super-resolution. In the same frequency spectrum range, the more the number of sampling points, the higher the resolution.

[0049] S103. Obtain the sparse constraint coefficient according to the frequency-domain spectrum of the expanded initial radar range image.

[0050] Specifically, the sparse constraint coefficient is obtained through the following steps.

[0051] S1031. Assume that the frequency-domain spectrum S of the expanded initial radar range image fe obeys the same distribution, and obtain the same Laplacian factor γ for each point in the frequency-domain spectrum S of the expanded initial radar range image fe , and its expression is:

[0052] γ = N / ||S fe ||1;

[0053] where ||·||1 is the l1 norm, and N is the number of super-resolution sampling points.

[0054] S1032. Extract the noise unit S in the initial radar range image N , vectorize the noise unit, and the vectorized noise unit is represented as S no ; it should be noted that the initial radar range image includes a target area and a noise area, and the noise unit obviously does not include the target signal;

[0055] Using the vectorized noise unit S no Estimate the noise variance σ 2 , and its expression is:

[0056] σ 2 = E{(s no ) H s no};

[0057] where (s no ) H is the conjugate transpose of the noise unit S N .

[0058] S1033. According to the Laplacian factor γ and the noise variance σ 2 , obtain the sparse constraint coefficient μ, and its expression is:

[0059] μ = σ 2 γ.

[0060] It should be noted that in this embodiment, the influence of noise on the range super-resolution performance is considered. The noise variance is estimated using the radar initial range image, and the Laplacian scale factor is estimated using the range aperture expansion result of the initial range image. Then, the sparse constraint coefficient is obtained, and the influence of noise is considered in the sparse solution process to achieve high-performance range super-resolution of the target under low noise signal-to-noise ratio.

[0061] S104. According to the obtained observation matrix, dictionary matrix, and initial observation signal, construct a range super-resolution compressive sensing model, and combine the sparse constraint coefficient to construct an optimization function corresponding to the range super-resolution compression model.

[0062] Specifically, in this embodiment, first, an observation matrix, a dictionary matrix, and an initial observation signal need to be obtained; among them, the process of obtaining the observation matrix includes:

[0063] When performing range aperture expansion by padding 0 to the radar initial range image, the observation matrix U is an N×N diagonal matrix, and the elements corresponding to the actual sampling points in the diagonal matrix are 1, and the elements corresponding to the range image aperture expansion are 0;

[0064] When performing range aperture expansion by extrapolating the spectrum of the radar initial range image, the observation matrix U is an N×N diagonal matrix, and all elements in the diagonal matrix are 1.

[0065] The process of obtaining the dictionary matrix includes:

[0066] According to the observation matrix, obtain the dictionary matrix ψ, and its expression is:

[0067] ψ = U·F;

[0068] where F is the inverse Fourier basis matrix;

[0069] The initial observation signal is the time-domain spectrum of the extended initial radar range image.

[0070] S1041. According to the obtained observation matrix, dictionary matrix, and initial observation signal, construct a range super-resolution compressive sensing model. The expression of the range super-resolution compressive sensing model is:

[0071] min(||WS f ||1), subject to ||s t -UFS f ||2 ≤ ξ;

[0072] where U is the observation matrix, F is the inverse Fourier basis matrix, s t is the initial observation signal, W is the target reweighting coefficient, ξ is the noise level, and S f is the range super-resolution result.

[0073] It should be noted that in the process of reweighting the super-resolution range image, while restoring the signals in the target area, the signals in the non-target area are suppressed. The weighting method is to apply a lower weight value to the target support area and a larger weight value to the non-target support area.

[0074] S1042. According to the range super-resolution compressive sensing model, construct a corresponding optimization function. Its expression is:

[0075]

[0076] To avoid the problem that S f is not differentiable at 0, the following approximation is made:

[0077] |S fn | = (|S fn | 2 + τ) 1 / 2 ;

[0078] where τ is a non-negative small component. Then the corresponding optimization function can be expressed as:

[0079]

[0080] where S fn is the value corresponding to the nth (1 ≤ n ≤ N) element in S f , τ is a non-negative small component, and N is the number of sampling points for super-resolution.

[0081] S105. According to the frequency-domain spectrum of the extended initial radar range image, obtain the target reweighting coefficient.

[0082] Specifically, the target reweighting weight coefficient includes the target initial reweighting weight coefficient, and the target initial reweighting weight coefficient is obtained through the following steps.

