An iterative hard thresholding sparse signal recovery method and system based on reweighted l1 norm

Abstract

The application discloses an iterative hard threshold sparse signal recovery method and system based on a heavy ball method, and belongs to the technical field of communication signal processing. The method comprises the following steps: S1, inputting data, wherein the data comprises a single-bit observation vector, a sensing matrix, a random dithering vector and a sparse estimation upper limit; S2, establishing a sparse signal optimization problem based on random dithering based on the input data; S3, solving the sparse signal optimization problem by using an iterative hard threshold algorithm based on the heavy ball method, and outputting a final sparse signal estimation value. Compared with existing complex optimization methods, the method can greatly reduce the calculation complexity while maintaining high recovery accuracy, has a significant advantage in the sparse signal recovery task, can quickly and accurately recover the amplitude and direction of the sparse signal, and provides an efficient sparse signal recovery tool for the practical application of single-bit compressive sensing.

Description

Technical Field

[0001] This invention relates to the field of communication signal processing technology, and specifically to an iterative hard threshold sparse signal recovery method and system based on the heavy ball method. Background Technology

[0002] Compressed sensing (CS) has been widely applied in electronic engineering across various technical fields, including communication and signal processing, demonstrating significant value, particularly in signal acquisition and reconstruction. This method leverages the sparsity or compressibility of signals to effectively reconstruct the original signal even at sampling rates far below the Nyquist-Shannon criterion. Unlike the traditional "sample first, compress later" approach, compressed sensing performs data compression during the sampling process, significantly alleviating the bottlenecks of traditional methods in terms of cost, efficiency, and data redundancy. However, in some resource-constrained systems, due to limitations in storage capacity and hardware complexity, measurement data often requires quantization. Single-bit compressed sensing (1-bit CS) is an extreme form of this quantization strategy, retaining only the symbolic information (positive or negative) of each measurement, thereby greatly reducing the demand for storage space and hardware resources.

[0003] In traditional single-bit compressed sensing frameworks, a unit-magnitude normalization constraint is typically imposed on the original signal, resulting in the recovery process only obtaining the signal's direction information and failing to accurately recover its amplitude information. Therefore, reconstructing both the amplitude and direction of a signal simultaneously using only single-bit measurements remains a significant challenge in current research. To alleviate this problem, some researchers have proposed introducing random dithering techniques, which involve adding carefully designed random dithering to the signal during the measurement phase. This enhances the ability to characterize the complete structure of the original signal, enabling the effective recovery of both its amplitude and direction. Nevertheless, most existing single-bit signal recovery methods still rely on solving complex convex or non-convex optimization problems, the computational cost of which increases significantly with the signal's dimensionality. This leads to low computational efficiency and difficulty in guaranteeing recovery quality in high-dimensional scenarios. Therefore, researching a sparse signal recovery method that combines high recovery accuracy with computational efficiency remains urgently needed. Summary of the Invention

[0004] To overcome the shortcomings and deficiencies of existing single-bit signal recovery methods, this invention provides an iterative hard-threshold sparse signal recovery method and system based on the heavy ball method, which achieves the goal of reducing the computation time of signal recovery and improving the performance of sparse signal recovery.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] In a first aspect, the present invention provides an iterative hard-threshold sparse signal recovery method based on the heavy ball method, comprising:

[0007] S1, Input data, which includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit;

[0008] S2, based on the input data, establish a sparse signal optimization problem based on random jitter;

[0009] S3. The sparse signal optimization problem is solved using an iterative hard thresholding algorithm based on the heavy ball method, and the final sparse signal estimate is output.

[0010] Optionally, given a sparse estimated signal x k The established optimization problem for sparse signals based on random jitter can be expressed in the following form:

[0011]

[0012] Where y represents a single-bit observation vector, A represents the sensing matrix, τ represents the random jitter vector, s represents the upper bound of sparse estimation, ⊙ represents the element-wise multiplication operation, ‖x‖0 represents the number of non-zero elements in vector x, and ||·||2 represents... Norm.

