CN110166055A - A kind of compressed sensing based multichannel compression sensing optimization method and system - Google Patents

Abstract

The invention discloses a kind of compressed sensing based multichannel compression sensing optimization method and systems, belong to compressed sensing technology field, including carrying out singular value decomposition to calculation matrix, observation vector after being optimized, and combine algorithm for reconstructing using synchronous orthogonal matching pursuit to rebuild original signal.The present invention is by carrying out singular value decomposition to calculation matrix, realize the separate design of calculation matrix and reconstruction matrix, obtain separable restructuring matrix, since the restructuring matrix row of optimization is mutually orthogonal, reduce the correlation between measured value, it uses the measurement to reconstruct original signal, substantially increases the reconstruction precision of signal.

Description

A multi-channel compressed sensing optimization method and system based on compressed sensing

technical field

The invention relates to the technical field of compressed sensing, in particular to a multi-channel compressed sensing optimization method and system based on compressed sensing.

Background technique

The current information acquisition technology is mainly based on the Nyquist sampling theorem, but when the signal is sampled, it will lead to a lot of data acquisition redundancy and waste of sensor resources. Compressed sensing (CS) theory suggests that if a signal is sparse or compressible, it is possible to use a set of incoherent projections from a small number of measurements below the Nyquist sampling rate while maintaining signal reconstruction accuracy to accurately restore the original signal. This theory has been widely used in wireless sensor networks, image super-resolution reconstruction, seismic exploration and so on.

At present, CS theory is only used for the internal signal structure of a single sensor, considering that there are many application scenarios in real life that are networks containing multiple sensors. In 2005, on the basis of compressed sensing theory, Baron et al. further studied how to fully integrate the sparse characteristics of signals and the correlation between signals to jointly process distributed signals and then propose distributed compressed sensing. DCS usually uses a Joint Sparse Model (JSM) to characterize the sparsity among multiple signals. In 2005, Baron et al. studied three simple joint sparse signal models in detail according to different application scenarios.

Distributed compressed sensing is mainly aimed at the recovery of multi-channel sparse signals. Compared with traditional CS, the number of measured values can be further reduced by using the correlation between channels. In a typical distributed compressed sensing (Distributed Compressed Sensing, DCS) situation, for signals measured by different sensors, each of which is sparse on a certain group basis, and each sensor is related to each other.

DCS is based on compressed sensing, and extends the research target from a single signal to distributed sensing of multi-channel signals. If multiple signals are sparse under a certain transformation base, and there is a certain correlation between these signals, then the coding The end can compress, sample and transmit each sparse signal independently by using another observation matrix that is not concerned with the transform basis, and obtain the number of measurement values far smaller than the signal length, and then use all the measurement values at the decoding end to jointly reconstruct the signal. If the structure is used, accurate reconstruction of all signals can be achieved, thereby improving data compression and signal reconstruction accuracy. The system block diagram is shown in Figure 1. Aiming at the problem of multi-channel compressed sensing in distributed compressed sensing, the present invention aims to improve the reconstruction accuracy of multi-channel signals and reduce the waste of resources.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a multi-channel compressed sensing optimization method and system based on compressed sensing, so as to improve the reconstruction accuracy of multi-channel signals.

In order to achieve the above object, on the one hand, the present invention adopts a multi-channel compressed sensing optimization method based on compressed sensing, which includes the following steps:

Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j , ...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

The measurement matrix Φ is decomposed by the singular value decomposition method, and the optimized observation value vector is obtained. Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

According to the optimized observation vector, by solving the constraint optimization The norm reconstructs the original signal.

Further, the observed value vector is a measurement vector obtained by measurement with a single measurement vector model, or J measurement vectors obtained by measurement with a multi-measurement vector model.

Further, the measurement matrix Φ is decomposed by the singular value decomposition method to obtain an optimized observation value vector, including:

The measurement matrix Φ is decomposed by the singular value decomposition method, and a new sensing system is obtained:

Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, Φ=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, that is E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero;

Left-multiply the matrix on both sides of the calculation formula of the new sensing system Get the optimized observation vector:

in: Φ _SVD =V ₁ ^T , Further, the sparseness between the signals of each channel is characterized by using a joint sparse signal model JSM-2.