[0083] Based on the extended frequency-domain spectrum S of the radar initial range profile fe , the target initial reweighting weight coefficient W0 is obtained;

[0084] For the target region, the weight coefficient of the nth element in the target initial reweighting weight coefficient W0 is expressed as:

[0085]

[0086] where is the reciprocal of the nth element in the extended frequency-domain spectrum S of the radar initial range profile fe ;

[0087] For the non-target region, the weight coefficient of the nth element in the target initial reweighting weight coefficient W0 is expressed as:

[0088]

[0089] where ω is a constant, ω is a constant to prevent the phenomenon of false targets in the non-target region due to excessive weight values, and it is a positive number. The value of ω is 5% to 50% of the mean value of S fe ;

[0090] Based on the obtained target initial reweighting weight coefficient W0, in each iteration process, the corresponding target reweighting weight coefficient is obtained.

[0091] S106. Solve the optimization function according to the target reweighting weight coefficient and the distance super-resolution compressive sensing model to obtain the iterative solution function of the target reweighting.

[0092] Specifically, the iterative solution function of the target reweighting is obtained through the following steps.

[0093] S1061. According to the target reweighting weight coefficient and the distance super-resolution compressive sensing model, solve the derivative of the optimization function with respect to S f , and its expression is:

[0094]

[0095] where Λ(S f ) is a diagonal matrix, and its nth element is μ is the sparse constraint coefficient, U is the observation matrix, F is the inverse Fourier basis matrix, S f is the distance super-resolution result, and W is the target reweighting weight coefficient;

[0096] S1062. Set H(S f ) = 2(UF) H UF + μWΛ(S f ) is the approximate Hessian matrix for solving the optimization function. Then the iterative solution function of the target initial reweighting is expressed as:

[0097]

[0098] where H(S f ) is the approximate Hessian matrix for solving the optimization function.

[0099] S107. Use the method of reweighted l1 - norm minimization to solve the iterative solution function of the target reweighting, and then use the conjugate gradient algorithm to solve the complex equation to obtain the reconstructed super - resolution range image.

[0100] Specifically, the reconstructed super - resolution range image is obtained through the following steps.

[0101] S1071. Use the method of reweighted l1 - norm minimization to obtain the optimal solution when the iterative solution function of the target reweighting equals 0, and its expression is:

[0102]

[0103] where U is the observation matrix, F is the inverse Fourier basis matrix, S f is the range super - resolution result, W is the target reweighting coefficient, and s t is the initial observation signal;

[0104] S1072. Use the conjugate gradient algorithm to solve the complex equation of the reweighted l1 - norm minimization equation to obtain the reconstructed super - resolution range image is a complex number, and the reconstructed super - resolution range image retains the position and phase information.

[0105] It should be noted that in this embodiment, when using the conjugate gradient iterative solution to the optimization function, the phase characteristics at the target are retained to provide support for subsequent radar signal processing.

[0106] S108. Determine whether the reconstructed super - resolution range image meets the first condition. If it meets the first condition, obtain the super - resolution target distance value and the super - resolution range image; if it does not meet the first condition, modify the target reweighting coefficient and the iterative solution function of the target reweighting according to the reconstructed super - resolution range image, and obtain the reconstructed super - resolution range image again according to the modification result until the reconstructed super - resolution range image meets the first condition.

[0107] Specifically, in this embodiment, the first condition is:

[0108]

[0109] wherein, if the number of iterations is 0, then S f is S fe ; if the number of iterations is greater than 0, then S f is the reconstructed super-resolution range image obtained in the previous iteration, is a preset threshold, and its value is a relatively small threshold discrimination constant.

[0110] The process of modifying the target reweighting weight coefficient and the iterative solution function of the modified target reweighting is described as follows.

[0111] S1081. According to the frequency spectrum S f of the reconstructed range image, obtain the target reweighting weight coefficient W;

[0112] For the target region, the weight coefficient w n of the nth element in the target reweighting weight coefficient W is expressed as:

[0113]

[0114] wherein, w n is the reciprocal of the nth element in the frequency spectrum S f of the reconstructed range image;

[0115] For the non-target region, the weight coefficient w n of the nth element in the target reweighting weight coefficient W is expressed as:

[0116]

[0117] wherein, ω is a constant, and ω is a constant to prevent the phenomenon of false targets in the non-target region due to excessive weight values. ω is a positive number, and its value is 5% - 50% of the mean value of S f ;

[0118] S1082. According to the modified target reweighting weight coefficient, update the iterative solution function of the target reweighting, and obtain the reconstructed super-resolution range image again.

