Compressive sensing reconstruction method and system based on iterative weighted least mean square error

Abstract

The present application belongs to the technical field of compressed sensing reconstruction, and particularly relates to a compressed sensing reconstruction method based on iterative weighted least mean square error, which comprises: parameter initialization of a sampling matrix, an initial weight and a regularization coefficient; according to an iterative weighted least mean square error algorithm, reconstructing a compressed sensing signal to obtain an original recovery signal; updating the regularization coefficient according to the original recovery signal; judging whether the convergence degree meets a threshold according to the convergence degree of the original recovery signal of the current iteration and the last iteration to obtain a final recovery signal; through signal reconstruction of compressed sensing, the problem of low accuracy of traditional signal reconstruction algorithms is effectively solved, and the accuracy of signal reconstruction is ensured; and through the introduction of the regularization coefficient and the updating algorithm, the number of iterations is reduced, the convergence speed of the iterative weighted least mean square error algorithm is improved, and the problem of high calculation cost caused by the high number of iterations of the traditional iterative weighted least mean square error algorithm is solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of compressed sensing reconstruction, and particularly relates to a compressed sensing reconstruction method and system based on iterative weighted least mean square error. BACKGROUND

[0002] Compared with the traditional Nyquist sampling system which firstly samples at a high speed and then compresses data, compressed sensing directly samples a signal with sparsity or compressibility at a Nyquist sampling rate. Therefore, an under-Nyquist sampling system based on the compressed sensing theory can use a low-power low-speed analog-to-digital converter to complete high-speed signal sampling, and relatively low-speed digital devices to complete signal processing, storage and transmission. Since compressed sensing adopts under-Nyquist rate sampling, the signal obtained by sampling needs to be processed by a signal reconstruction algorithm to obtain the correct initial signal. Therefore, the signal reconstruction algorithm is the research focus of compressed sensing technology.

[0003] Current signal reconstruction algorithms mainly fall into two categories. One is a signal reconstruction algorithm based on a greedy algorithm, which has the characteristics of low complexity and fast convergence speed. However, due to the local optimization characteristic of the algorithm, the accuracy of signal reconstruction is low. The second category is an optimization algorithm based on 0 norm minimization. Since 0 norm minimization is an NP-hard problem, in practice, an algorithm for minimizing a norm greater than 0, such as 1 norm and (0 < v < 1, v is the norm size) norm, is often used to solve the signal reconstruction problem. Compared with the greedy algorithm, this method improves the accuracy of signal reconstruction, especially the (0 < v < 1) norm minimization method, which can obtain better signal reconstruction accuracy because it is closer to 0 norm. However, the traditional solution to the (0 < v < 1) norm minimization problem, such as the Bayesian learning method, has a high computational complexity and is difficult to apply in practical environments. Therefore, the present application proposes an iterative weighted least mean square error algorithm with a regularization coefficient update, which improves the accuracy of signal reconstruction in compressed sensing and reduces the number of iterations, thereby reducing the computational complexity of signal reconstruction. SUMMARY

[0004] The present application aims to provide a compressed sensing reconstruction method and system based on iterative weighted least mean square error, which aims to solve the technical problems in the prior art that signal reconstruction converges quickly but has low accuracy, or the signal is accurate but the calculation is complex, which cannot meet the demand of keeping high accuracy and low computational complexity in signal reconstruction, resulting in difficulty in application in practical environments.

[0005] To achieve the above-mentioned purpose, the embodiments of the present application provide a compressed sensing reconstruction method based on iterative weighted least mean square error, characterized in that the method comprises:

[0006] S100, parameter initialization of a sampling matrix, an initial weight and a regularization coefficient;

[0007] S200 reconstructs the compressed sensing signal using an iterative weighted least mean square error algorithm to obtain the original recovered signal;

[0008] S300 updates the regularization coefficients based on the original recovery signal;

[0009] S400 determines whether the convergence degree meets the threshold based on the convergence degree of the original recovery signals of the current iteration and the previous iteration, and obtains the final recovery signal.

