WO2020020001A1

WO2020020001A1 - Method and system employing compressed sensing to construct sensing matrix when disturbances occur in measurement matrix, and a medium

Info

Publication number: WO2020020001A1
Application number: PCT/CN2019/095795
Authority: WO
Inventors: 黄磊; 张亮; 包为民; 廖桂生; 罗丰; 孙维泽; 张沛昌
Original assignee: 深圳大学
Priority date: 2018-07-26
Filing date: 2019-07-12
Publication date: 2020-01-30
Also published as: CN108988867A; CN108988867B

Abstract

A method and system employing compressed sensing to construct a sensing matrix when disturbances occur in a measurement matrix, and a storage medium. The method comprises: generating a random matrix to serve as a desired measurement matrix, performing sparsity measurement on a sampling signal, and constructing actual measurement data corresponding to an actual measurement matrix (S10); performing optimization processing on the desired measurement matrix and obtaining an optimal estimation value of the actual measurement matrix (S20); constructing, on the basis of the optimal estimation value of the actual measurement matrix, a sensing matrix (S30); and reconstructing the actual measurement data by means of the sensing matrix, and recovering an original signal (S40). The method is employed to estimate an actual measurement matrix in a disturbed environment, thereby constructing a sensing matrix and using the received data to accurately recover original data.

Description

Method, system and medium for constructing compressed sensing perception matrix during measurement matrix disturbance

Technical field

The present invention relates to the technical field of signal processing, and in particular, to a method, a system, and a medium for constructing a compressed sensing perception matrix when measuring a matrix disturbance.

Background technique

Compressed sensing is a new signal processing method. Its core idea is to recover the original sparse signal through non-adaptive and incomplete measurement of the signal. Because compressed sensing can break through the limitation of Nyquist sampling theorem, it is widely used in data compression, image processing, medical signal processing, signal parameter estimation and other related fields.

Traditional compressive sensing uses a measurement matrix to sparsely measure the signal, and implements sparse reconstruction of the signal through a recovery algorithm. However, in practical applications, the measurement matrix is often disturbed, which causes many sources of disturbance in the measurement matrix, such as the electrical noise during the operation of the digital-to-analog converter, the accuracy limit of the memory, the discretization accuracy of the parameter space, etc. There is a difference between the actual measurement matrix and the expected measurement matrix during the measurement process, which affects the reconstruction effect of the sparse signal.

Therefore, the prior art needs to be improved and improved.

Summary of the Invention

The present invention is necessary to solve the problem that the disturbance of the measurement matrix in the prior art causes a difference between the actual measurement matrix and the expected measurement matrix, so that the success rate of recovering the original signal from the signal reconstruction is low. Provided is a method, system, and medium for constructing a compressed sensing perceptual matrix during measurement matrix disturbance. The purpose is to construct a perceptual matrix by estimating the actual perceptual matrix under the interference environment, so that the received data can restore the accurate and complete output. Raw data, improve the success rate of raw data recovery.

The technical solutions adopted by the present invention to solve the above technical problems are as follows:

The present invention provides a method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed. The method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed includes:

Generate a random matrix as the expected measurement matrix, perform sparse measurement on the sampled signal, and construct the actual measurement data corresponding to the actual measurement matrix;

Performing optimization processing on the expected measurement matrix to obtain an optimal estimation value of the actual measurement matrix;

Constructing a perception matrix according to an optimal estimation value of the actual measurement matrix;

The actual measurement data is reconstructed through the perception matrix to recover the original signal.

The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed, wherein generating the random matrix as an expected measurement matrix, performing sparse measurement on the sampled signal, and before constructing actual measurement data corresponding to the actual measurement matrix includes:

Receive all sent original signals;

Sampling the original signal to obtain a sampling signal.

The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed, wherein generating the random matrix as an expected measurement matrix, performing sparse measurement on a sampled signal, and constructing actual measurement data corresponding to the actual measurement matrix specifically include:

Generate a random matrix as the expected measurement matrix by software, and define the difference between the actual measurement matrix and the expected measurement matrix as the disturbance difference matrix;

Sparse measurement is performed on the sampled signal through the actual measurement matrix to construct actual measurement data corresponding to the actual measurement matrix.

