Intersecting dual-channel down-sampling method and system based on dictionary matrix rip criterion

Abstract

The application relates to a downsampling method and system, in particular to a mutual prime double-channel downsampling method and system based on a dictionary matrix RIP criterion. The application overcomes the problems of poor sampling accuracy and difficult hardware implementation of an existing random downsampling method and the problems of high data processing cost and resource waste caused by a deterministic downsampling scheme. Based on the RIP performance of a dictionary matrix, the application determines an optimal mutual prime double-channel combination for downsampling; and the optimal mutual prime double-channel combination is used to downsample a scene signal. Uniform sampling is performed in each channel, the hardware is easy to implement, the system error is small, and the sampling accuracy is easy to guarantee, compared with a random sampling method; and compared with a deterministic downsampling method, the application selects an optimal mutual prime double-channel combination for down sampling a signal based on a compressed sensing dictionary matrix RIP criterion, and sampling data is reduced to a certain extent, and the hardware resource occupation is small.

Description

Technical Field

[0001] This invention relates to a downsampling method and system, specifically a coprime dual-channel downsampling method and system based on the dictionary matrix RIP criterion. Background Technology

[0002] In 1982, Nyquist proposed the Nyquist sampling theorem, which states that to achieve accurate reconstruction of the original signal, the sampling frequency must be at least twice the highest frequency of the original signal. The Nyquist sampling theorem can convert analog signals into digital signals, and its main applications include communications, radar, image compression, and video acquisition. Due to the advent of this theorem, digital signals are widely used in daily life. However, with the rapid development of the internet and big data, various signals are growing exponentially, placing increasingly higher demands on digital signal processing. The strict limitations of the traditional Nyquist sampling theorem have become a bottleneck in digital signal processing. In many scenarios, such as accurate radar target ranging, satellite remote sensing image fusion and reconstruction, and medical image processing, the frequencies are typically high. Applying the Nyquist sampling theorem would result in excessively high sampling rates, placing many demands on equipment hardware and causing serious problems in acquisition, processing, and transmission, severely hindering the development of these applications.

[0003] The compressed sensing theory proposed by Candes, Romberg, Tao and Donoho in 2006 ([1] E. Candès, J. Romberg, and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Information Theory, 2006, 52(2): 489–509. [2] D. Donoho, Compressed sensing, IEEE Trans. Information Theory, 2006, 52(4): 5406–5425.) provides a new sampling and reconstruction method, breaks the limitations of the traditional sampling theorem, and provides a method to recover the original signal from a small number of non-adaptive linear measurements. It can achieve low-speed sampling and high-probability accurate reconstruction of the received signal at a rate lower than the Nyquist sampling rate. Signal downsampling based on compressed sensing has played an important role in many fields, such as accurate ranging of radar targets, fusion and reconstruction of satellite remote sensing images, screening and classification of gene expression data, medical image processing and face recognition. It effectively reduces the pressure of front-end ADC sampling and saves the cost of back-end transmission and processing of massive amounts of data, and has extremely important research value and significance.

[0004] Currently, the downsampling methods commonly used in compressed sensing are mainly divided into two types: one is the random downsampling method, which can reconstruct the original signal well, but the sampling accuracy is low and the hardware design is difficult, making it difficult to implement compressed sensing in engineering; the other is the deterministic downsampling scheme, in which the sampling position is determined once the system and construction parameters are determined. Although this sampling scheme is easier to implement than the random downsampling method, there may be a large number of useless data points, the data processing cost is high, and system resources are wasted.