[0119] It should be noted that updating the iterative solution function of the target reweighting means updating the approximate Hessian matrix.

[0120] In summary, the distance super-resolution method based on the joint envelope and phase reweighted l1 norm optimization provided by the present invention can effectively utilize short observation data, break through the system response bandwidth limitation, and achieve high-resolution radar range images far below the Nyquist sampling law. At the same time, the present invention considers the influence of noise on distance super-resolution, reduces the influence of noise on the solution of the compressive sensing method through sparse constraint coefficients, and can perform high-performance distance super-resolution on targets under low signal-to-noise ratios. Finally, the present invention effectively retains the phase characteristics of the target after super-resolution, improves the distance resolution ability, and provides support for subsequent radar signal processing, having high application value.

[0121] In an optional embodiment of the present application, the effects of the above embodiments are verified through the following simulation experiments, specifically:

[0122] I. Determine the radar electromagnetic parameters, application scenario parameters, and radar snapshot number

[0123] In this embodiment, a radar with a center frequency f c of 10 GHz, a wavelength λ of 0.03 m, a bandwidth B of 200 MHz, a pulse width T P of 2 μs, and a range resolution of 0.75 m is taken as an example. The specific parameters are shown in Table 1. The radar ranging range ΔR in the scenario is 180 m, and the radar snapshot number is single snapshot or 100 snapshots.

[0124] Table 1 Radar basic parameters

[0125] Parameter Name Parameter Value Wavelength λ 0.03m Bandwidth B 200MHZ <![CDATA[Pulse width T P > 2μs Ranging Range ΔR 180m Ideal Distance Resolution 0.75m Number of Fast Snapshot of Radar Fast Snapshot 100

[0126] II. Calculate the initial range image

[0127] For the processing of echo data under single snapshot, please refer to Figures 3(a) to 3(b) As shown. Fig. 3(a) is a schematic diagram of a radar one-dimensional range image obtained under four times the bandwidth condition provided by an embodiment of the present invention, and Fig. 3(b) is a schematic diagram of the initial range image of the radar provided by an embodiment of the present invention; when using single snapshot data for distance super-resolution, the radar initial range image is directly calculated from the single snapshot data as shown in Fig. 3(b). Fig. 3(a) is the radar one-dimensional range image obtained under the condition of 4 times the bandwidth (B = 800 MHz) (ideal 4 times resolution, resolution of 0.1875 m), and it can be seen that there are 4 targets; Fig. 3(b) is the initial range image of the radar, and it can be seen that the middle two targets cannot be distinguished due to insufficient resolution, and only 3 targets can be seen.

[0128] For the processing of echo data under multiple snapshots, please refer to Figures 4(a) to 4(f)As shown in the figure, Fig. 4(a) is a schematic diagram of a two-dimensional radar spectrum obtained under the condition of 4 times bandwidth provided by an embodiment of the present invention. Fig. 4(b) is a schematic diagram of a one-dimensional range profile of the radar at the target obtained under the condition of 4 times bandwidth provided by an embodiment of the present invention. Fig. 4(c) is a schematic diagram of a two-dimensional radar spectrum provided by an embodiment of the present invention. Fig. 4(d) is a schematic diagram of an initial range profile of the radar at the target provided by an embodiment of the present invention; when using multi-snapshot data for range super-resolution, the multi-snapshot data is accumulated to obtain a two-dimensional spectrum, and the initial range profile at the target can be further obtained as shown in Fig. 4(d). Fig. 4(a) is a two-dimensional radar spectrum obtained under the condition of 4 times bandwidth (B = 800 MHz); Fig. 4(b) is a one-dimensional range profile of the radar at the target obtained under the condition of 4 times bandwidth (B = 800 MHz) (ideal 4 times resolution, resolution is 0.1875 m), and it can be seen that there are 4 targets; Fig. 4(d) is the initial range profile of the radar at the target, and it can be seen that the middle two targets cannot be resolved due to insufficient resolution, and only 3 targets can be seen.

[0129] III. Based on the reweighted l1-norm range super-resolution compressive sensing model, obtain the super-resolution range profile of envelope-phase joint reconstruction

[0130] According to the observation matrix U obtained after the range profile aperture expansion, the inverse Fourier basis matrix F, the initial observation signal s t , the dictionary matrix ψ, and the target reweighted weight coefficient W obtained according to the range profile spectrum, approximate the Hessian matrix H(S f ), and use iterative solution to calculate the super-resolution range profile of envelope-phase joint reconstruction

[0131]

[0132] According to the super-resolution range profile The position information of the target can be calculated based on the resolution ability of the cell where the target is located in the super-resolution range profile and the cells of the image after super-resolution.