[0010] Optionally, the step of reconstructing the compressed sensing signal and obtaining the original recovered signal according to the iterative weighted least mean square error algorithm specifically includes:

[0011] S210 acquires the undersampled signal and uses the weighted least mean square error algorithm to obtain the original recovered signal for this iteration.

[0012] S220 obtains the weight coefficients for this iteration based on the original recovery signal and regularization coefficients of this iteration;

[0013] S230 updates the penalty coefficient based on the weight coefficients obtained in this iteration and the original recovery signal.

[0014] Optionally, the step of obtaining the undersampled signal and obtaining the original recovered signal for the current iteration using the weighted least mean square error algorithm specifically includes:

[0015] S211 obtains the under-Nyquist sampling rate;

[0016] S212 obtains the undersampled signal based on the undersampled Nyquist sampling rate, and obtains the original recovered signal for this iteration based on the following formula:

[0017] x (l) =W (l) Φ t (ΦW (l) Φ t +λ(x (l-1) )*I) -1 y, where y is the undersampled signal, x (l) This is the solution for this round, i.e., the original recovered signal, W. (l) It is an N-dimensional diagonal matrix, with diagonal elements being the weight coefficients obtained in the previous round, I being the identity matrix, and λ being the penalty coefficient.

[0018] Optionally, the step of obtaining the weight coefficients for the current iteration based on the original recovery signal and regularization coefficients of the current iteration specifically includes:

[0019] Obtain the original recovery signal and the regularization coefficients from the previous round, and then obtain the weight coefficients for the current iteration based on the following formula:

[0020] Where, x (l) The original recovery signal, This represents the regularization coefficient from the previous round.

[0021] Optionally, the step of updating the penalty coefficient based on the weight coefficients obtained in this iteration and the original recovery signal specifically includes:

[0022] Obtain the undersampled signal, the original recovered signal obtained after this iteration, and the weight coefficients, and update the penalty coefficients based on the following formula three:

[0023] Where y is the undersampled signal, x (l) The original recovery signal, These are the weighting coefficients.

[0024] Optionally, the step of updating the regularization coefficients based on the original recovery signal specifically includes:

[0025] Obtain the original recovery signal and update the regularization coefficients based on the original recovery signal according to the following formula:

[0026] Where, h(x) i represents the i-th largest element in vector x, and k represents the sparsity of the signal.

[0027] Optionally, the step of determining whether to terminate the iteration and obtain the final recovery signal based on the convergence degree of the original recovery signals of the current iteration and the previous iteration specifically includes:

[0028] S410 calculates the difference between two adjacent iterations to obtain the degree of convergence.

[0029] S420 compares the degree of convergence with a fixed threshold to determine whether the original recovered signal meets the fixed threshold.

[0030] If the convergence degree is less than a fixed threshold, then the original recovered signal is determined to meet the fixed threshold, and the final recovered signal is obtained.

[0031] If the convergence degree is greater than the fixed threshold in step S440, return to step S200 and proceed to the next iteration.

[0032] Optionally, the step of comparing the degree of convergence with a fixed threshold to determine whether the original recovered signal meets the fixed threshold specifically includes:

[0033] S421 calculates the difference between the original recovered signals from two adjacent iterations to obtain the iterative signal difference;

[0034] S422 obtains a fixed threshold and compares the difference between the iterative signals and the fixed threshold.

[0035] A compressed sensing reconstruction system based on iterative weighted minimum mean square error includes:

[0036] The initialization module is used to initialize the parameters of the sampling matrix, initial weights, and regularization coefficients.

[0037] The signal reconstruction module is used to reconstruct the compressed sensing signal and obtain the original recovered signal according to the iterative weighted least mean square error algorithm.

[0038] The regularization coefficient update module is used to update the regularization coefficients based on the original recovery signal;

[0039] The judgment module is used to determine whether the convergence degree meets the threshold based on the convergence degree of the original recovery signal in the current iteration and the previous iteration, and to obtain the final recovery signal.