[0005] To overcome the aforementioned problems of current downsampling methods, Mao Ying et al. proposed a method for coprime compression sampling of compressed sensing radar echo signals based on chaotic digital filters in their published paper "Coprime Compression Sampling of Compressed Sensing Radar Based on Chaotic Filters" (Mao Ying, Niu Xu. Coprime Compression Sampling of Compressed Sensing Radar Based on Chaotic Filters [J]. Electronic Measurement Technology, 2017, 40(10): 211-215.). Although the downsampling matrix based on chaotic digital filters can avoid the hardware design difficulties of the observation matrix in traditional random downsampling methods, making it difficult to implement compressed sensing in engineering, this method still uses a deterministic coprime sampling function to sample within the channel, which is still a deterministic downsampling scheme. During the acquisition process, there will still be a large number of useless data points, resulting in high post-processing costs. In addition, the method uses a coprime sampling function to achieve coprime sampling of the signal within the channel, resulting in low sampling accuracy, which will greatly affect the sparse reconstruction performance. Summary of the Invention

[0006] To overcome the problems of poor sampling accuracy and difficult hardware implementation in existing random downsampling methods, and the high data processing cost and resource waste in deterministic downsampling schemes, this invention proposes a coprime dual-channel downsampling method and system based on the dictionary matrix RIP criterion. This method achieves sparse reconstruction using fewer measurements while effectively utilizing useful information from the scene compressed sensing model. It evaluates coprime dual-channel sampling combinations, selects the optimal combination, and implements coprime sampling using this optimal combination, resulting in high sampling accuracy and good sparse reconstruction performance.

[0007] The technical solution of this invention is to provide a coprime dual-channel downsampling method based on the dictionary matrix RIP criterion, which is characterized by including the following steps:

[0008] Step 1: Based on the RIP criterion of the compressed sensing dictionary matrix, select the optimal downsampled coprime dual-channel combination;

[0009] Calculate the RIP performance corresponding to the dictionary matrix of multiple downsampled coprime dual-channel combinations; based on the RIP performance of the dictionary matrix, determine the optimal downsampled coprime dual-channel combination.

[0010] Step 2: Based on the optimal downsampling coprime dual-channel combination, downsample the scene signal.

[0011] Furthermore, step 1 specifically includes:

[0012] Step 1.1: Determine the dictionary matrix Ψ for each group of downsampled coprime dual-channel combinations in the current application scenario. 12 ;

[0013] Ψ 12 =U12 Φ

[0014] Among them, U 12 Φ is the observation matrix for each set of downsampled coprime dual-channel combinations, and Φ is the basis matrix corresponding to the current application scenario.

[0015] Step 1.2: Dictionary matrix Ψ based on each group of downsampled coprime dual-channel combinations 12 Determine the partial dictionary matrix for each downsampled coprime dual-channel combination related to the number and location of strong scattering points in the scene. This refers to the positions of k strong scattering points in the sparse vector θ corresponding to the target signal in the scene, corresponding to Ψ. 12 A matrix composed of columns in the matrix;

[0016] Step 1.3: Calculate the partial dictionary matrix for each downsampled coprime dual-channel combination under the condition that the number of strong scattering points is the same but their locations are different. The corresponding limiting constant mean;

[0017] Step 1.4: Compare the partial dictionary matrices of various downsampled coprime dual-channel combinations under the condition that the number of strong scattering points is the same but their locations are different. The mean of the corresponding restricted equidistant constants is selected, with the minimum restricted equidistant constant mean being chosen.

[0018] Step 1.5: Determine whether the mean of the minimum limiting equidistant constants satisfies the RIP criterion. If it does, then the downsampled coprime dual-channel combination corresponding to the mean of the minimum limiting equidistant constants is taken as the optimal downsampled coprime dual-channel combination for the number of strong scattering points. If it does not satisfy the requirements, then it is necessary to go back and modify the downsampled coprime dual-channel combination, and repeat the process of Step 1.1 and Step 1.4 until the requirements are met.

[0019] Further, in step 1.1, the observation matrix U of each downsampled coprime dual-channel combination is determined by the following method. 12 :

[0020] Calculate the observation matrix for each channel in each downsampled coprime dual-channel combination. Arrange each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position to obtain the observation matrix U formed by each downsampled coprime dual-channel combination. 12 .