The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed, wherein the optimal processing of the desired measurement matrix to obtain the optimal estimation value of the actual measurement matrix specifically includes:

Constructing an estimation model of the actual measurement matrix according to the actual measurement data;

Performing optimization processing on the estimation model to obtain an optimal solution of the estimation model;

According to the optimal solution of the estimation model, an optimal estimation value of the actual measurement matrix is obtained.

The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed, wherein the obtaining the optimal estimation value of the actual measurement matrix according to the optimal solution of the estimation model specifically includes:

When the square of the second norm absolute value of the perturbation difference between the column vectors corresponding to the actual measurement matrix and the expected measurement matrix is not greater than a preset perturbation threshold, a Lagrange of the estimated model is constructed by a Lagrangian multiplier algorithm Lange equation

Obtaining the interval range of the Lagrange multiplier corresponding to the Lagrange equation according to the Lagrange equation;

Randomly select a value in the interval range as an initial value, and obtain an optimal value of the Lagrange equation by a Newton method;

According to the optimal value, an optimal solution of the estimation model, that is, an optimal estimated value of the actual measurement matrix is obtained.

The method for constructing a compressed sensing perceptual matrix when the measurement matrix is disturbed, wherein the constructing the perceptual matrix according to the optimal estimation value of the actual measurement matrix specifically includes:

Obtain the optimal estimate of the actual measurement matrix;

A perception matrix is constructed according to the optimal estimation value of the actual measurement matrix.

The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed, wherein the reconstructing the actual measurement data through the sensing matrix and recovering the original signal specifically includes:

Obtaining the perception matrix;

Perform reconstruction processing on the actual measurement data to recover the original signal.

The present invention also provides a system, the system comprising: a memory, a processor, and a compressed sensing and perception matrix construction program stored in the memory and capable of running on the processor when the measurement matrix is disturbed, the measurement Steps of the method for constructing the compressed sensing and perceptual matrix when the matrix perturbation is executed when the program is executed by the processor when the matrix perturbation is performed by the processor.

The present invention also provides a storage medium that stores a compressed sensing and perception matrix construction program when the measurement matrix is disturbed, and implements the foregoing quantity when the compressed sensing and perception matrix construction program is executed by the processor when the measurement matrix is disturbed. Steps of the method for constructing the compressed sensing perceptual matrix when measuring matrix disturbance.

Beneficial effects:

1. Make full use of the actual measurement data, and replace the traditional measurement matrix with the constructed sensing matrix during the signal reconstruction phase, to avoid the error of recovery of the signal support set, and to ensure the accuracy of the original signal estimation.

2. Determine the actual measurement matrix through Newton's method and Lagrangian multiplier algorithm

Estimated value

An unknown perception matrix 作为 is constructed based on its estimated value as a known variable, so that the measured data can reconstruct and output a complete and accurate original signal after reconstruction, and improve efficiency.

3. Based on the random selection of initial values and measurement matrices, a suitable perceptual matrix is generated, which makes the signal compression sensing process more adjustable and artificially controlled, and restores the data to the greatest extent, such as restoring the original image.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed according to an embodiment of the present invention; FIG.

FIG. 2 is a relationship diagram between the recovery probability and the sparsity of the sparse signal support set of the method for constructing the compressed sensing perception matrix when the measurement matrix is disturbed according to an embodiment of the present invention; FIG.

3 is a relationship diagram between a root mean square error of a sparse reconstructed signal and a sparsity of a method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed according to an embodiment of the present invention;

FIG. 4 is a structural block diagram of a preferred embodiment of the system of the present invention.

detailed description

In order to make the objectives, technical solutions, and advantages of the present invention more clear and specific, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

It should be noted that the present invention is based on the compressed sensing theory, and its processing process includes three stages, which are sparse representation of the signal, sparse measurement of the signal, and sparse reconstruction of the signal to implement the present invention.

The present invention provides a method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed. As shown in FIG. 1, the method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed includes:

S10. Generate a random matrix as the expected measurement matrix, perform sparse measurement on the sampled signal, and construct actual measurement data corresponding to the actual measurement matrix.