[0040] A computer device for running a program, wherein the program executes the compressed sensing reconstruction method based on iterative weighted minimum mean square error.

[0041] The compressed sensing reconstruction method based on iterative weighted minimum mean square error provided in this invention has at least one of the following technical effects:

[0042] By initializing the sampling matrix, initial weights, and regularization coefficients, multiple initialization parameters are obtained, enabling the first calculation based on iterative weighted minimum mean square error. The compressed sensing signal is reconstructed using the iterative weighted minimum mean square error algorithm to obtain the original recovered signal. This signal reconstruction effectively addresses the low accuracy problem of traditional signal reconstruction algorithms, ensuring the accuracy of signal reconstruction. Furthermore, by introducing regularization coefficients and an update algorithm, the number of iterations is reduced, improving the convergence speed of the iterative weighted minimum mean square error algorithm. This solves the problem of high computational cost caused by excessive iterations in traditional iterative weighted minimum mean square error algorithms, significantly reducing computational cost and improving computational efficiency. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 A flowchart of a compressed sensing reconstruction method based on iterative weighted minimum mean square error provided in an embodiment of the present invention;

[0045] Figure 2 A flowchart for obtaining the original recovery signal provided in an embodiment of the present invention;

[0046] Figure 3 This is a flowchart of obtaining the original recovered signal using the weighted least mean square error algorithm, provided in an embodiment of the present invention.

[0047] Figure 4 A flowchart for determining the degree of convergence provided in an embodiment of the present invention;

[0048] Figure 5 A flowchart of the convergence degree judgment method provided in the embodiments of the present invention;

[0049] Figure 6 A schematic diagram of a compressed sensing reconstruction system based on iterative weighted minimum mean square error provided in an embodiment of the present invention;

[0050] Figure 7 A structural block diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0051] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0052] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0053] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0054] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0055] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0056] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0057] In one embodiment of the present invention, such as Figure 1 As shown, a compressed sensing reconstruction method based on iterative weighted minimum mean square error is provided, characterized in that the method includes:

[0058] S100: Initialize the parameters of the sampling matrix, initial weights, and regularization coefficients;

[0059] Specifically, in this step, the sampling matrix, initial weight coefficients, and regularization coefficients are redefined and initialized. The initial sampling matrix is ​​defined as Φ∈R. M×N The initial weight coefficient is defined as w (0) =1,…,1, the initial regularization coefficient is defined as It should be understood that this parameter is initialized only once during the first iteration of this method, and will be updated based on the results of the previous iteration during the second iteration.

[0060] S200: Reconstruct the compressed sensing signal using the iterative weighted least mean square error algorithm to obtain the original recovered signal;

[0061] Specifically, in this step, by using the iterative weighted least mean square error algorithm for compressed sensing signal reconstruction, the accuracy of reconstruction can be effectively improved, and high-precision compressed sensing signals can be obtained.

[0062] S300: Update the regularization coefficients based on the original recovery signal;

[0063] Specifically, in this step, by introducing a regularization coefficient update algorithm, the convergence speed of the iterative weighted minimum mean square error algorithm can be significantly improved, and the number of iterations can be significantly reduced. This solves the problem of high computational cost caused by excessive iterations in the traditional iterative weighted minimum mean square error algorithm, and reduces the computational complexity of signal reconstruction.

[0064] S400: Based on the convergence degree of the original recovery signals in the current iteration and the previous iteration, determine whether the convergence degree meets the threshold and obtain the final recovery signal.

[0065] Specifically, in this step, the accuracy of compressed sensing reconstructed signals is improved by comparing the convergence of the original recovered signal with the threshold value to determine whether to terminate the iteration.

[0066] By initializing the sampling matrix, initial weights, and regularization coefficients, multiple initialization parameters are obtained, enabling the first calculation based on iterative weighted minimum mean square error. The compressed sensing signal is reconstructed using the iterative weighted minimum mean square error algorithm to obtain the original recovered signal. This signal reconstruction effectively addresses the low accuracy problem of traditional signal reconstruction algorithms, ensuring the accuracy of signal reconstruction. Furthermore, by introducing regularization coefficients and an update algorithm, the number of iterations is reduced, improving the convergence speed of the iterative weighted minimum mean square error algorithm. This solves the problem of high computational cost caused by excessive iterations in traditional iterative weighted minimum mean square error algorithms, significantly reducing computational cost and improving computational efficiency.