[0021] Furthermore, if the two channels in the downsampled coprime dual-channel combination have the same sampling time, then when arranging each row of the observation matrix of the two channels in the same matrix according to the sampling order and sampling position, only the row of the observation matrix corresponding to either channel at that sampling time is retained.

[0022] Further, in step 1.1, the observation matrix of each channel in each downsampled coprime dual-channel combination is determined by the following method:

[0023] First, the Nyquist sampling theorem observation matrix U and the basis matrix Φ corresponding to the scene are calculated based on the number of sampling points N at the Nyquist sampling rate.

[0024] Then, based on the sampling time of each channel in each downsampled coprime dual-channel combination, the corresponding row in the Nyquist sampling theorem observation matrix U corresponding to the sampling time is retained to obtain the observation matrix of each channel in each downsampled coprime dual-channel combination.

[0025] Furthermore, step 1.2 specifically includes the following steps:

[0026] Step 1.21: Determine the number and location of strong scattering points in the scene;

[0027] Based on the requirements of the scenario, determine the maximum number K of strong scattering points in the scenario; among the K strong scattering points, select k strong scattering points as a strong scattering point group, where k is traversed from 1 to K, and K is an integer greater than 1;

[0028] For each group of strong scattering points, randomly select its position in the scene; for each group of strong scattering points, determine M random positions, where M is an integer greater than 1;

[0029] Step 1.22: Based on the number and location of strong scattering points in the scene, obtain a partial dictionary matrix for each set of downsampled coprime dual-channel combinations;

[0030] Based on the number of strong scattering points k in each group of strong scattering points determined in step 1.21 and the position of each strong scattering point in the scene, extract the downsampled coprime dual-channel combination dictionary matrix Ψ for each group. 12 In the corresponding region, obtain multiple partial dictionary matrices for each group of downsampled coprime dual-channel combinations.

[0031] Furthermore, step 1.3 specifically includes the following steps:

[0032] Step 1.31, Calculation The eigenvalues ​​are used to determine the range of eigenvalues;

[0033] Step 1.32: Based on the range of eigenvalues ​​[1-δ] k ,1+δ k Determine the limiting equidistant constant δ corresponding to each part of the dictionary matrix of each downsampled coprime dual-channel combination. k ;

[0034] Step 1.33: Calculate the mean value of the constraint equidistant constants corresponding to the dictionary matrix of each downsampled coprime dual-channel combination under the condition that the number of strong scattering points is the same but the positions are different.

[0035] The present invention also provides a coprime dual-channel downsampling system based on the dictionary matrix RIP criterion, comprising a processor and a memory, wherein the memory stores a computer program, and the special feature is that when the computer program is executed by the processor, it implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion described above.

[0036] The present invention also provides a computer-readable storage medium storing a computer-readable program thereon, wherein the computer-readable program, when executed by a processor, implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion described above.

[0037] The beneficial effects of this invention are:

[0038] 1. This invention presents a coprime dual-channel downsampling method based on the dictionary matrix RIP criterion, achieving signal sampling under conditions far below the Nyquist sampling law, significantly reducing the amount of sampled data. Uniform sampling within each channel, compared to random sampling methods, is easier to implement in hardware and has smaller system errors, making it easier to ensure sampling accuracy. Compared to deterministic downsampling methods, this invention uses the RIP criterion based on the compressed sensing dictionary matrix to select the optimal coprime dual-channel combination for downsampling the signal, reducing the amount of sampled data to a certain extent and requiring less hardware resources.

[0039] 2. Before signal downsampling, this invention effectively utilizes useful information in the scene compressed sensing model. It analyzes the signal sparse recovery performance using the RIP performance of the compressed sensing dictionary matrix corresponding to the downsampled coprime dual-channel combination. Based on the analysis results, it selects an optimal downsampled coprime dual-channel combination from the available downsampled coprime dual-channel combinations for system downsampling, ensuring the rationality of the optimal downsampled coprime channel selection and further improving the sampling accuracy. Attached Figure Description

[0040] Figure 1 This is a flowchart of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion of this invention;

[0041] Figure 2 In this invention Statistical average plot of maximum and minimum eigenvalues;

[0042] Figure 3 δ in this invention k Statistical average chart;

[0043] Figure 4aThis invention utilizes downsampling coprime dual-channel combination 1 for sampling to obtain a comparison image of the target distance information and the target distance information under ideal sampling.