That is, step S10 specifically includes:

S11. Generate a random matrix as the expected measurement matrix by software, and define the difference between the actual measurement matrix and the expected measurement matrix as the disturbance difference matrix;

S12. Perform sparse measurement on the sampled signal through the actual measurement matrix, and construct actual measurement data corresponding to the actual measurement matrix.

Specifically, sampling is performed in advance, that is, all sent original signals are received, and the original signals are sampled to obtain a sampled signal. The original signal refers to that when the source sends data to the terminal, messages are transmitted to each other through corresponding signals, and the message to be expressed by the other party can be known only when the corresponding signal is received. For example, if user A needs to send an image to user B, then user A sends an image signal (that is, the original signal corresponding to the embodiment of the present invention) to user B. After receiving the image signal, user B starts to receive the image and feeds back to user A. Receive the image signal to complete a complete data transmission. For another example, a doctor needs to probe the patient's diseased area, and the photons detected by medical instrument scanning are converted into electrons to form an electrical pulse signal (that is, the original signal corresponding to the embodiment of the present invention). After signal analysis, digital-to-analog conversion, and data processing, etc. Imaging.

During the transmission of signal data, environmental factors, such as noise and obstacles, often make the information received by the terminal incomplete, missing, or prolonged, such as blurred images and damaged images. Therefore, in order to improve the quality of the data received by the terminal, it is necessary to perform a preset sparsity k sampling on the original signal. The original image was successfully reconstructed by measuring and optimizing the reconstruction. In this way, the sampling rate can be reduced under the premise of ensuring the signal quality. Therefore, the reduction of sampling data can significantly reduce the cost of storage, transmission, and processing of data such as images and videos.

Further, if the image signal is sparsely represented, a random matrix is generated by the software as the desired measurement matrix Φ∈R ^{M × N} (M represents the number of rows of the measurement matrix, N represents the number of columns of the measurement matrix, M and The specific value of N is determined by actual engineering problems.) The random matrix obeys the Gaussian distribution. After sampling, the sparse signal is measured on the sparse signal with the desired measurement matrix at this time. Obtain L expected measurement data, and construct a first multiple measurement vectors (MMV, multiple measurement vectors) based on the expected measurement matrix and the expected measurement data, as shown in equation (1):

Y = ΦX + N (1)

Among them, Y = [y ₁ y ₂ … y _L ] represents the expected measurement data matrix, y _l ∈ R ^M (l = 1, 2 ..., L) represents the lth measurement vector, and X = [x ₁ x ₂ … X _L ] represents a set of multiple sampled signals, referred to as joint sparse signals, that is, only the elements of some rows in X have non-zero values and the elements of other rows are all zero, X _l ∈ R ^N (l = 1, 2 ..., L) and M≤L represents the set of non-zero row numbers in X represents the support set of sparse signals, N represents the measurement noise, Φ∈R ^{M × N} represents the expected measurement matrix, and M represents the expected measurement matrix The number of rows, N represents the number of desired measurement matrix columns, and M <<N; l = 1, 2, ..., L represents the number of measurements of the joint sparse signal X. At the lth measurement, The corresponding sparse signal is x _l , the expected measurement data is y _l , and the expected measurement data matrix Y is obtained after L measurements.

In the actual environment, such as the process of transmitting image signals, the measurement matrix used for receiving and extracting the image signal data will be affected by environmental factors such as environmental noise, electrical noise, etc. and the measurement we expect. There are differences in the matrices, so the actual measurement matrix is used to define

Representation, actual measurement matrix

The difference from the expected measurement matrix Φ is expressed as a disturbance difference matrix with ΔΦ, also called a disturbance term, where ΔΦ ∈ R ^{M × N} and obeying a Gaussian distribution with zero mean and one variance. At this time, according to

Performing sparse measurement on the sampling signal through the actual measurement matrix to obtain an actual measurement matrix

The corresponding actual measurement data, that is, the second multi-vector measurement model based on the actual measurement matrix and the actual measurement data is constructed, that is, the

Substituting into the above formula (1), the conversion is obtained as formula (2), namely:

Where Φ∈R ^{M × N} represents the desired measurement matrix, that is, Φ in equation (1),

Represents the actual measurement matrix, and N represents the measurement noise.

Of course, the magnitude of the disturbance between the aforementioned desired measurement matrix and the actual measurement matrix can be characterized by equation (3), that is:

Among them, η represents the preset disturbance threshold value, which is a constant not greater than 1, and i = 1,2, ..., N represents the i-th column of the matrix.