Further, according to the optimized observation value vector, by solving the constraint optimization The norm reconstructs the original signal, specifically:

The optimized observation value vector is processed by using the synchronous orthogonal matching pursuit joint reconstruction algorithm to reconstruct the original signal.

In the second aspect, a multi-channel compressed sensing optimization system based on compressed sensing is adopted, including an observation value vector calculation module, an observation value vector optimization module and an original signal reconstruction module;

Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j , ...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

The observation value vector optimization module is used to decompose the measurement matrix Φ using the singular value decomposition method to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

The original signal reconstruction module is used to optimize the optimization by solving constraints according to the optimized observation vector The norm reconstructs the original signal.

Further, the observed value vector is a measurement vector obtained by measurement with a single measurement vector model, or J measurement vectors obtained by measurement with a multi-measurement vector model.

Further, the observation value vector optimization module includes a singular value decomposition unit and an optimization unit;

The singular value decomposition unit is used to decompose the measurement matrix Φ using the singular value decomposition method to obtain a new sensing system:

Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, Φ=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero;

The optimization unit is used to left multiply the matrix on both sides of the calculation formula Y _MMV Get the optimized observation vector:

in: Φ _SVD =V ₁ ^T ,

Further, the sparseness between the signals of each channel is characterized by adopting the joint sparse signal model JSM-2;

Correspondingly, according to the optimized observation value vector, the optimization is obtained by solving the constraints The norm reconstructs the original signal, specifically:

The optimized observation value vector is processed by using the synchronous orthogonal matching pursuit joint reconstruction algorithm to reconstruct the original signal.

In a third aspect, a computer-readable storage medium is adopted, including a program, and when the program is executed, the device including the computer-readable storage medium is caused to perform the following steps:

Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j , ...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

The measurement matrix Φ is decomposed by the singular value decomposition method, and the optimized observation value vector is obtained. Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

According to the optimized observation vector, by solving the constraint optimization The norm reconstructs the original signal.

Compared with the prior art, the present invention has the following technical effects: the present invention realizes the separation design of the measurement matrix and the reconstruction matrix by performing singular value decomposition on the measurement matrix, and obtains a separable reconstruction matrix. Orthogonal, reduces the correlation between the measured values, and uses the measured values to reconstruct the original signal, which greatly improves the reconstruction accuracy of the signal.

Description of drawings

Below in conjunction with the accompanying drawings, the specific embodiments of the present invention are described in detail:

Figure 1 is a block diagram of a distributed compressed sensing system;

FIG. 2 is a schematic flowchart of a multi-channel compressed sensing optimization method based on compressed sensing;

Figure 3 is a schematic diagram of the principle of the multi-measurement vector model;

4 is a schematic structural diagram of a multi-channel compressed sensing optimization system based on compressed sensing;

Figure 5 is a schematic diagram of a single test result of the original signal, the observed signal and the reconstructed signal;

6 is a schematic diagram of the relationship between the success probability and the number of measurements of the original signal reconstruction using different methods;

FIG. 7 is a schematic diagram of the relationship between the success probability and the sparsity of the original signal reconstruction using different methods;

FIG. 8 is a schematic diagram showing the relationship between the success probability and the noise change of the original signal reconstruction using different methods.

Detailed ways

To further illustrate the features of the present invention, please refer to the following detailed description and accompanying drawings of the present invention. The attached drawings are for reference and description only, and are not intended to limit the protection scope of the present invention.

As shown in FIG. 2 , this embodiment adopts a multi-channel compressed sensing optimization method based on compressed sensing, including the following steps S1 to S3:

S1. Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j ,...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

S2. Use the singular value decomposition method to decompose the measurement matrix Φ to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

S3. According to the optimized observation value vector, the optimization is obtained by solving the constraints The norm reconstructs the original signal.

It should be noted that in the case of DCS, the signals of the J channels are all compressible (sparse) or compressible on a sparse basis, that is, any channel signal can use N×1 wiki vector A linear representation is given as follows:

Among them, θ _j is the projection coefficient. When the signal can be linearly represented by K basis vectors, the signal is said to be K-sparse, 1≤i≤N, 1≤j≤J.

