A method and device for compressed sensing signal processing based on deterministic measurement matrix

Abstract

A method and device for compressive sensing signal processing based on a deterministic measurement matrix, belonging to the field of signal transmission technology, includes the following steps: constructing a compressive sensing measurement matrix; obtaining an original signal and preprocessing the original signal; performing a sparse transformation on the preprocessed original signal to obtain a sparse transformation signal; compressing the sparse transformation signal according to the compressive sensing measurement matrix to obtain a measurement signal; transmitting the measurement signal; wherein the construction of the compressive sensing measurement matrix includes the following steps: determining the original signal length, the measurement signal length and the column weight; generating a subspace; generating an affine surface according to the subspace; constructing an initial measurement matrix according to the affine surface; normalizing the initial measurement matrix according to the column weight to obtain a compressive sensing measurement matrix. The matrix compression rate of the present application is low, and the storage space of the measurement signal is small.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal transmission, and in particular relates to a method and device for compressive sensing signal processing based on a deterministic measurement matrix. Background Art

[0002] Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems, used to acquire and reconstruct sparse or compressible signals. This theory breaks through the traditional Nyquist sampling theorem and can obtain discrete samples of the signal through random sampling at a rate much lower than the Nyquist sampling rate, and then perfectly reconstruct the signal using a nonlinear reconstruction algorithm. It is widely used in wireless communications, direction of arrival estimation, beamforming, and imaging.

[0003] At present, the main compressed sensing measurement matrix is ​​a random Gaussian matrix. For example, the Chinese patent with the publication number CN117375624A discloses a method for constructing a half-tensor compressed sensing measurement matrix based on KL transformation, which includes: step 1, generating a Gaussian random matrix A and a sparse basis matrix Ψ according to the dimension and characteristics of the signal to be compressed; step 2, performing a half-tensor product on A to obtain a measurement matrix Φ, and then multiplying it by Ψ to obtain a sensing matrix D; step 3, performing a KL transformation on D to obtain a new sensing matrix D′; step 4, reversely calculating the final measurement matrix Φ′ from D′. It fully adapts to the signal diversity and security requirements in WSN data compression and acquisition, while enhancing the effect of signal reconstruction.

[0004] However, when using a random Gaussian matrix as a compressed sensing measurement matrix, since the random Gaussian matrix is ​​usually a dense matrix, which means that most elements in the matrix are not zero, the storage requirements are high and the computational complexity is high.

[0005] Therefore, there is an urgent need to develop a compressed sensing signal processing method and device based on a deterministic measurement matrix to solve the problems in the prior art. Summary of the invention

[0006] The purpose of the present invention is to provide a compressed sensing signal processing method and device based on a deterministic measurement matrix, by replacing a random Gaussian matrix with a deterministic compressed sensing measurement matrix, so as to solve the problems of high storage requirements and high computational complexity of using a random Gaussian matrix as a compressed sensing measurement matrix proposed in the above background technology.

[0007] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0008] A method for compressive sensing signal processing based on a deterministic measurement matrix comprises the following steps:

[0009] Construct compressed sensing measurement matrix;

[0010] Obtaining the original signal and preprocessing the original signal;

[0011] Performing sparse transformation on the preprocessed original signal to obtain a sparse transformation signal;

[0012] According to the compressed sensing measurement matrix, the sparse transformation signal is compressed to obtain a measurement signal;

[0013] transmitting the measurement signal;

[0014] The construction of the compressed sensing measurement matrix includes the following steps:

[0015] Determine the original signal length, measured signal length and column weight;

[0016] generate Type subspace and Type subspace;

[0017] according to Type subspace and Type subspace, generating affine Faces and Affine noodle;

[0018] According to affine Faces and Affine Surface, construct the initial measurement matrix;

[0019] According to the column weight, the initial measurement matrix is ​​normalized to obtain the compressed sensing measurement matrix.

[0020] Furthermore, the original signal length is calculated by the following formula:

[0021] ;

[0022] in, is the original signal length,

[0023] ;

[0024] The measurement signal length is calculated by the following formula:

[0025] ;

[0026] in, To measure the signal length,

[0027] ;

[0028] The column weight is calculated by the following formula:

[0029] ;

[0030] Where W is the column weight,

[0031] ;

[0032] in, is a prime power;

[0033] are all integers and satisfy:

[0034] ;

[0035] ;

[0036] .