[0044] Figure 4b This invention utilizes a downsampling coprime dual-channel combination 2 for sampling to obtain a comparison image of the target distance information and the target distance information under ideal sampling.

[0045] Figure 4c This invention utilizes a downsampling coprime dual-channel combination 3 for sampling to obtain a comparison image of the target distance information and the target distance information under ideal sampling.

[0046] Figure 4d This invention utilizes a downsampling coprime dual-channel combination 4 for sampling to obtain a comparison image of the target distance information and the target distance information under ideal sampling.

[0047] Figure 4e This invention utilizes a downsampling coprime dual-channel combination 5 for sampling to obtain a comparison image of the target distance information and the target distance information under ideal sampling. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings.

[0049] Compressed sensing breaks the limitations of traditional sampling theorems, providing a method to recover the original signal from a small number of non-adaptive linear measurements. It enables low-speed sampling of received signals at rates lower than the Nyquist sampling rate and high-probability, accurate reconstruction. Signal undersampling based on compressed sensing has played a crucial role in various fields, including accurate ranging of radar targets, satellite remote sensing image fusion and reconstruction, screening and classification of gene expression data, medical image processing, and face recognition. It effectively reduces the sampling pressure on the front-end ADC and saves costs associated with transmitting and processing massive amounts of data at the back end, making it extremely valuable and significant for research. Among existing downsampling techniques, random downsampling methods can reconstruct the original signal relatively well, but their sampling accuracy is poor and hardware implementation is difficult. In deterministic downsampling methods, once the system and construction parameters are determined, the sampling location is also determined. This sampling scheme is easy to implement, but it may contain a large number of useless data points, significantly wasting system resources. To address the aforementioned issues, this invention presents a method for selecting coprime dual channels based on the RIP criterion of the compressed sensing dictionary matrix. This method achieves signal downsampling with high sampling accuracy and low data volume. Furthermore, before downsampling, the method utilizes the RIP criterion to rationally select the optimal downsampled coprime dual channels, ensuring subsequent sparse recovery performance and saving resources and time, thus possessing high application value.

[0050] from Figure 1 As can be seen, the present invention mainly includes the following steps:

[0051] Step 1. Input application scenario parameters and downsampling coprime dual-channel combination;

[0052] This includes basic parameters for the application scenario. For example, in a lidar ranging scenario, the basic parameters should include the lidar's carrier frequency f. c Wavelength λ, frequency modulation bandwidth B1, frequency modulation period T p Ranging range ΔR, difference frequency signal bandwidth B2, and Nyquist sampling rate F s In communication scenarios, the basic parameters should include the Nyquist sampling rate F. s Frame length, etc.; multiple selectable downsampling coprime dual-channel combinations; downsampling coprime dual-channel ADC combination refers to using a dual-channel ADC for signal sampling, where the sampling intervals of the two channels are uniform and coprime, performing coprime sampling on the signal, with the sampling intervals of the two ADC channels being U / F respectively. s and V / F s U and V are coprime pairs, and the sampling rates of the corresponding two channels are F and F, respectively. s / U and F s / V.

[0053] Step 2. Establish a scene compression sensing model;

[0054] For different application scenarios, corresponding compressed sensing models are established, which can be represented as:

[0055] min(||θ||1),subjuect toΦθ=s

[0056] Where s is the observable target signal, θ is the sparse vector corresponding to the target signal in the scene (with very few large-value elements), and Φ is the basis matrix corresponding to the scene.