[0133] IV. Simulation result analysis

[0134] In the single-snapshot scenario, the super-resolution range profile of envelope-phase joint reconstruction obtained according to formula (1) Compare the reconstructed super-resolution range profile with the range profile under the large-bandwidth Nyquist sampling theorem (ideal sampling under the condition of 4 times bandwidth), as Figure 3(c) and 3(d)As shown, Figure 3(c) is a schematic diagram of the super-resolution provided by an embodiment of the present invention, and Figure 3(d) is a comparison diagram of the ideal 4-fold resolution under the condition of large bandwidth and the 4-fold super-resolution image obtained under the condition of small bandwidth; Figure 3(c) is the calculated super-resolution range image, which can resolve the targets in the middle area, and 4 target positions can be found; Figure 3(d) is a comparison diagram of the ideal 4-fold resolution under the condition of large bandwidth and the 4-fold super-resolution image calculated under the condition of small bandwidth. In the multi-snapshot scenario, the super-resolution range image reconstructed by envelope-phase joint according to Equation (1) The reconstructed super-resolution range image is compared with the range image under the large-bandwidth Nyquist sampling theorem (ideal sampling under the condition of 4-fold bandwidth), as shown in Figures 4(e) and 4(f). Figure 4(e) is another schematic diagram of the super-resolution provided by an embodiment of the present invention, and Figure 4(f) is a comparison schematic diagram of the ideal 4-fold resolution under the condition of large bandwidth and the 4-fold super-resolution image obtained under the condition of small bandwidth; Figure 4(e) is the obtained super-resolution range image, which can resolve the targets in the middle area, and 4 target positions can be found.

[0135] In the presence of noise, the super-resolution range image reconstructed by envelope-phase joint is obtained using Equation (1), and the method used in the present invention is compared with the Burg extrapolation algorithm and the time-domain zero-padding interpolation algorithm. The comparison results Figures 5(a) to 5(i) are shown. Figure 5(a) is a comparison schematic diagram of the sparse reconstruction and the ideal 4-fold resolution range image at 20 dB provided by an embodiment of the present invention, Figure 5(b) is a comparison schematic diagram of the Burg extrapolation and the ideal 4-fold resolution range image at 20 dB provided by an embodiment of the present invention, Figure 5(c) is a comparison schematic diagram of the time-domain interpolation zero-padding and the ideal 4-fold resolution range image at 20 dB provided by an embodiment of the present invention, Figure 5(d) is a comparison schematic diagram of the sparse reconstruction and the ideal 4-fold resolution range image at 10 dB provided by an embodiment of the present invention, Figure 5(e) is a comparison schematic diagram of the Burg extrapolation and the ideal 4-fold resolution range image at 10 dB provided by an embodiment of the present invention, Figure 5(f) is a comparison schematic diagram of the time-domain interpolation zero-padding and the ideal 4-fold resolution range image at 10 dB provided by an embodiment of the present invention, Figure 5(g) is a comparison schematic diagram of the sparse reconstruction and the ideal 4-fold resolution range image at 5 dB provided by an embodiment of the present invention, Figure 5(h) is a comparison schematic diagram of the Burg extrapolation and the ideal 4-fold resolution range image at 5 dB provided by an embodiment of the present invention, and Figure 5(i) is a comparison schematic diagram of the time-domain interpolation zero-padding and the ideal 4-fold resolution range image at 5 dB provided by an embodiment of the present invention; Calculate the correlation coefficient between the spectrum after super-resolution of each distance and the ideal multi-fold resolution spectrum, expressed as:

[0136]

[0137] Among them, S and respectively represent the spectra of the ideal multi-resolution and the spectrum after super-resolution of the ideal low-resolution data. Both are complex data. The correlation coefficient represents the similarity between the super-resolution spectrum and the reference template, further indicating the similarity in amplitude and phase between the super-resolution spectrum and the reference template. The results are shown in Table 2.