[0037] Further, the Type subspace and The subspace is generated by the following steps:

[0038] by is a finite field, express superior dimensional row vector space, for a finite field All satisfied The non-singular matrix , plus matrix multiplication operations form a singular symplectic group ,in,

[0039] ;

[0040] express The zero-order matrix, represents the identity matrix, Representation Matrix The transpose of , a non-singular matrix Indicates that the determinant of the matrix is ​​non-zero;

[0041] When the singular symphony In vector space The mapping on is:

[0042] ;

[0043] ;

[0044] Then the vector space And the above mappings constitute a finite field on Vicchi Space ;

[0045] Limited domain The unit row vector on Composition Dimensional subspace ,in .

[0046] When a finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met:

[0047] and Contracts, where ;and hour, for Type subspace;

[0048] When a finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met:

[0049] and Contracts, where ;and hour, for Type subspace.

[0050] Further, the generated affine Faces and Affine The following steps are included:

[0051] Finite field on Vicchi Space The vectors on are denoted as points, singular symplectic space about The coset of the subspace of type is affine Surface; Strange Similitude about The coset of the subspace of type is affine noodle.

[0052] Furthermore, the construction of the initial measurement matrix comprises the following steps:

[0053] Define a binary matrix , , whose rows are given by the affine Surface calibration, columns by affine Surface calibration.

[0054] When Affine Includes Affine When the surface, the element is equal to 1;

[0055] When Affine The surface does not contain Affine Surface, then the element is equal to 0.

[0056] Furthermore, the initial measurement matrix is ​​normalized according to the column weight to obtain the compressed sensing measurement matrix, which is performed by the following formula:

[0057] ;

[0058] in, is the compressed sensing measurement matrix, W is the column weight, is the initial measurement matrix.

[0059] Further, the preprocessing of the original signal comprises the following steps:

[0060] The original signal is divided into frames, and the length of each frame signal is .

[0061] A computer-readable storage medium stores a computer program, which implements the steps of the method when executed by a processor.

[0062] A computer device comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0063] A computer program product comprises a computer program or instructions, which implement the steps of the method when executed by a processor.

[0064] The present invention provides a deterministic compressed sensing measurement matrix, which, as a compressed sensing measurement matrix for compressing an original signal, has the following beneficial effects:

[0065] (1) The measurement matrix can be generated and stored first, and does not need to be generated on the hardware every time a signal is transmitted, thus ensuring the certainty of the effect.

[0066] (2) Small storage space required, only storage data, and only multiplication operations and addition operations, where . Since the Gaussian random matrix has non-zero elements, it needs to store data, and each signal compression requires multiplication operations and An addition operation.

[0067] (3) Less computation is required for signal compression.

[0068] The column weight of the compressed sensing measurement matrix in this application and The ratio is:

[0069] ;

[0070] The ratio of the deterministic measurement matrix constructed based on the singular symplectic space over a finite field is:

[0071] ;

[0072] It can be seen that the amount of calculation required for signal compression in the present application is less than the amount of calculation for constructing a deterministic measurement matrix in a singular symplectic space over a finite field.

[0073] Other features and advantages of the present invention will be disclosed in detail in the following specific embodiments and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 Flowchart of this application. DETAILED DESCRIPTION

[0075] A method for compressed sensing signal processing based on deterministic measurement matrix, such as Figure 1 As shown, the following steps are included:

[0076] S1: construct compressed sensing measurement matrix;

[0077] S2: Acquire an original signal, and preprocess the original signal;

[0078] S3: Perform sparse transformation on the preprocessed original signal to obtain a sparse transformed signal;

[0079] S4: compressing the sparse transformation signal according to the compressed sensing measurement matrix to obtain a measurement signal;

[0080] S5: Transmitting the measurement signal.