[0067] In another embodiment of the invention, such as Figure 2 As shown, the step of reconstructing the compressed sensing signal and obtaining the original recovered signal based on the iterative weighted least mean square error algorithm specifically includes:

[0068] S210: Obtain the undersampled signal and obtain the original recovered signal for this iteration according to the weighted least mean square error algorithm.

[0069] S220: Obtain the weight coefficients for this iteration based on the original recovery signal and regularization coefficients of this iteration;

[0070] S230: Update the penalty coefficient based on the weight coefficients obtained in this iteration and the original recovery signal.

[0071] Specifically, in this step, the undersampled signal is obtained from the undersampled Nyquist sampling rate, and the signal is calculated and defined as the original recovered signal; the updated weight coefficient is calculated based on the original recovered signal and the regularization coefficient of the previous round; and the updated penalty coefficient is obtained based on the updated weight coefficient and the original recovered signal.

[0072] In another embodiment of the invention, such as Figure 3 As shown, the step of obtaining the undersampled signal and obtaining the original recovered signal for the current iteration using the weighted least mean square error algorithm specifically includes:

[0073] S211: Obtain the under-Nyquist sampling rate;

[0074] S212: Obtain the undersampled signal based on the undersampled Nyquist sampling rate, and obtain the original recovered signal for this iteration based on the following formula:

[0075] x (l) =W (l) Φ t (ΦW (l) Φ t +λ(x (l-1) )*I) -1 y, where y is the undersampled signal, x (l) This is the solution for this round, i.e., the original recovered signal, W. (l) It is an N-dimensional diagonal matrix, with diagonal elements being the weight coefficients obtained in the previous round, I being the identity matrix, and λ being the penalty coefficient.

[0076] Specifically, in this step, the undersampled signal is obtained based on the acquired pre-Nyquist sampling rate, and then the presampled signal is substituted into Formula 1. Based on the weight coefficient and penalty coefficient, the updated original recovered signal is obtained. It should be understood that when this round is the first iteration, the initialized weight coefficient and penalty coefficient are used. When this round is the second iteration or subsequent iterations, the weight coefficient and penalty coefficient of the previous round are used for calculation.

[0077] In another embodiment of the present invention, the step of obtaining the weight coefficients of the current iteration based on the original recovery signal and the regularization coefficient of the current iteration specifically includes:

[0078] Obtain the original recovery signal and the regularization coefficients from the previous round, and then obtain the weight coefficients for the current iteration based on the following formula:

[0079] Where, x (l) The original recovery signal, This represents the regularization coefficient from the previous round.

[0080] Specifically, in this step, the obtained original recovery signal and the regularization coefficient of the previous round are substituted into Formula 2 to obtain the updated weight coefficient. It should be understood that when this round is the first iteration, the initialized regularization coefficient is selected, and when this round is the second iteration or subsequent iterations, the regularization coefficient of the previous round is selected for iterative calculation.

[0081] In another embodiment of the present invention, the step of updating the penalty coefficient based on the weight coefficients obtained in the current iteration and the original recovery signal specifically includes:

[0082] Obtain the undersampled signal, the original recovered signal obtained after this iteration, and the weight coefficients, and update the penalty coefficients based on the following formula three:

[0083] Where y is the undersampled signal, x (l) The original recovery signal, These are the weighting coefficients.

[0084] Specifically, in this step, the obtained undersampled signal, original recovered signal, and weighting coefficients are substituted into Formula 3 to obtain the updated penalty coefficients.

[0085] In another embodiment of the present invention, the step of updating the regularization coefficients based on the original recovery signal specifically includes:

[0086] Obtain the original recovery signal and update the regularization coefficients based on the original recovery signal according to the following formula:

[0087] Where, h(x) i represents the i-th largest element in vector x, and k represents the sparsity of the signal.