[0138] Table 2 Comparison Table of Correlation Coefficients

[0139] 20dB 10dB 5dB Sparse Reconstruction (Method of the Present Invention) 98.9％ 98.6％ 98.1％ Burg Extrapolation 64.8％ 53.8％ 44.4％ Zero Padding Interpolation in Time Domain 35.1％ 33.8％ 30.4％

[0140] From the super-resolved image in Figure 5 and Table 2 when there is noise, it can be seen that when using Burg spectrum extrapolation for range image super-resolution, noise has a great impact on it. As the signal-to-noise ratio decreases, the estimation performance deteriorates, and some noise points will be introduced; for the time-domain interpolation and zero-padding algorithm, it can improve the target resolution ability in the case of high signal-to-noise ratio, but it cannot retain the phase characteristics, and as the signal-to-noise ratio decreases, more and more noise points are introduced, greatly affecting the radar detection performance. In contrast, the range super-resolution method based on envelope-phase joint reconstruction with reweighted l1-norm minimization proposed in the present invention can not only break through the system response bandwidth limitation, effectively utilize short observation data to achieve radar range image super-resolution, but also ensure the accuracy of the target position and amplitude after super-resolution, retain the phase characteristics at the target, and have good noise suppression ability.

[0141] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant is intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed. Without more limitations, an element defined by the statement "including one..." does not exclude the existence of another identical element in the article or device including the element. "Connection" or "connected" and other similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The orientation or positional relationship indicated by "up", "down", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention.

[0142] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc. means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0143] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A distance super-resolution method based on reweighted l1 norm optimization that combines envelope and phase, characterized in that Including: Obtain the initial radar range image; Perform inverse Fourier transform on the initial radar range image, and then perform range image aperture extension to obtain the extended initial radar range image time-domain spectrum and the extended initial radar range image frequency-domain spectrum; Obtain the sparse constraint coefficient according to the extended initial radar range image frequency-domain spectrum; Construct a range super-resolution compressive sensing model based on the obtained observation matrix, dictionary matrix, and initial observation signal, and combine the sparse constraint coefficient to construct an optimization function corresponding to the range super-resolution compression model; Obtain the target reweighting weight coefficient according to the extended initial radar range image frequency-domain spectrum; Solve the optimization function according to the target reweighting weight coefficient and the range super-resolution compressive sensing model to obtain an iterative solution function of target reweighting; Solve the iterative solution function of target reweighting using the method of minimizing the reweighted l1 norm, and then use the conjugate gradient algorithm to solve the complex equation to obtain the reconstructed super-resolution range image; Judge whether the reconstructed super-resolution range image meets the first condition. If it meets the first condition, obtain the super-resolution target range value and the super-resolution range image; If it does not meet the first condition, modify the target reweighting weight coefficient and the iterative solution function of target reweighting according to the reconstructed super-resolution range image, and obtain the reconstructed super-resolution range image again according to the modification result until the reconstructed super-resolution range image meets the first condition.

2. The distance super-resolution method optimized by the reweighted l1 norm of the combined envelope and phase according to claim 1, characterized in that The obtaining of the initial radar range image includes: When performing range super-resolution using single snapshot data, the initial radar range image is directly obtained based on the single snapshot data When performing range super-resolution using multi-snapshot data, an initial radar range image is accumulated based on the multi-snapshot data Among them, the single-snapshot data and the multi-snapshot data are both radar snapshot data.

3. The distance super-resolution method optimized by the reweighted l1 norm of the combined envelope and phase according to claim 1, characterized in that The performing of inverse Fourier transform on the initial radar range image and then performing range image aperture extension to obtain the extended initial radar range image time-domain spectrum and the extended initial radar range image frequency-domain spectrum includes: Perform inverse Fourier transform on the initial radar range image to obtain the initial radar range image time-domain spectrum; Determine the number of sampling points N for super-resolution according to the required super-resolution multiple of the radar scene target, and perform zero-padding on the initial radar range profile or range image aperture expansion by spectral extrapolation to obtain the extended time-domain spectrum S of the initial radar range profile. te and the extended frequency-domain spectrum S of the initial radar range profile fe ; where the number of extended points is the same as the number of super-resolution sampling points.

4. The distance super-resolution method optimized by the reweighted l1 norm for jointly enveloping and phase according to claim 1, characterized in that, The obtaining of the sparse constraint coefficient according to the extended initial radar range image frequency-domain spectrum includes: Set the frequency spectrum S of the initial range profile of the expanded radar fe Subject to the same distribution, obtain the frequency spectrum S of the initial range profile of the expanded radar fe The same Laplacian factor γ for each point in it, and its expression is: γ = N / ||S fe ||1; Where, ||·||1 is the l1 norm, and N is the number of sampling points for super-resolution; Extract the noise unit S from the initial radar range profile N , vectorize the noise unit, and the vectorized noise unit is denoted as S no ; Using the vectorized noise unit S no Estimate the noise variance σ 2 , and its expression is: σ 2 = E{(s no ) H s no}; where (s no ) H is the noise unit S N conjugate transpose; According to the Laplacian factor γ and the noise variance σ 2 , the sparse constraint coefficient μ is obtained, and its expression is as follows: μ = σ 2 γ.