S20. Perform optimization processing on the expected measurement matrix to obtain an optimal estimation value of the actual measurement matrix.

That is, step S20 specifically includes:

S21. Construct an estimation model based on the actual measurement matrix according to the actual measurement data;

S22. Perform optimization processing on the estimation model to obtain an optimal solution of the estimation model.

S23. Obtain an optimal estimation value of the actual measurement matrix according to the optimal solution of the estimation model.

Further, step S22 in the embodiment specifically includes:

S221. When the square of the second norm absolute value of the column vector disturbance difference matrix corresponding to the actual measurement matrix and the expected measurement matrix is not greater than a preset disturbance threshold, a Lagrange multiplier algorithm is used to construct a pull of the estimation model. Grange's equation

S222. Obtain the interval range of the Lagrangian multiplier corresponding to the Lagrange equation according to the Lagrange equation;

S223: Randomly select a value in the interval range as an initial value, and obtain an optimal value of the Lagrange equation by a Newton method;

S224. Obtain an optimal solution of the estimation model, that is, an optimal estimation value of the actual measurement matrix according to the optimal value.

In the present invention, the system of the terminal obtains a perception matrix through the above-mentioned method of constructing a multi-measurement compressed perception perception matrix, and then reconstructs the actual measurement data received through the perception matrix, extracts and recovers the original signal, and then obtains The original data is achieved by recovering a large number of multi-dimensional original data from a small amount of low-dimensional sampling data.

Based on this, the specific embodiment of the present invention is to obtain the actual measurement matrix through the known expected amount matrix, actual measurement data, and perturbation threshold.

Estimated value

Specifically, an actual measurement matrix is constructed according to a second multi-vector measurement model corresponding to the actual measurement matrix, such as formula (2).

An estimation model of

To solve the actual measurement matrix

Estimated value

Then the solution is to solve the optimization problem of the actual measurement matrix, which is also converted to find the maximum value of the above estimation model under the first constraint condition, and is realized by the following formula (4):

Among them, R = YY ^T represents the covariance matrix of the actual measurement data matrix Y, the superscript T represents the transpose operation of the matrix, and the superscript -1 represents the reverse operation of the matrix. Equation (4) is used to satisfy: 1) the i-th column of the actual measurement matrix

The difference from the i-th column Φ _{· i of the} desired measurement matrix is not greater than η, that is,

That is, the first constraint; 2) the estimation model (that is, the objective function)

Get the maximum value; the optimal actual measurement matrix under these two conditions, therefore, the best estimate of the actual measurement matrix can be obtained by solving equation (4)

Where || · || ₂ represents the second norm of the vector,

Used to indicate that the constraint is the i-th column of the actual measurement matrix

The difference from the i-th column Φ _{· i} of the expected measurement matrix is not greater than η after taking the square of the second norm; max (·) means taking the maximum operation.

Because the optimal solution of the optimization problem in Equation (4) must be located on the boundary of the first constraint, that is, the optimal solution must satisfy the second constraint, and the second constraint is

In simple terms, when the i-th column of the actual measurement matrix

When the absolute value of the difference between the i-th column Φ _{· i} of the desired measurement matrix and the second norm square is equal to η, the optimal solution of the above formula (4) is obtained, that is, the problem shown in the following formula (5) is solved :

Therefore, the actual measurement matrix can be obtained by solving equation (5).

An accurate estimate of

Then, through the Lagrangian multiplier algorithm, the optimization processing in equation (5) is transformed into a solution as shown in equation (6), that is,

among them,

Represents the Lagrange function,

Represents the i-th column of the actual measurement matrix, and δ> 0 represents a Lagrangian multiplier.

Then solve equation (6) to get the estimated value of the actual measurement matrix

The equation is as shown in equation (7), that is,

Then, the equation (7) is brought into the constraint condition in the equation (5) (the second constraint condition in the equation (5)

We can get formula (8), that is,

Among them, I represents the identity matrix, and formula (8) is used to represent an equation satisfied by the Lagrangian multiplier δ, and the variable of the equation is δ, and the value of δ can be estimated by this equation.