[0081] The construction of the compressed sensing measurement matrix in step S1 includes the following steps:

[0082] S11: Determine the original signal length, the measured signal length and the column weight;

[0083] S12: Generate Type subspace and Type subspace;

[0084] S13: Generate Affine Faces and Affine Surface, and according to affine Faces and Affine Surface, construct affine singular symplectic space;

[0085] S14: construct an initial measurement matrix;

[0086] S15: Normalize the initial measurement matrix according to the column weight to obtain a compressed sensing measurement matrix.

[0087] The original signal length in step S11 , measure signal length And column weight , calculated by the formula.

[0088] The original signal length Calculated by the following formula:

[0089] ;

[0090] in, is the original signal length,

[0091] ;

[0092] The measurement signal length Calculated by the following formula:

[0093] ;

[0094] in, To measure the signal length,

[0095] ;

[0096] The column weight W is calculated by the following formula:

[0097] ;

[0098] Where W is the column weight,

[0099] ;

[0100] The data can be substituted into the following formula:

[0101] ;

[0102] ;

[0103] Among them, the parameters is a prime power;

[0104] parameter are all integers and satisfy:

[0105] ;

[0106] ;

[0107] .

[0108] Preferably, the original signal length can be confirmed based on the original signal And measure the signal length Or the original signal length And measure the signal length range, and then adjust the parameters according to the formula The column weight You can also confirm first.

[0109] In step S12, the Type subspace and The subspace includes the following steps:

[0110] by is a finite field, where is a prime power, express superior dimensional row vector space, for a finite field All satisfied The non-singular matrix , plus matrix multiplication operations form the singular symplectic group ,in,

[0111] ;

[0112] express The zero-order matrix, express The unit matrix, Representation Matrix The transpose of , a non-singular matrix Indicates that the determinant of the matrix is ​​nonzero.

[0113] When the singular symphony In vector space The mapping on is:

[0114] ;

[0115] ;

[0116] Then the vector space And the above mappings constitute a finite field on Vicchi Space .

[0117] Limited domain The unit row vector on Composition Dimensional subspace ,in .

[0118] When a finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met:

[0119] and Contracts, where ;

[0120] Subspace and subspace The dimension of the intersection of ,Right now hour, for Type subspace.

[0121] Similarly, the parameter Change to , we can get To the type subspace Q. Type subspace and The subspace Q is generated Type subspace and Type subspace.

[0122] That is, when the finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met:

[0123] and Contracts, where ;

[0124] Subspace and subspace The dimension of the intersection of ,Right now hour, for Type subspace.

[0125] Finite Fields superior dimensional row vector space All The set of subspaces is denoted as , the number of sets is recorded as . The same is true for the subspace.

[0126] In step S13, an affine Faces and Affine The following steps are included:

[0127] Finite field on Vicchi Space The vectors on are denoted as points, singular symplectic space about The coset of the subspace of type is affine Surface, strange and simplistic space about The coset of the subspace of type is affine noodle.

[0128] In step S13, according to the affine Faces and Affine Surface, construct affine singular symplectic space, including the following steps:

[0129] when or When With face Associating this association with the affine Surface on dimensional affine singular symplectic space, denoted by . Affine The dimension of the face is .

[0130] From the above, we can see that affine singular symplectic space and singular symplectic space based on finite field are two related but different concepts in finite field algebra. Affine singular symplectic space is an affineization of a singular symplectic space, which translates points in linear space to a new set through vectors, inheriting the degenerate bilinear form properties of singular symplectic space, but because the origin is removed, there is no longer a fixed zero vector, and singular symplectic space geometrically corresponds to a degenerate symplectic geometric structure with a fixed origin. In addition, the association relationship, that is, the inclusion relationship, in affine singular symplectic space based on finite field is essentially different from that in singular symplectic space, and the counting formula of the space is also different.

[0131] The initial measurement matrix is ​​constructed in S14, comprising the following steps:

[0132] Define a binary matrix , , whose rows are given by the affine Surface calibration, columns by affine Surface calibration.

[0133] When Affine Includes Affine When the surface, the element is equal to 1;

[0134] When Affine The surface does not contain Affine Surface, then the element is equal to 0.

[0135] Right now noodle,

[0136] .