[0057] Step 3. Obtain the observation matrix composed of each group of downsampled coprime dual-channel combinations;

[0058] Calculate the observation matrix for each channel in each downsampled coprime dual-channel combination. Arrange the observation matrices of the two channels together according to the sampling order and sampling position to obtain the observation matrix U formed by each downsampled coprime dual-channel combination. 12 .

[0059] In lidar ranging scenarios, the following process can be used to determine the observation matrix U formed by each set of downsampled coprime dual-channel combinations. 12 :

[0060] First, based on the frequency modulation period T of the lidar p The Nyquist sampling rate F of the lidar sThe number of sampling points N under the Nyquist sampling rate is obtained, and the Nyquist sampling theorem observation matrix U and the basis matrix Φ corresponding to the scene are calculated based on the number of sampling points N under the Nyquist sampling rate.

[0061] Then, based on the frequency modulation period T of the lidar p The sampling rate of each downsampled coprime dual-channel combination is used to obtain the number of sampling points for each downsampled coprime dual-channel combination. Based on the sampling time and the order of the sampling time for each downsampled coprime dual-channel combination, the corresponding rows in the observation matrix U corresponding to the sampling time are retained to obtain the observation matrix U1 of the first channel in each downsampled coprime dual-channel combination, with a matrix size of M1×N, and the observation matrix U2 of the second channel, with a matrix size of M2×N. M1 and M2 are the number of sampling points for the first channel and the second channel, respectively.

[0062] Finally, each row of observation matrices U1 and U2 is arranged in the observation matrix U according to the sampling order and position. 12 Middle,U 12 This is the observation matrix for each set of downsampled coprime dual-channel combinations. If two channels have the same sampling time, only the row of the observation matrix corresponding to one of the channels at that sampling time is retained.

[0063] In communication scenarios, it is necessary to determine the frame length and Nyquist sampling rate F. s Obtain the number of sampling points N at the Nyquist sampling rate, and calculate the Nyquist sampling theorem observation matrix U and the basis matrix Φ corresponding to the scene based on the number of sampling points N at the Nyquist sampling rate; the subsequent steps are consistent with the steps for the lidar ranging scene.

[0064] Step 4. Calculate the dictionary matrix for each group of downsampled coprime dual-channel combinations;

[0065] Based on the basis matrix Φ corresponding to the scene obtained in step 3 and the observation matrix U corresponding to each group of downsampled coprime dual-channel combinations... 12 Calculate the dictionary matrix Ψ for each group of downsampled coprime dual-channel combinations. 12 =U 12 Φ.

[0066] Step 5. Determine the number and location of strong scattering points in the scene;

[0067] Based on the scenario requirements, determine the maximum number K of strong scattering points in the scenario (determined according to requirements and specific application scenarios); among the K strong scattering points, select k strong scattering points as a strong scattering point group, where k iterates from 1 to K; K is an integer greater than 1.

[0068] For each group of strong scattering points, its position in the scene is randomly selected; for each group of strong scattering points, M random positions can be determined according to the scene, and the position can be represented by the sparse vector θ corresponding to the target signal in the scene, where M is an integer greater than 1.

[0069] Step 6. Based on the number and location of strong scattering points in the scene, obtain a partial dictionary matrix for each set of downsampled coprime dual-channel combinations;

[0070] Based on the number of strong scattering points k in each group of strong scattering points determined in step 5 and the position of each strong scattering point in the scene, extract the downsampled coprime dual-channel combined dictionary matrix Ψ for each group. 12 In the corresponding region, obtain multiple partial dictionary matrices for each group of downsampled coprime dual-channel combinations. This refers to the positions of k strong scattering points in the sparse vector θ corresponding to the target signal in the scene, corresponding to Ψ. 12 A matrix composed of columns in the matrix.

[0071] Step 7. Calculate the constraint equidistant constants corresponding to each part of the dictionary matrix of each downsampled coprime dual-channel combination;

[0072] 7a. Using a partial dictionary matrix calculate eigenvalues;

[0073] 7b. Based on the range of eigenvalues ​​[1-δ] k ,1+δ k Determine the limiting equidistant constant δ corresponding to each part of the dictionary matrix of each downsampled coprime dual-channel combination. k .