[0013] Optionally, step S3 includes:

[0014] S30, Initialize the number of iterations k = 1, and estimate the sparse signal x. 1 =x 0 =0

[0015] S31, set the iteration stopping condition, step size parameter α, momentum parameter β;

[0016] S32, for each iteration x, perform the following steps:

[0017] S321, Calculate the magnitude estimate b for the current iteration. k

[0018] S322, Calculate the gradient of the objective function.

[0019] S323, Update the sparse signal estimate Where H s (·) represents a hard thresholding operation, which retains the s components with the largest absolute values ​​in the vector and sets the remaining components to zero.

[0020] S33, Repeat step 32 until the stopping condition is met, then stop the iteration and output the final sparse signal estimate x. k .

[0021] Optionally, the iteration stopping condition includes reaching a preset maximum number of iterations or the difference between two consecutive iterations of the signal estimate satisfying a preset convergence threshold.

[0022] Optionally, the iteration stopping condition is expressed as: ||x k -x k-1 ||2≤∈

[0023] Where ∈ is the preset convergence threshold, and k represents the number of iterations.

[0024] Optionally, the amplitude estimate b k The calculation method is as follows:

[0025] b k =|Ax k -τ|

[0026] Where A is the perception matrix, x k Let τ be the signal estimate for the current iteration, τ be the random jitter vector, and the symbol |·| denotes taking the absolute value of each component of the vector.

[0027] Optionally, the step size parameter α and momentum parameter β are selected based on the constraints of strong convexity and strong smoothness of the objective function, as follows:

[0028]

[0029] Where, ξ s and ρ s These are the parameters for restricting strong smoothness and restricting strong convexity of the objective function, respectively.

[0030] Secondly, the present invention provides an iterative hard-threshold sparse signal recovery system based on the heavy ball method, comprising:

[0031] The data input module is used to input data, which includes a single-bit observation vector, a sensing matrix, a random jitter vector, and a sparse estimation upper limit.

[0032] The optimization problem construction module establishes a sparse signal optimization problem based on random jitter based on the input data;

[0033] The recovery module uses an iterative hard thresholding algorithm based on the heavy ball method to solve the sparse signal optimization problem and outputs the final sparse signal estimate.

[0034] Thirdly, the present invention provides an electronic device comprising a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the iterative hard threshold sparse signal recovery method based on the heavy ball method as described in any of the preceding claims.

[0035] Fourthly, the present invention provides a computer-readable storage medium storing at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the iterative hard threshold sparse signal recovery method based on the heavy ball method as described in any of the preceding claims.

[0036] Compared with the prior art, the advantages of this invention are as follows:

[0037] In traditional single-bit compressed sensing frameworks, a unit-magnitude normalization constraint is typically imposed on the original signal. This means that the recovery process can only obtain the signal's direction information, but cannot accurately recover its amplitude information. This limitation severely restricts the efficiency of single-bit compressed sensing in practical applications, especially in scenarios requiring precise recovery of signal amplitude. To alleviate this problem, although some researchers have proposed introducing random dithering techniques to improve the ability to characterize the complete structure of the original signal, most existing single-bit signal recovery methods still rely on solving complex convex or non-convex optimization problems. The computational cost increases significantly with the signal dimension, resulting in low computational efficiency and difficulty in guaranteeing recovery quality in high-dimensional scenarios.

[0038] To address the aforementioned issues, this invention proposes an iterative hard thresholding method for sparse signal recovery based on the heavy sphere method, overcoming the shortcomings of traditional single-bit compressed sensing methods in recovering signal amplitude. Compared to existing complex optimization methods, the iterative hard thresholding algorithm based on the heavy sphere method (HBIHT-DOCS algorithm) significantly reduces computational complexity while maintaining high recovery accuracy, giving it a significant advantage in sparse signal recovery tasks. It can quickly and accurately recover the amplitude and direction of sparse signals, providing an efficient sparse signal recovery tool for the practical application of single-bit compressed sensing. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating the iterative hard threshold sparse signal recovery method based on the heavy ball method according to an embodiment of this application.