[0137] The initial measurement matrix Compression ratio Calculated by the following formula:

[0138] .

[0139] The step S15 normalizes the initial measurement matrix according to the column weight to obtain the compressed sensing measurement matrix, which is performed by the following formula:

[0140] Normalize the measurement matrix .

[0141] The step S2 pre-processes the original signal, including the following steps:

[0142] The original signal is divided into frames, and the length of each frame signal is .

[0143] The step S3 performs sparse transformation on the preprocessed original signal to obtain a sparse transformation signal, which is specifically:

[0144] The framed signal is subjected to discrete cosine sparse transform, which is a prior art and will not be described in detail in this application.

[0145] In step S4, the sparse transformation signal is compressed according to the compressed sensing measurement matrix to obtain a measurement signal;

[0146] Its mathematical model is ;

[0147] in, To measure the signal, is the compressed sensing measurement matrix, is the original signal.

[0148] The method further includes step S6: restoring the received signal through a reconstruction algorithm.

[0149] The reconstruction algorithm is a prior art and may be an OMP algorithm or the like.

[0150] Preferably, the parameters can be selected as follows:

[0151] ,but

[0152] ;

[0153] ;

[0154] ;

[0155] .

[0156] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for compressed sensing signal processing based on a deterministic measurement matrix, characterized in that: The steps include: Construct compressed sensing measurement matrix; Obtaining the original signal and preprocessing the original signal; Performing sparse transformation on the preprocessed original signal to obtain a sparse transformation signal; According to the compressed sensing measurement matrix, the sparse transformation signal is compressed to obtain a measurement signal; transmitting the measurement signal; The construction of the compressed sensing measurement matrix includes the following steps: Determine the original signal length, measured signal length and column weight; generate Type subspace and Type subspace; according to Type subspace and Type subspace, generating affine Faces and Affine noodle; According to affine Faces and Affine Surface, construct the initial measurement matrix; According to the column weight, the initial measurement matrix is ​​normalized to obtain the compressed sensing measurement matrix; The calculation formula of the original signal length is as follows: ； in, is the original signal length, ； The calculation formula of the measurement signal length is as follows: ； in, To measure the signal length, ； The calculation formula of the column weight is as follows: ； Where W is the column weight, ； in, is a prime power; are all integers and satisfy: ； ； ； Type subspace and The subspace is generated by the following steps: by is a finite field, express superior dimensional row vector space, for a finite field All satisfied The non-singular matrix , plus matrix multiplication operations form a singular symplectic group ,in, ； express The zero-order matrix, express The unit matrix, Representation Matrix The transpose of , a non-singular matrix Indicates that the determinant of the matrix is ​​non-zero; When the singular symphony In vector space The mapping on is: ； ； Then the vector space And the above mappings constitute a finite field on Vicchi Space ; Limited domain The unit row vector on Composition Dimensional subspace ,in ; When a finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met: with a contract where ;and hour, for Type subspace; When a finite field superior dimensional row vector space one of the Dimensional subspace When the following conditions are met: and Contracts, where ;and hour, for Type subspace; The generated affine Faces and Affine The following steps are included: Finite field on Vicchi Space The vectors on are denoted as points, singular symplectic space about The coset of the subspace of type is affine Surface; Strange Similitude about The coset of the subspace of type is affine noodle; The construction of the initial measurement matrix comprises the following steps: Define a binary matrix , , whose rows are given by the affine Surface calibration, columns by affine Surface calibration; When Affine Noodles include Affine When the surface, the element is equal to 1; When Affine The surface does not contain Affine Surface, then the element is equal to 0.

2. The method for compressed sensing signal processing based on a deterministic measurement matrix according to claim 1, characterized in that: The initial measurement matrix is ​​normalized according to the column weight to obtain the compressed sensing measurement matrix, which is performed by the following formula: ； in, is the compressed sensing measurement matrix, For column weight, is the initial measurement matrix.

3. The method for compressive sensing signal processing based on deterministic measurement matrix according to claim 1 or 2, characterized in that: The preprocessing of the original signal comprises the following steps: The original signal is divided into frames, and the length of each frame signal is .

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

5. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

6. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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