[0074] Step 8. Calculate the mean value of the constrained equidistant constants corresponding to the dictionary matrix of each downsampled coprime dual-channel combination under the condition that the number of strong scattering points is the same but the locations are different, that is, under the same group of strong scattering points but different locations;

[0075] For the same group of strong scattering points, the limiting equidistant constant δ at M random locations k Taking the average, we obtain the constrained equidistant constants corresponding to the partial dictionary matrices of downsampled coprime dual-channel combinations at different locations, under the condition of the same number of strong scattering points.

[0076] Step 9. Obtain the constraint interval constant that minimizes the mean;

[0077] According to step 8, under the condition of the same number of strong scattering points (the same group of strong scattering points), the mean value of the constraint equidistant constant corresponding to the dictionary matrix of each downsampling coprime dual-channel combination can be obtained, and the constraint equidistant constant with the smallest mean value is selected.

[0078] Step 10. Determine if the RIP criteria are met;

[0079] Determine whether the minimum limiting equidistant constant satisfies the RIP criterion. If it does, then the downsampled coprime dual-channel combination corresponding to the minimum limiting equidistant constant is taken as the optimal downsampled coprime dual-channel combination for that group of strong scattering points. If it does not satisfy the requirement, then it is necessary to go back and modify the downsampled coprime dual-channel combination scheme, and repeat the process of steps 2 and 9 until the requirement is met.

[0080] The present invention also discloses a coprime dual-channel downsampling system based on the dictionary matrix RIP criterion, comprising a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion.

[0081] This invention discloses a computer-readable storage medium storing a computer-readable program that, when executed by a processor, implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion described above. In some possible embodiments, this invention can also be implemented as a program product comprising program code that, when run on a terminal device, causes the terminal device to perform the steps described in the method section of this specification according to various exemplary embodiments of the invention. The program product for implementing the above method may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of this invention is not limited thereto. In this invention, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The program product can employ any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0082] The following simulation experiments verify the beneficial effects of the present invention:

[0083] I. Determine application scenario parameters and downsampling coprime dual-channel combination

[0084] In this embodiment, a laser ranging radar is used as an example, wherein the laser wavelength λ is 10.6 μm, the frequency modulation bandwidth B1 is 3 GHz, the ranging range ΔR is 100 m, and the frequency modulation period T is... p The difference frequency signal bandwidth is 1μs, B2 = 2B1 × ΔR / (cT) p The frequency is 2GHz, and the Nyquist sampling rate is F. s It is 1.25 times the bandwidth of the difference frequency signal. The specific parameters are shown in Table 1. There are 5 selectable downsampling coprime dual-channel combinations. The sampling rate of each downsampling coprime dual-channel combination is shown in Table 2.

[0085] Table 1 Basic parameters of lidar

[0086]

[0087] Table 2 Downsampling Coprime Dual-Channel Combination

[0088]

[0089] II. Establishing a Scene Compressed Sensing Model

[0090] For lidar ranging scenarios, a compressed sensing model corresponding to the lidar ranging scenario is established, as shown in formula (1):

[0091] min(||θ||1),subject toΦθ=s (1)

[0092] In a lidar ranging scenario, s is the observable time-domain difference frequency signal, Φ is the inverse Fourier basis matrix, and θ is the difference frequency signal spectrum, which is a sparse vector. The distance to the target in the scenario can be obtained from the difference frequency signal spectrum.

[0093] 3. Calculate the RIP performance of the dictionary matrix corresponding to different downsampling coprime dual-channel combinations in this scenario, and determine the optimal downsampling coprime dual-channel combination in this scenario.