[0041] Figure 2 This is a schematic diagram showing the signal-to-noise ratio (SNR) of the recovered signal and the sparsity s of the real signal in the simulation experiment of this application;

[0042] Figure 3 This is a schematic diagram of the iterative hard threshold sparse signal recovery system based on the heavy ball method in an embodiment of this application;

[0043] Figure 4 This is a schematic diagram of an electronic device implementing iterative hard threshold sparse signal recovery based on the heavy ball method in an embodiment of this application. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0045] Example:

[0046] It should be noted that the terms "comprising" and "having" and any variations thereof in the embodiments of the present invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products, or devices.

[0047] The word “exemplary” as used below means “serving as an example, embodiment, or illustration.” Any embodiment illustrated as an “exemplary” need not be construed as superior to or better than other embodiments.

[0048] The following explanations of some terms used in the embodiments of this application are provided to facilitate understanding by those skilled in the art.

[0049] Traditional single-bit compressed sensing: Generally speaking, the mathematical model of traditional single-bit compressed sensing can be expressed as y = sign(Ax) * ), where A is the perception matrix, x * This is the real sparse signal, i.e., the signal that needs to be recovered, where y is a single-bit measurement. In this model, the real sparse signal is often subject to a unit-magnitude normalization constraint, i.e.: ||x *||2=1. The task of sparse signal recovery is: given a known sensing matrix A and a single-bit measurement y, to recover the true sparse signal x. * .

[0050] Random Jitter Single-Bit Compressed Sensing: Based on traditional single-bit compressed sensing, a carefully designed random jitter is introduced. Its mathematical model can be expressed as y = sign(Ax) * -τ), where each element of the random jitter vector τ follows an independent and identically distributed uniform distribution, i.e., τ i ~U[-λ,λ], the selection of the uniform distribution parameter λ is related to the upper limit of the magnitude of the real sparse signal.

[0051] Sparse signals: In the field of compressed sensing, sparse signals refer to signals in which the number of non-zero elements is far less than the number of zero elements. In other words, the value of most elements in the signal is 0.

[0052] Sparsity: In the field of compressed sensing, sparsity is used to measure the number of non-zero elements in a sparse signal. If the sparsity of a sparse signal is s, it means that the number of non-zero elements in the sparse signal does not exceed s.

[0053] Restricting strong convexity: If there exists a constant ρ s >0, such that for any vectors x and x' satisfying ||xx′||0≤s, the differentiable function f(x) satisfies:

[0054]

[0055] Then f(x) is said to have a parameter ρ s The constraint of strong convexity is defined by , where <·> denotes the inner product operation.

[0056] Constraint on strong smoothness: If there exists a constant ξ s >0, such that for any vectors x and x' satisfying ||xx′||0≤s, the differentiable function f(x) satisfies:

[0057]

[0058] Then f(x) is said to have a parameter ξ. s The restriction of strong smoothness.

[0059] In single-bit compressed sensing problems based on random jitter, most existing single-bit signal recovery methods still rely on solving complex convex or non-convex optimization problems. When the signal dimension is large, these methods are computationally time-consuming and produce unsatisfactory signal recovery results. To address these issues, this invention proposes an iterative hard-threshold sparse signal recovery method based on the heavy-ball method, achieving better signal recovery results with less computation time.

[0060] like Figure 1 As shown, this embodiment provides an iterative hard-threshold sparse signal recovery method based on the heavy ball method, which may specifically include the following steps:

[0061] S1, Input data, the data includes single-bit measurements. Perception Matrix Random jitter vector Sparse estimation upper bound s;

[0062] S2, based on the input data, establish a sparse signal optimization problem based on random jitter;

[0063] S3. The sparse signal optimization problem is solved by using an iterative hard thresholding algorithm based on the heavy ball method, and the final sparse signal estimate is output, so that the sparse signal can be recovered from the single-bit measurement with random jitter vector.

[0064] Therefore, this method uses an iterative hard thresholding algorithm based on the heavy ball method to solve the sparse signal optimization problem, overcoming the shortcomings of traditional single-bit compressed sensing methods in recovering signal amplitude.