[0088] Specifically, in this step, by substituting the original recovered signal into Formula 4, it can be ensured that the regularization coefficient can adapt to the signal recovery accuracy corresponding to the current iteration number in each iteration. This can prevent premature convergence or difficulty in convergence of the iteration, and improve the high accuracy of signal reconstruction.

[0089] In another embodiment of the invention, such as Figure 4 As shown, the step of determining whether to terminate the iteration and obtain the final recovery signal based on the convergence degree of the original recovery signals of the current iteration and the previous iteration specifically includes:

[0090] S410: Calculate the difference between two adjacent iterations to obtain the degree of convergence;

[0091] Specifically, in this step, the degree of convergence is calculated as the difference between the original recovered signals in two adjacent iterations; that is, the degree of convergence can be defined as x. (l) -x (l-1) .

[0092] S420: Compare the degree of convergence with a fixed threshold to determine whether the original recovered signal meets the fixed threshold.

[0093] Specifically, in this step, the fixed threshold is set to one percent of the required recovery accuracy.

[0094] S430: If the convergence degree is less than the fixed threshold, the original recovered signal is determined to meet the fixed threshold, and the final recovered signal is obtained;

[0095] S440: If the convergence is greater than the fixed threshold, return to step S200 and proceed to the next iteration.

[0096] Specifically, in this step, if the convergence does not meet the fixed threshold, the process returns to the second step for the next iteration. If the threshold is met, the recovery process is terminated, and the final recovered signal is obtained. This ensures the accuracy of the compressed sensing signal, making the computational complexity low while maintaining high accuracy, enabling its application in real-world environments.

[0097] In another embodiment of the invention, such as Figure 5 As shown, the step of comparing the convergence degree with a fixed threshold to determine whether the original recovered signal meets the fixed threshold specifically includes:

[0098] S421: Obtain the iterative signal difference by subtracting the original recovered signals from two adjacent iterations;

[0099] Specifically, in this step, the difference between the original recovered signals of two adjacent iterations is obtained to obtain the difference of the iterative signal, which is then compared with the fixed threshold to determine whether the condition is met. If so, the final recovered signal is obtained, and the reconstruction of the compressed sensing signal is completed.

[0100] S422: Obtain a fixed threshold and compare the difference between the iterative signals and the fixed threshold.

[0101] Specifically, in this step, the fixed threshold is one percent of the required recovery accuracy.

[0102] Specifically, the present invention also provides a compressed sensing reconstruction system based on iterative weighted minimum mean square error, such as... Figure 6 As shown, it includes:

[0103] The initialization module is used to initialize the parameters of the sampling matrix, initial weights, and regularization coefficients.

[0104] The signal reconstruction module is used to reconstruct the compressed sensing signal and obtain the original recovered signal according to the iterative weighted least mean square error algorithm.

[0105] The regularization coefficient update module is used to update the regularization coefficients based on the original recovery signal;

[0106] The judgment module is used to determine whether the convergence degree meets the threshold based on the convergence degree of the original recovery signal in the current iteration and the previous iteration, and to obtain the final recovery signal.

[0107] In another embodiment of the present invention, the signal reconstruction module is further configured to:

[0108] Obtain the undersampled signal, and use the weighted least mean square error algorithm to obtain the original recovered signal for this iteration;

[0109] Based on the original recovery signal and regularization coefficient of this iteration, obtain the weight coefficient of this iteration;

[0110] The penalty coefficient is updated based on the weight coefficients obtained in this iteration and the original recovery signal.

[0111] In another embodiment of the present invention, the signal reconstruction module is further configured to:

[0112] Obtain the under-Nyquist sampling rate;

[0113] Based on the undersampled Nyquist sampling rate, the undersampled signal is obtained, and the original recovered signal for this iteration is obtained based on Formula 1.

[0114] In another embodiment of the present invention, the signal reconstruction module is further configured to:

[0115] Obtain the original recovery signal and the regularization coefficient of the previous round, and obtain the weight coefficient of the current iteration based on Formula 2.