The following are the steps to estimate the value of δ:

Perform feature decomposition on R as shown in formula (9), that is,

R = VΛV ^T (9)

Where V = [v ₁ , v ₂ , ..., v _M ] represents M feature vector matrices, and v _m represents the m-th feature vector, where m = 1, ..., M, Λ = diag (r ₁ , r ₂ , ..., r _M ) A diagonal matrix composed of eigenvalues, where r _m represents the eigenvalue corresponding to the feature vector v _m , and r ₁ ≥r ₂ ≥ ... ≥r _M represents that the eigenvalues of R are arranged in descending order.

Then, let z = V ^T Φ _{· i} , where z represents an intermediate variable, and V represents the eigenvector matrix. Substituting z = V ^T Φ _{· i} and formula (9) into formula (8), then formula (8) is transformed into As shown in formula (10),

According to the eigenvalues of R in descending order, solve formula (10) to obtain the interval range of the estimated value of δ, as shown in formula (11), that is,

Among them, min (·) represents the minimum operation, | · | ² represents the square operation of the absolute value, and {,} represents the interval range.

Randomly select a value in the interval range of formula (11), record it as the initial value δ ₀ , construct a function f (δ) of δ, and perform first-order and second-order derivatives on f (δ), respectively corresponding to the formulas (12) and formula (13). among them,

among them,

Represents the first-order derivative of a function,

Second-order derivative

According to equations (12) and (13), then use Newton's method to find the optimal value that satisfies equation (8)

The downward direction of the function when the optimal solution is obtained is shown in equation (14), that is,

The best value of formula (8) is obtained by formulas (9)-(14)

The actual measurement matrices in equations (6) and (7) are obtained.

And its estimates

Furthermore, the actual measurement matrix in equation (5) is determined.

And its estimates

S30. Construct a perception matrix according to an optimal estimation value of the actual measurement matrix.

Specifically, a perception matrix is constructed according to an optimal estimation value of the actual measurement matrix.

Let the perceptual matrix to be constructed be denoted by Ψ, according to the known measurement matrix

Estimated value

Construct the perceptual matrix 采样 of the sampled signal, whose form is shown in Equation (15), that is,

Among them, R = YY ^T represents the covariance matrix of the measurement data matrix Y, i = 1,2, ..., N; the superscript -1 represents the inverse operation of taking the matrix. Equation (15) represents the form of the i-th column of the perception matrix. Equation (15) is calculated N times, that is, i takes different values from 1 to N, and a complete required perception matrix can be obtained.

S40. Reconstruct the actual measurement data through the perception matrix to recover the original signal.

Specifically, the perceptual matrix in step S30 is acquired, and the perceptual matrix is reconstructed from the actual measurement data to recover the original signal.

That is, the terminal reconstructs the sparse signal (ie, the sampled signal) by using the joint orthogonal matching tracking algorithm to recover the original signal, that is, the original data, such as the original image.

In order to better understand the technical scheme of the method for constructing the compressed sensing perception matrix when the measurement matrix is disturbed according to the present invention, a specific experimental data is used to explain in detail:

Computer simulation experiments are used, and the simulation conditions are as follows: SNR = 20dB; η = 0.25; Φ ∈ R ^{128 × 256} and ΔΦ ∈ R ^{128 × 256} are Gaussian random matrices, where the elements obey the mean with zero variance and one Gaussian distribution, where the number of rows M is 128 and the number of columns N is 256; in order to obtain statistical performance, each experiment is repeated 500 times independently, that is, L = 500; the sparsity of the sampled signal (labeled as K) gradually increase from 5 to 100; for comparison, the simulation results of traditional compressed sensing (Ψ = Φ), alternate projection APM, and weighted algorithm RWA are also given; the recovery algorithm used in the present invention is joint orthogonal Match tracking algorithm SOMP. The experimental results are shown in Figures 2 and 3.

Figure 2 illustrates the changes in the probability and sparseness of the sparse signal support set in the case of SNR = 20dB, L = 500, and η = 0.25. In FIG. 2, the abscissa represents the sparsity K, and the ordinate represents the probability of successful recovery of the sparse signal support set. With the increase of sparseness, the success rates of the four algorithms for sparse signal support set recovery are decreasing. Traditional compressed sensing (Ψ = Φ), alternate projection method APM, and heavy weighting algorithm RWA successively fail with increasing K. When K = 20, the algorithm proposed by the present invention can still recover sparse signals with a 100% probability. The support set shows that the method proposed by the present invention is effective, the data recovery success rate is higher, and the reconstruction effect is significant.