[0094] According to the frequency modulation period T of the lidar p The Nyquist sampling rate F of the lidar s Given the sampling rate of each coprime dual-channel pair, calculate the dictionary matrix Ψ corresponding to each coprime dual-channel pair. 12 Based on the scenario requirements, the maximum number of strong scattering points K in the scenario is determined to be 100. Under each combination of downsampled coprime dual channels, the number of strong scattering points k iterates from 1 to 100. For each k, M random trials are performed. If M is 1000, then there are 1000 random locations. The maximum and minimum eigenvalues ​​are statistically averaged to obtain the following result: Figure 2 As shown, the limiting equidistant constant δ for each group of downsampled coprime dual channels is calculated simultaneously.k , for δ k Take the average value to get like Figure 3 As shown in Table 3, the specific results are as follows.

[0095] Table 3. RIP performance of coprime dual-channel combinations

[0096]

[0097] Note:

[0098] The average value corresponds to the strong scattering points 1 to 100. Find the average

[0099] δ k The closer to 0, the better the RIP performance of the dictionary matrix. Choose the matrix closest to 0. The corresponding coprime two-channel combinations are considered the optimal coprime two-channel combinations, as shown in Table 3 and... Figure 3 It can be seen from all of them that combination 2 Since the average value is minimized, combination 2 is the optimal coprime dual-channel combination in the entire scenario, thus yielding the optimal sampling rate F for the first channel of the coprime dual-channel combination. s / 17, Second channel sampling rate F s / 18; If the number of targets in the scene is determined, it should be based on the number of targets corresponding to... Select coprime dual channels.

[0100] IV. Simulation Results and Analysis

[0101] Using the five downsampled coprime dual-channel combinations in Table 2, downsampling was performed in the lidar ranging scenario. The compressed sensing model under downsampling was then sparsely solved to obtain the difference frequency signal spectrum reconstructed from each coprime dual-channel combination. This difference frequency signal spectrum was then used to obtain the target distance information, which was compared with the target distance information obtained from the difference frequency signal spectrum under the Nyquist sampling theorem (ideal sampling). Figures 4a-4e As shown. From Figures 4a-4e It can be seen that the optimal coprime dual-channel downsampling combination selected by the proposed coprime dual-channel downsampling method based on the compressed sensing dictionary matrix RIP criterion can ensure the subsequent sparse recovery performance while achieving high sampling accuracy and low data volume signal downsampling. It can accurately reconstruct the distance between the target and the radar, and at the same time ensure the accuracy of the target amplitude.

Claims

1. A coprime dual-channel downsampling method based on the dictionary matrix RIP criterion, characterized in that, Includes the following steps: Step 1: Based on the RIP criterion of the compressed sensing dictionary matrix, select the optimal downsampling coprime dual-channel combination; the coprime dual-channel combination refers to using a dual-channel ADC for signal sampling, where the sampling intervals of the two channels are uniform and coprime. Step 1.1: Determine the dictionary matrix for each set of downsampled coprime dual-channel combinations in the current application scenario. ; ； in, For each group of downsampled coprime dual-channel combinations, the observation matrix is... This is the basis matrix corresponding to the current application scenario; Step 1.2: Dictionary matrix based on each group of downsampled coprime dual-channel combinations Determine a partial dictionary matrix for each downsampled coprime dual-channel combination, which is related to the number and location of strong scattering points in the scene. ; It means The sparse vector corresponding to the target signal at each strong scattering point in the scene. The position in the middle corresponds A matrix composed of columns in the matrix; Step 1.3: Calculate the partial dictionary matrix for each downsampled coprime dual-channel combination under the condition that the number of strong scattering points is the same but their locations are different. The corresponding limiting constant mean; Step 1.4: Compare the partial dictionary matrices of various downsampled coprime dual-channel combinations under the condition that the number of strong scattering points is the same but their locations are different. The mean of the corresponding restricted equidistant constants is selected, with the minimum restricted equidistant constant mean being chosen. Step 1.5: Determine whether the mean of the minimum limiting equidistant constants meets the RIP criterion. If it does, then the downsampled coprime dual-channel combination corresponding to the mean of the minimum limiting equidistant constants is taken as the optimal downsampled coprime dual-channel combination for the number of strong scattering points. If it does not meet the requirements, then it is necessary to go back and modify the downsampled coprime dual-channel combination, and repeat the process from Step 1.1 to Step 1.4 until the requirements are met. Step 2: Based on the optimal downsampling coprime dual-channel combination, downsample the scene signal.