Further, the observed value vector is a measurement vector obtained by measurement with a single measurement vector model, or J measurement vectors obtained by measurement with a multi-measurement vector model. in:

(1) Single Measurement Vector (SMV) problem:

On appropriately chosen sparse basis such as standard orthonormal basis, with K sparse signal An accurate reconstruction can be obtained by its M linear projections on another set of incoherent bases. Then the single-measure vector problem can be defined as:

Since X is a column vector, there is only a single measurement vector after observation, so the above problem is also called a single measurement vector problem (Single Measurement Vector, SMV) in CS. in, is the measurement matrix of the jth signal, Ψ is the sparse basis of the signal X, in this paper Take the identity matrix. In general, Φ _j varies with x _j . e is Gaussian noise, represents the field of real numbers.

Then there are:

where the measurement matrix Φ is a block diagonal matrix, each diagonal element is a random matrix, and each sparse signal x _j shares a common vector support, j∈{1,2,…,J}.

(2) Multiple Measurement Vector (MMV) problem:

when When j∈{1,2,...,J} are all the same, that is, using the same measurement matrix for each channel, the signal X=[x ₁ ;x ₂ ;...;x _j ;...;x _J ] can be The transmission is carried out in multiple channels, and there are multiple measurement vectors after observation, so this kind of problem is also called the Multiple Measurement Vector (MMV) problem. is defined as follows:

As shown in Figure 3,

Among them, θ _ij is the i-th element of the j-th channel, j∈{1,2,...,J}. For each individual channel, a measurement vector y _j =Φ _j x _j =Φ _j Ψ _j θ _j can be obtained.

Then the measurement value of J sensing nodes is expressed by the following formula:

Further, the above step S2: using the singular value decomposition method to decompose the measurement matrix Φ to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the Gaussian noise after optimization. Specifically, it includes the following steps S21 to S22:

S21. Decompose the measurement matrix Φ using the singular value decomposition method to obtain a new sensing system:

Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, Φ=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero;

S22. Left multiply the matrix on both sides of the calculation formula Y _MMV Get the optimized observation vector:

in: Φ _SVD =V ₁ ^T ,

Specifically, Singular Value Decomposition (SVD) can decompose any full-rank measurement matrix Φ into the following:

Φ=UDV ^T ;

where Φ represents the measurement matrix in the signal reconstruction process, and are all orthogonal matrices, that is:

^UUT = _EM ,

VV ^T ₌ EN ,

In the formula: D∈R ^M×N , is a semi-positive definite diagonal matrix, and its off-diagonal elements are all zero, that is, D=diag(σ ₁ ,σ ₂ ,...,σ _M ), k is the matrix The rank of , which is equal to the number of non-zero singular values, σ _k (k=1,...,M) is all non-zero singular values of the matrix Φ, all σ _k are uniquely determined by this decomposition, the formula UDV ^T is called Φ singular value decomposition of .

Take the measurement matrix decomposition in the multi-measurement vector model process as an example:

Perform SVD operation on the measurement matrix Φ _j , and rewrite the formula Y _MMV =Φ _j [x ₁ ,x ₂ ,...,x _J ]+e as the following formula:

In the formula: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, 0 is an M×(NM)-dimensional all-zero matrix, a sub-matrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , where E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively. By left multiplying the matrix on both sides of Y _MMV You can get:

A new measurement system is available:

where:

Φ _SVD =V ₁ ^T ,

Compared with Y _MMV =ΦX+e=Aθ+e, the measurement matrix _ΦSVD at this time is a row orthogonal matrix, that is,

It should be noted that the sparsity among the signals of each channel described in this embodiment is characterized by using the joint sparse signal model JSM-2. When the JSM-2 model is used, all signals share the same vector support, and different JSMs correspond to different reconstruction algorithms. In this embodiment, the Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm is mainly used. The orthogonal matching pursuit joint reconstruction algorithm processes the optimized observation vector, and optimizes by solving constraints The norm reconstructs the original signal.

It should be noted that, in this embodiment, singular value decomposition is applied to the measurement matrix, and then an optimized separable reconstruction matrix and an optimized measurement are obtained. Since the rows of the optimized reconstruction matrix are mutually orthogonal, the correlation between the measurement values is reduced. , which optimizes the selection of the true support set, so the reconstruction accuracy of the signal is greatly improved.