[0116] In another embodiment of the present invention, the signal reconstruction module is further configured to:

[0117] Obtain the undersampled signal, the original recovered signal obtained after this round of iteration, and the weight coefficients, and update the penalty coefficients based on Formula 3.

[0118] In another embodiment of the present invention, the regularization coefficient update module is further configured to:

[0119] Obtain the original recovery signal and update the regularization coefficients based on Formula 4 according to the original recovery signal.

[0120] In another embodiment of the present invention, the determining module is further configured to:

[0121] Calculate the difference between two consecutive iterations to obtain the degree of convergence;

[0122] Compare the degree of convergence with a fixed threshold to determine whether the original recovered signal meets the fixed threshold.

[0123] If the convergence is less than a fixed threshold, the original recovered signal is determined to meet the fixed threshold, and the final recovered signal is obtained.

[0124] If the convergence is greater than a fixed threshold, proceed to the next iteration.

[0125] In another embodiment of the present invention, the determining module is further configured to:

[0126] The difference between the original recovered signals from two consecutive iterations is calculated to obtain the difference in the iterative signals.

[0127] Obtain a fixed threshold and compare the difference between the iterative signals and the fixed threshold.

[0128] In another embodiment of the invention, a computer device is also provided, including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by one or more processors, the programs including control instructions for performing an iterative weighted minimum mean square error compressed sensing reconstruction method.

[0129] The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 7 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a compressed sensing reconstruction method based on iterative weighted minimum mean square error. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0130] In another embodiment of the present invention, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described iterative weighted minimum mean square error compressed sensing reconstruction method.

[0131] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0132] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An iterative weighted least mean square error based compressive sensing reconstruction method, characterized in that, The method comprises: S100: parameter initialization of a sampling matrix, an initial weight and a regularization coefficient; S200: reconstructing a compressed sensing signal according to an iterative weighted least mean square error algorithm to obtain an original recovery signal; S300: updating the regularization coefficient according to the original recovery signal; S400: judging whether the convergence degree meets a threshold value according to the convergence degree of the original recovery signal of the current iteration and the last iteration to obtain a final recovery signal; The step of reconstructing the compressed sensing signal according to the iterative weighted least mean square error algorithm to obtain the original recovery signal specifically comprises: S210: obtaining an undersampling signal, and obtaining the original recovery signal of the current iteration according to the weighted least mean square error algorithm; S220: obtaining the weight coefficient of the current iteration according to the original recovery signal of the current iteration and the regularization coefficient; S230: updating the penalty coefficient according to the weight coefficient and the original recovery signal obtained in the current iteration; The step of obtaining the undersampling signal and obtaining the original recovery signal of the current iteration according to the weighted least mean square error algorithm specifically comprises: S211: obtaining an undersampling rate; S212: obtaining the undersampling signal according to the undersampling rate, and obtaining the original recovery signal of the current iteration based on the following formula one: x (l) = W (l) Φ t (ΦW (l) Φ t + λ(x (l-1) )*I) -1 y, where y is the under-sampled signal, x (l) is the solution of this round, i.e., the original recovered signal, W (l) is an N-dimensional diagonal matrix with the weight coefficients obtained in the last round as the diagonal elements, I is an identity matrix, λ is a penalty coefficient, l is the lth round, and Φ represents the initial sampling matrix. The step of obtaining the weight coefficient of the current iteration according to the original recovery signal of the current iteration and the regularization coefficient specifically comprises: obtaining the original recovery signal and the regularization coefficient of the last iteration, and obtaining the weight coefficient of the current iteration based on the following formula two: where x (l) is the original recovered signal, is the regularization coefficient of the last iteration, denotes the value of the jth element of the original recovered signal, denotes the weight coefficient value of the jth element of the current iteration.