FIG. 3 illustrates the variation of the root mean square error of the sparse reconstructed signal (ie, the original signal) with the sparsity in the case of SNR = 20dB, L = 500, and η = 0.25. In FIG. 3, the abscissa represents the sparsity K, and the ordinate represents the root mean square error of the sparse reconstructed signal. With the increase of the sparseness, the root mean square error of the sparse signals reconstructed by the traditional compressed sensing (Ψ = Φ), the alternate projection method APM, the heavy weighting algorithm RWA, and the method proposed by the present invention has been successively increased. The rms error of the signal reconstructed by the proposed algorithm is the smallest, which shows that under the same conditions, the method proposed by the present invention guarantees the accuracy and completeness of the original data restored, and the reconstruction effect is better.

Example two

Further, the present invention also provides a system accordingly. As shown in FIG. 4, the system includes a processor 10, a memory 20, a display 30, and stored on the memory 20 and can run on the processor 10. Procedures for the construction of compressed sensing perceptual matrix when the measurement matrix is disturbed. FIG. 4 shows only some of the components of the system, but it should be understood that it is not required to implement all the illustrated components, and more or fewer components may be implemented instead.

The memory 20 may be an internal storage unit of the system in some embodiments, such as a hard disk or a memory of the system. The memory 20 may also be an external storage device of the system in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), and a secure digital (Secure Digital, SD) card, flash card, etc. Further, the memory 20 may include both an internal storage unit of the system and an external storage device. The memory 20 is configured to store application software and various types of data installed in the system, such as a program code for constructing a compressed sensing and perception matrix when the measurement matrix of the system is disturbed. The memory 20 may also be used to temporarily store data that has been or will be output. In one embodiment, the memory 20 stores a compressed sensing and perception matrix construction program 40 when the measurement matrix is disturbed. The compressed sensing and perception matrix construction program 40 when the measurement matrix is disturbed may be executed by the processor 10 to implement the measurement matrix. Construction method of compressed sensing perceptual matrix during disturbance.

In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, configured to run program codes or process data stored in the memory 20, such as A method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed is performed.

In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-type liquid crystal display, and an OLED (Organic Light-Emitting Diode) touch device. The display 30 is used to display information on the system and to display a visualized user interface. The components 10-30 of the system communicate with each other via a system bus.

In an embodiment, when the processor 10 executes the compressed sensing and perception matrix construction program 40 when measuring the matrix disturbance in the memory 20, the following steps are implemented:

The actual measurement data is reconstructed by using the perception matrix to recover the original signal; specifically, it is described in the above S10-S40.

Example three

The present invention also provides a storage medium that stores a compressed sensing perception matrix construction program 40 when the measurement matrix is disturbed, and implements the foregoing when the compressed sensing perception matrix construction program 40 is executed by the processor 10 when the measurement matrix is disturbed. The steps of the method for constructing the compressed sensing sensing matrix when the measurement matrix is disturbed are as described above.

In summary, the present invention discloses a method, system and medium for constructing a compressed sensing perception matrix when measuring a matrix disturbance. The method includes generating a random matrix as an expected measurement matrix, performing sparse measurement on a sampled signal, constructing actual measurement data corresponding to the actual measurement matrix, and performing optimization processing on the expected measurement matrix to obtain an actual measurement matrix. Constructing a perceptual matrix according to the best estimated value of the actual measurement matrix; reconstructing the actual measurement data through the perceptual matrix to recover the original signal. The present invention constructs a perception matrix by estimating an actual perception matrix in an interference environment, accurately recovers original data by using the received data, and improves the signal reconstruction effect.

Of course, a person of ordinary skill in the art can understand that the implementation of all or part of the processes in the methods of the foregoing embodiments can be accomplished by using a computer program to instruct related hardware (such as a processor, a controller, etc.). In a computer-readable storage medium, when the program is executed, the program may include processes according to the foregoing method embodiments. The storage medium may be a memory, a magnetic disk, an optical disk, or the like.