5. The distance super-resolution method optimized by reweighted l1 norm for joint envelope and phase according to claim 1, characterized in that The expression of the range super-resolution compressive sensing model is: min(||WS f ||1), subject to ||s t -UFS f ||2 ≤ ξ; where U is the observation matrix, F is the inverse Fourier basis matrix, s t is the initial observation signal, W is the target reweighting weight coefficient, ξ is the noise level, and S f is the range super-resolution result; The expression of the optimization function is: Simplify the optimization function to obtain: Among them, S fn is the value corresponding to the nth (1 ≤ n ≤ N) element in S f , τ is a non-negative small component, and N is the number of sampling points for super-resolution.

6. The distance super-resolution method optimized by the reweighted l1 norm of the combined envelope and phase according to claim 1, characterized in that, The target reweighting weight coefficient includes the target initial reweighting weight coefficient; According to the frequency domain spectrum S of the extended initial radar range profile fe , the initial reweighting weight coefficient W0 of the target is obtained; For the target region, the weight coefficient of the nth element in the target initial reweighting weight coefficient W0 is expressed as: Among them, is the reciprocal of the nth element in the frequency domain spectrum S of the initial radar range profile after expansion; fe in the For the non-target region, the weight coefficient of the nth element in the target initial reweighting weight coefficient W0 is expressed as: Where, ω is a constant.

7. The distance super-resolution method optimized by the reweighted l1 norm for jointly enveloping and phase according to claim 1, characterized in that, The solving of the optimization function according to the target reweighting weight coefficient and the range super-resolution compressive sensing model to obtain an iterative solution function of target reweighting includes: Solve the derivative of the optimization function with respect to S f The expression is as follows: where, Λ(S f ) is a diagonal matrix, and its nth element is μ is the sparse constraint coefficient, U is the observation matrix, F is the inverse Fourier basis matrix, S f is the distance super-resolution result, and W is the target reweighting coefficient; Set H(S f ) = 2(UF) H UF + μWΛ(S f ) is the approximate Hessian matrix for solving the optimization function, then the target initial reweighted iterative solution function is expressed as: Among them, H(S f ) is an approximate Hessian matrix for solving the optimization function.

8. The distance super-resolution method optimized by the reweighted l1 norm of the combined envelope and phase according to claim 1, characterized in that The solving of the iterative solution function of target reweighting using the method of minimizing the reweighted l1 norm and then using the conjugate gradient algorithm to solve the complex equation to obtain the reconstructed super-resolution range image includes: Using the method of reweighted l1 norm minimization, an iterative solution function for the target reweighting is obtained The optimal solution when it is equal to 0, and its expression is: where U is the observation matrix, F is the inverse Fourier basis matrix, S f is the distance super-resolution result, W is the target reweighting weight coefficient, s t is the initial observation signal; Solve the complex equation of the reweighted l1-norm minimization equation using the conjugate gradient algorithm to obtain the reconstructed super-resolution range image The reconstructed super-resolution range image Retain the position and phase information.

9. The distance super-resolution method optimized by the reweighted l1 norm of the combined envelope and phase according to claim 1, characterized in that, The first condition is: Among them, if the number of iterations is 0, then S f is S fe ; if the number of iterations is greater than 0, then S f is the reconstructed super-resolution range image obtained in the previous iteration, is a preset threshold, is the super-resolution range image.

10. The distance super-resolution method optimized by reweighted l1 norm for joint envelope and phase according to claim 1, characterized in that The process of modifying the target reweighting weight coefficient and the iterative solution function of target reweighting according to the reconstructed super-resolution range image includes: According to the frequency spectrum S of the reconstructed range profile f , the target reweighting weight coefficient W is obtained; For the target region, the weight coefficient w of the n-th element in the target reweighting weight coefficient W n has the following expression: where w n is the reciprocal of the n-th element in the range profile frequency spectrum S f after reconstruction; For the non-target region, the weight coefficient w of the nth element in the target reweighting weight coefficient W n has the following expression: Where, ω is a constant; Update the iterative solution function of target reweighting according to the modified target reweighting weight coefficient, and obtain the reconstructed super-resolution range image again.

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