2. The coprime dual-channel downsampling method based on the dictionary matrix RIP criterion according to claim 1, characterized in that, In step 1.1, the observation matrix for each downsampled coprime dual-channel combination is determined through the following process. : Calculate the observation matrix for each channel in each downsampled coprime dual-channel combination. Arrange each row of the observation matrices of the two channels in the same matrix according to the sampling order and sampling position to obtain the observation matrix formed by each downsampled coprime dual-channel combination. .

3. The coprime dual-channel downsampling method based on the dictionary matrix RIP criterion according to claim 2, characterized in that: If two channels in a downsampled coprime dual-channel combination have the same sampling time, then when arranging each row of the observation matrix of the two channels in the same matrix according to the sampling order and sampling position, only the row of the observation matrix corresponding to either channel at that sampling time is retained.

4. The coprime dual-channel downsampling method based on the dictionary matrix RIP criterion according to claim 3, characterized in that, In step 1.1, the observation matrix for each channel in each downsampled coprime dual-channel combination is determined through the following process: First, the number of sampling points based on the Nyquist sampling rate. Calculate the Nyquist sampling theorem observation matrix and the basis matrix corresponding to the scene ; Then, based on the sampling time of each channel in each downsampled coprime dual-channel combination, the sampling time is mapped to the Nyquist sampling theorem observation matrix. The corresponding rows are retained to obtain the observation matrix of each channel in each downsampled coprime dual-channel combination.

5. The coprime dual-channel downsampling method based on the dictionary matrix RIP criterion according to any one of claims 1-4, characterized in that, Step 1.2 specifically includes the following steps: Step 1.21: Determine the number and location of strong scattering points in the scene; Based on the scenario requirements, determine the maximum number K of strong scattering points in the scenario; from the K strong scattering points, select... A group of strong scattering points is formed, among which Iterate through the numbers from 1 to K, where K is an integer greater than 1; For each group of strong scattering points, randomly select their positions in the scene; for each group of strong scattering points, determine... The next random position, where It is an integer greater than 1; Step 1.22: Based on the number and location of strong scattering points in the scene, obtain a partial dictionary matrix for each set of downsampled coprime dual-channel combinations; Based on the number of strong scattering points included in each group of strong scattering points determined in step 1.21 And the location of each strong scattering point in the scene, extract the dictionary matrix of each downsampled coprime dual-channel combination. In the corresponding region, obtain multiple partial dictionary matrices for each group of downsampled coprime dual-channel combinations. .

6. The coprime dual-channel downsampling method based on the dictionary matrix RIP criterion according to claim 5, characterized in that, Step 1.3 specifically includes the following steps: Step 1.31, Calculation The eigenvalues ​​are used to determine the range of eigenvalues; Step 1.32: Based on the range of eigenvalues Determine the limiting equidistant constants corresponding to each part of the dictionary matrix of each downsampled coprime dual-channel combination. ; Step 1.33: Calculate the mean value of the constraint equidistant constants corresponding to the dictionary matrix of each downsampled coprime dual-channel combination under the condition that the number of strong scattering points is the same but the positions are different.

7. A coprime dual-channel downsampling system based on the dictionary matrix RIP criterion, comprising a processor and a memory, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion as described in any one of claims 1-6.

8. A storage medium having a computer-readable program stored thereon, characterized in that, When the computer-readable program is executed by a processor, it implements the steps of the coprime dual-channel downsampling method based on the dictionary matrix RIP criterion as described in any one of claims 1-6.

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