Further, in the JSM-2 model, the principle of the SOMP algorithm is: in each greedy iterative process, the correlation between different measurement values and the corresponding compressed sensing measurement matrix is obtained, and then the correlation corresponding to the signal set support set is calculated. The coefficients are summed, and the support set with the largest correlation is selected as the support set for signal reconstruction. The objective function is: To reconstruct the signal, is the sparse coefficient of the signal X Norm, which represents the number of non-zero elements in the vector θ.

As shown in FIG. 4 , this embodiment discloses a multi-channel compressed sensing optimization system based on compressed sensing, including an observation value vector calculation module 10 , an observation value vector optimization module 20 and an original signal reconstruction module 30 ;

The observation value vector calculation module 10 is used to obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, wherein: X=[x ₁ ; x ₂ ;...; x _j ;...; x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

The observation value vector optimization module 20 is used to decompose the measurement matrix Φ by using the singular value decomposition method to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

The original signal reconstruction module 30 is used to solve the constraint optimization according to the optimized observation value vector The norm reconstructs the original signal.

Further, the observed value vector is a measurement vector obtained by measurement with a single measurement vector model, or J measurement vectors obtained by measurement with a multi-measurement vector model.

Further, the observed value vector optimization module 20 includes a singular value decomposition unit 21 and an optimization unit 22;

The singular value decomposition unit 21 is used to decompose the measurement matrix Φ using the singular value decomposition method to obtain a new sensing system:

Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, Φ=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero;

The optimization unit 22 is used to left multiply the matrix on both sides of the formula Y _MMV Get the optimized observation vector:

in: Φ _SVD =V ₁ ^T ,

Further, the sparseness between the signals of each channel is characterized by the joint sparse signal model JSM-2; when the JSM-2 model is used, all signals share the same vector support, and different JSMs correspond to different reconstruction algorithms, This embodiment mainly adopts the Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm, that is, uses the Simultaneous Orthogonal Matching Pursuit Joint Reconstruction Algorithm to process the optimized observation value vector, and optimizes by solving constraints. The norm reconstructs the original signal.

This embodiment also discloses a computer-readable storage medium, including a program, when the program is executed, the device including the computer-readable storage medium is caused to perform the following steps S1 to S3:

S1. Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j ,...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise;

S2. Use the singular value decomposition method to decompose the measurement matrix Φ to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise;

S3. According to the optimized observation value vector, the optimization is obtained by solving the constraints The norm reconstructs the original signal.

Those of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments may be completed by program instructions related to hardware, the aforementioned program may be stored in a computer-readable storage medium, and when the program is executed, execute It includes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

It should be noted that the compressive sensing-based multi-channel compressed sensing optimization system and computer-readable storage medium disclosed in this embodiment correspond to the disclosed steps of the compressive sensing-based multi-channel compressed sensing optimization method, which are not repeated here. Repeat.

To verify the effectiveness of the method proposed in this paper, four groups of experiments are designed for the same sparse signal in this section.

Experiment 1: Single Reconstruction Experiment

For the single-shot multi-channel signal recovery problem, the signal recovery in the formulas Y _SMV =ΦX _+e and Y _MMV =Φ _j [x ₁ ,x ₂ ,...,x _J ]+e are named SMV and MMV models, and SVD is introduced. Afterwards, they are named SMV+SVD and MMV+SVD respectively. A single reconstruction experiment is performed on the SMV, MMV, SMV+SVD and MMV+SVD problems, as shown in Figure 5: Figure 5(a) and Figure 5(b) are the original signal and the observed signal, respectively, Figure 5(c), 5(d), 5(e), and 5(f) are the reconstruction results of the original signals of the SMV, MMV, SMV+SVD, and MMV+SVD methods in turn. In this experiment, the length of the signal is N=150, the number of measurements M=100, and the signal sparsity K=40. The OMP algorithm and the SOMP algorithm are used for signal reconstruction in the SMV and MMV problems, respectively.