2. The compressive sensing reconstruction method based on iterative weighted least mean square error according to claim 1, characterized in that, The step of updating the penalty coefficient according to the weight coefficient and the original recovery signal obtained in the current iteration specifically comprises: obtaining the undersampling signal, the original recovery signal and the weight coefficient obtained after the current iteration, and updating the penalty coefficient based on the following formula three: where y is the under-sampled signal, x (l) is the original recovered signal, represents the weight coefficient value of the i-th element of this round of iteration, λ is the penalty coefficient, Φ represents the initial sampling matrix, and N represents the total number of elements, represents the value of the i-th element of the original recovered signal.

3. The method of claim 1, wherein, The step of updating the regularization coefficient according to the original recovery signal specifically comprises: obtaining the original recovery signal, and updating the regularization coefficient based on the following formula four according to the original recovery signal: where h(x (l+1) ) k+1 denotes the k+1th largest element in the original recovered signal, k represents the sparsity of the signal, denotes updating the regularization coefficient.

4. The method of claim 1, wherein, The step of judging whether to terminate the iteration according to the convergence degree of the original recovery signal of the current iteration and the last iteration to obtain the final recovery signal specifically comprises: S410: calculating the difference value of the adjacent two iterations to obtain the convergence degree S420: comparing the convergence degree with a fixed threshold value to judge whether the original recovery signal meets the fixed threshold value; S430: if the convergence degree is less than the fixed threshold value, it is judged that the original recovery signal meets the fixed threshold value, and the final recovery signal is obtained, S440: if the convergence degree is greater than the fixed threshold value, return to step S200 for the next iteration.

5. The compressive sensing reconstruction method based on iterative weighted least mean square error of claim 4, wherein, The step of comparing the convergence degree with the fixed threshold value to judge whether the original recovery signal meets the fixed threshold value specifically comprises, S421: obtaining the iteration signal difference value by subtracting the original recovery signals of the adjacent two iterations; S422: obtaining the fixed threshold value, and comparing the iteration signal difference value with the fixed threshold value.

6. A compressed sensing reconstruction system based on an iterative weighted least mean square error, comprising: an initialization module configured to perform parameter initialization of a sampling matrix, an initial weight and a regularization coefficient; The signal reconstruction module is configured to reconstruct the compressed sensing signal according to an iterative weighted least mean square error algorithm to obtain an original recovery signal. S210: Obtain an undersampling signal, and obtain an original recovery signal of the current iteration according to a weighted least mean square error algorithm. S220: Obtain a weight coefficient of the current iteration according to the original recovery signal of the current iteration and a regularization coefficient. S230: Update a penalty coefficient according to the weight coefficient obtained in the current iteration and the original recovery signal. The step of obtaining the undersampling signal and obtaining the original recovery signal of the current iteration according to the weighted least mean square error algorithm specifically includes: S211: Obtain an undersampling rate. S212: Obtain the undersampling signal according to the undersampling rate, and obtain the original recovery signal of the current iteration based on the following formula one: x (l) = W (l) Φ t (ΦW (l) Φ t + λ(x (l-1) )*I) -1 y, where y is the under-sampled signal, x (l) is the solution of this round, i.e., the original recovered signal, W (l) is an N-dimensional diagonal matrix with the weight coefficients obtained in the last round as the diagonal elements, I is an identity matrix, λ is a penalty coefficient, l is the lth round, and Φ represents the initial sampling matrix. The step of obtaining the weight coefficient of the current iteration according to the original recovery signal of the current iteration and the regularization coefficient specifically includes: Obtain the original recovery signal and the regularization coefficient of the last iteration, and obtain the weight coefficient of the current iteration based on the following formula two: where x (l) is the original recovered signal, is the regularization coefficient of the last iteration, denotes the value of the jth element of the original recovered signal, denotes the weight coefficient value of the jth element of the current iteration; The regularization coefficient updating module is configured to update the regularization coefficient according to the original recovery signal. The judging module is configured to judge whether the convergence degree meets a threshold according to the convergence degree of the original recovery signals of the current iteration and the last iteration, and obtain a final recovery signal.

7. A computer device, characterized by The computer device is configured to run a program, and the program is configured to execute the method in any one of claims 1 to 5 when running.

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