It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or changes can be made according to the above description, and all these improvements and changes should fall within the protection scope of the claims attached to the present invention.

Claims

A method for constructing a compressed sensing perception matrix when a measurement matrix is disturbed, characterized in that the method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed includes:

Generate a random matrix as the expected measurement matrix, perform sparse measurement on the sampled signal, and construct the actual measurement data corresponding to the actual measurement matrix;

Performing optimization processing on the expected measurement matrix to obtain an optimal estimation value of the actual measurement matrix;

Constructing a perception matrix according to an optimal estimation value of the actual measurement matrix;

The actual measurement data is reconstructed through the perception matrix to recover the original signal.
The method for constructing a compressed sensing perceptual matrix when the measurement matrix is disturbed according to claim 1, wherein the generated random matrix is used as an expected measurement matrix, performing sparse measurement on the sampled signal, and constructing an actual measurement matrix corresponding to the actual Before the measurement data included:

Receive all sent original signals;

Sampling the original signal to obtain a sampling signal.
The method for constructing a compressed sensing perceptual matrix when the measurement matrix is disturbed according to claim 1, wherein the generated random matrix is used as an expected measurement matrix, performing sparse measurement on the sampled signal, and constructing an actual measurement matrix corresponding to the actual measurement matrix. The measurement data includes:

Generate a random matrix as the expected measurement matrix by software, and define the difference between the actual measurement matrix and the expected measurement matrix as the disturbance difference matrix;

Sparse measurement is performed on the sampled signal through the actual measurement matrix to construct actual measurement data corresponding to the actual measurement matrix.
The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed according to claim 1, wherein the performing optimal processing on the expected measurement matrix to obtain an optimal estimation value of the actual measurement matrix specifically comprises:

Constructing an estimation model of the actual measurement matrix according to the actual measurement data;

Performing optimization processing on the estimation model to obtain an optimal solution of the estimation model;

According to the optimal solution of the estimation model, an optimal estimation value of the actual measurement matrix is obtained.
The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed according to claim 4, wherein the obtaining the optimal estimation value of the actual measurement matrix according to the optimal solution of the estimation model specifically comprises:

When the square of the second norm absolute value of the perturbation difference of the column vector corresponding to the actual measurement matrix and the expected measurement matrix is not greater than a preset perturbation threshold, a Lagrangian of the estimated model is constructed by a Lagrangian multiplier algorithm Lange equation

Obtaining the interval range of the Lagrange multiplier corresponding to the Lagrange equation according to the Lagrange equation;

Randomly select a value in the interval range as an initial value, and obtain an optimal value of the Lagrange equation by a Newton method;

According to the optimal value, an optimal solution of the estimation model, that is, an optimal estimated value of the actual measurement matrix is obtained.
The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed according to claim 5, wherein the constructing the perception matrix according to the optimal estimation value of the actual measurement matrix specifically comprises:

Obtain the optimal estimate of the actual measurement matrix;

A perception matrix is constructed according to the optimal estimation value of the actual measurement matrix.
The method for constructing a compressed sensing perception matrix when the measurement matrix is disturbed according to claim 6, wherein the reconstructing the actual measurement data through the sensing matrix to recover the original signal specifically comprises:

Obtaining the perception matrix;

Perform reconstruction processing on the actual measurement data to recover the original signal.
The method for constructing a compressed sensing perceptual matrix when a measurement matrix is disturbed according to claim 1, wherein the random matrix obeys a Gaussian distribution.
A system, characterized in that the system includes: a memory, a processor, and a compressed sensing and perception matrix construction program when the measurement matrix stored in the memory and operable on the processor is disturbed, the measurement When the matrix perturbation compressive sensing perceptual matrix construction program is executed by the processor, the steps of implementing the measurement matrix perturbation compressive perceptual perception matrix construction method according to any one of claims 1 to 8 are implemented.
A storage medium, characterized in that the storage medium stores a compressed sensing perception matrix construction program when the measurement matrix is disturbed, and implements claim 1- when the compressed sensing perception matrix construction program is executed by a processor when the measurement matrix is disturbed. Steps of the method for constructing a compressed sensing perceptual matrix when the measurement matrix is disturbed according to any one of 8 items.