The signal-to-noise ratio (SNR) is used to quantify the reconstruction effect of the image. It can be seen from Figure 5 that in the SMV, SMV+SVD, MMV, and MMV+SVD problems, the SNRs are 64dB, 83dB, 352dB, and 337dB, respectively. In a single experiment, the MMV method significantly outperforms the SMV problem, especially, when SVD is used as a preprocessing step for the observed signal, the signal reconstruction is significantly better than the SMV problem, and the reconstruction accuracy is significantly improved.

On the basis of a single reconstruction experiment, in order to further analyze the performance of the method proposed in this scheme, this scheme also performs 1000 times for three variables in the signal reconstruction process: signal length N, measurement times M and added noise N. The experiment was repeated, and the following experiments were designed considering the reconstruction success probability under various methods while keeping two parameters unchanged and changing the other variable.

Experiment 2: Reconstruction experiment with different number of measurements

This experiment is designed considering how the reconstruction probability changes under various methods of changing the measurement times M when the signal length N and the signal sparsity K are constant. In this experiment, the signal length N=150 and the signal sparsity K=40 are kept unchanged, the value of the measurement times M is changed from 40 to 160, the step size is set to 5, and each group of parameters (N, M, K) is set generate sparse signal and measurement matrices independently and randomly. Under the same set of sparse signals, SVD and no SVD are introduced into the measurement matrix respectively, and finally different methods are used for reconstruction.

Experiment 3: Different Sparsity Reconstruction Experiments

Similarly, this experiment is designed considering how the reconstruction probability changes under various methods of changing the signal sparsity K when the signal length N and the number of measurements M are constant. In this experiment, the signal length N=150 and the number of signal measurements M=100 are kept unchanged, the value of the sparsity K is changed from 10 to 100, the step size is set to 5, and each group of parameters (N, M, K) is set generate sparse signal and measurement matrices independently and randomly. Under the same set of sparse signals, SVD and no SVD are introduced into the measurement matrix respectively, and finally different methods are used to reconstruct.

Experiment 4: Robustness Test

Considering the anti-noise performance of the proposed method under noise, this experiment is designed. In this experiment, keep the signal length N=150, the signal measurement times M=100, and the signal sparsity K=40 unchanged, set the parameter σ to represent the noise standard deviation, and make the value of σ change from 0 to 0.5, step The length is set to 0.035. The sparse signal and measurement matrices are independently and randomly generated under each set of parameter (N, M, K) settings. Under the same set of sparse signals, SVD and no SVD are introduced into the measurement matrix respectively, and finally different methods are used to reconstruct.

As shown in Figures 5-8: In experiment 1, for SMV, SMV+SVD, MMV and MMV+SVD methods, the probability of successful signal reconstruction increases with the increase of the number of measurements M. In experiment 2, the success probability of signal reconstruction decreases as the signal sparsity K increases. In experiment 3, in the presence of noise, the probability of successful reconstruction of the signal decreases with the increase of the standard deviation of the added noise, but the reconstruction effect of the MMV problem is always better than that of the SMV problem; SVD is applied to the perception matrix as the signal After the preprocessing step of the reconstruction, the reconstruction is significantly better than without SVD. To sum up, their reconstruction performances are in order: the SMV method is the worst, followed by the SMV+SVD method, and then the MMV method. The MMV+SVD method proposed in this paper has the best reconstruction effect.

It should be noted that the singular value decomposition is applied to the measurement matrix, and then the optimized separable reconstruction matrix and the optimized measurement are obtained. Since the rows of the optimized reconstruction matrix are orthogonal to each other, the correlation between the measurement values is reduced, and the optimized The choice of the true support set, so the reconstruction accuracy of the signal is greatly improved. And the numerical experiment results show that, for the restoration of multi-channel signals, not only the complexity of the system design is reduced, but also the reconstruction accuracy of the signal is greatly improved. In addition, the reconstruction success probability is also significantly improved under the condition of noise interference.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection of the present invention. within the range.

Claims (10)

1. a multi-channel compressed sensing optimization method based on compressed sensing, is characterized in that, comprising: Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j , ...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise; The measurement matrix Φ is decomposed by the singular value decomposition method, and the optimized observation value vector is obtained. Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise; According to the optimized observation vector, the original signal is reconstructed by solving the constrained optimal l ₀ norm. 2. The multi-channel compressed sensing optimization method based on compressed sensing as claimed in claim 1, wherein the observed value vector is a measurement vector obtained by measuring a single measurement vector model, or is a measurement vector obtained by a multi-measurement vector model The measured J measurement vectors. 3. The multi-channel compressed sensing optimization method based on compressed sensing according to claim 1 or 2, characterized in that, the measurement matrix Φ is decomposed by the singular value decomposition method, and the optimized observation value vector is obtained, comprising: : The measurement matrix Φ is decomposed by the singular value decomposition method, and a new sensing system is obtained: Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, Φ=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero; Left-multiply the matrix on both sides of the Y _MMV Get the optimized observation vector: in: Φ _SVD =V ₁ ^T , 4 . The multi-channel compressed sensing optimization method based on compressed sensing according to claim 3 , wherein the sparseness among the signals of each channel is characterized by using a joint sparse signal model JSM-2. 5 . 5. The multi-channel compressed sensing optimization method based on compressed sensing according to claim 4, wherein the original signal is reconstructed by solving the optimal ₁₀ norm of constraints according to the optimized observation value vector, specifically for: The optimized observation value vector is processed by using the synchronous orthogonal matching pursuit joint reconstruction algorithm to reconstruct the original signal. 6. A multi-channel compressed sensing optimization system based on compressed sensing, characterized in that it comprises an observation value vector calculation module, an observation value vector optimization module and an original signal reconstruction module; The observation value vector calculation module is used to obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ , x ₂ ,…,x _j ,…,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise; The observation value vector optimization module is used to decompose the measurement matrix Φ using the singular value decomposition method to obtain the optimized observation value vector Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise; The original signal reconstruction module is used to reconstruct the original signal by solving the constrained optimal l ₀ norm according to the optimized observation value vector. 7. The multi-channel compressed sensing optimization system based on compressed sensing according to claim 6, wherein the observed value vector is a measurement vector obtained by measuring a single measurement vector model, or is a measurement vector obtained by a multi-measurement vector model The measured J measurement vectors. 8. The multi-channel compressed sensing optimization system based on compressed sensing according to claim 6 or 7, wherein the observed value vector optimization module comprises a singular value decomposition unit and an optimization unit; The singular value decomposition unit is used to decompose the measurement matrix Φ using the singular value decomposition method to obtain a new sensing system: Where: D ₁ =diag(σ ₁ ,σ ₂ ,...,σ _M ) is an M×M-dimensional diagonal square matrix, A=UDV ^T , a submatrix of matrix V is a column orthogonal matrix, namely V ₁ ^T V ₁ = _EM , E _M and E _NM are M×M and (NM)×(NM) dimensional identity matrices, respectively; D∈R ^M×N , is a positive semi-definite diagonal matrix whose off-diagonal elements are all zero; The optimization unit is used to left multiply the matrix on both sides of the calculation formula Y _MMV Get the optimized observation vector: in: Φ _SVD =V ₁ ^T , 9. The multi-channel compressed sensing optimization system based on compressed sensing according to claim 8, wherein the sparseness between the signals of each channel is characterized by using a joint sparse signal model JSM-2; Correspondingly, according to the optimized observation value vector, the original signal is reconstructed by solving the constrained optimal _l0 norm, specifically: The optimized observation value vector is processed by using the synchronous orthogonal matching pursuit joint reconstruction algorithm to reconstruct the original signal. 10. A computer-readable storage medium, comprising a program, and when the program is executed, a device including the computer-readable storage medium is caused to perform the following steps: Obtain the signal X of each channel, and perform projection measurement on the signal of each channel with the measurement matrix to obtain the observation value vector Y _MMV =ΦX+e=Aθ+e, where: X=[x ₁ ,x ₂ ,...,x _j , ...,x _J ], Φ is the measurement matrix, A is the perception matrix, θ is the projection coefficient, and e is the Gaussian noise; The measurement matrix Φ is decomposed by the singular value decomposition method, and the optimized observation value vector is obtained. Among them: Φ _SVD is a row orthogonal matrix, e' is the optimized Gaussian noise; According to the optimized observation value vector, the original signal is reconstructed by solving the constrained optimal l ₀ norm.