[0065] In one specific embodiment, given a sparse estimated signal x k The sparse signal optimization problem based on random jitter can be expressed in the following form:

[0066]

[0067] Among them, single-bit measurement value Let s be the sparse signal to be recovered (i.e., vector x has at most s non-zero elements out of n elements), sign denotes the sign function, which acts on each component of the vector and satisfies t≥0 if sign(t)=1, otherwise sign(t)=-1; ⊙ denotes element-wise multiplication, ||x||0 denotes the number of non-zero elements in vector x, and ||·||2 denotes the number of elements in vector x. Norm refers to the norm of a given vector. That norm is

[0068] In one specific embodiment, step S3 above includes the following sub-steps:

[0069] S30, Initialize the number of iterations k = 1, and estimate the sparse signal x. 1 =x 0 =0

[0070] S31, set the iteration stopping condition, step size parameter α, momentum parameter β;

[0071] S32, for each iteration k, perform the following sub-step:

[0072] S321, Calculate the magnitude estimate b for the current iteration. k

[0073] S322, Calculate the gradient of the objective function.

[0074] S333, Update the sparse signal estimate Where H s (·) denotes a hard thresholding operation, retaining the s components with the largest absolute values ​​in the vector and setting the remaining components to zero; the momentum term β(x k -x k-1 By utilizing information from the previous iteration, the convergence speed can be accelerated, significantly improving the computational efficiency of the algorithm.

[0075] S33, Repeat step 32 until the stopping condition is met, then stop the iteration and output the final sparse signal estimate x. k .

[0076] Thus, by following the steps described above, the final sparse signal estimate x can be output quickly and accurately. k This restores the amplitude and direction of the sparse signal.

[0077] For example, the stopping condition includes reaching a preset maximum number of iterations or the difference between two consecutive iterations of the signal estimate satisfying a preset convergence threshold, specifically expressed as:

[0078] ||x k -x k-1 ||2≤∈

[0079] Where ∈ is the preset convergence threshold, and k represents the number of iterations.

[0080] For example, magnitude estimate b k The calculation method is as follows:

[0081] b k =|Ax k -τ|

[0082] Where A is the perception matrix, x k Let τ be the signal estimate for the current iteration, and τ be a random jitter vector. The symbol |·| denotes taking the absolute value of each component of the vector. This amplitude estimate is used to approximate the amplitude information of a single-bit measurement, thereby transforming the nonlinear single-bit compressed sensing problem into an approximate linear compressed sensing problem, which facilitates subsequent signal recovery processing.

[0083] Thus, the magnitude estimate b k =|Ax k-τ| provides crucial amplitude information for the recovery process, enabling the complete structure of the signal to be accurately characterized.

[0084] For example, the step size parameter α and the momentum parameter β are selected based on the constraints of strong convexity and strong smoothness of the objective function, as follows:

[0085]

[0086] Where, ξ s and ρ s These are the parameters for restricting strong smoothness and restricting strong convexity of the objective function, respectively.

[0087] Thus, by selecting the step size parameter α and momentum parameter β in the above manner, and based on the constraints of strong convexity and strong smoothness of the objective function, the stability and efficiency of the algorithm under different signal dimensions and sparsity are ensured.

[0088] In summary, the amplitude estimation b of the HBIHT-DOCS algorithm provided in this embodiment is satisfactory. k =|Ax k -τ| provides crucial amplitude information for the recovery process, enabling the accurate characterization of the signal's complete structure. Simultaneously, the momentum term β(x) in the heavy ball method... k -x k-1 By utilizing information from the previous iteration, the convergence speed is accelerated, significantly improving the computational efficiency of the algorithm. Furthermore, this embodiment provides an optimal selection method for the step size parameter α and momentum parameter β. These parameters are chosen based on the constraints of strong convexity and strong smoothness of the objective function, ensuring the stability and efficiency of the algorithm under different signal dimensions and sparsity. Compared with existing complex optimization methods, the HBIHT-DOCS algorithm significantly reduces computational complexity while maintaining high recovery accuracy, giving it a significant advantage in sparse signal recovery tasks. It can quickly and accurately recover the amplitude and direction of sparse signals, providing an efficient sparse signal recovery tool for practical applications of single-bit compressed sensing.

[0089] In the above embodiments, each element in the perception matrix A is set to be independent and identically distributed and follow a standard normal distribution; the real sparse signal x * Each element of the random jitter vector τ is independent and identically distributed and follows a standard normal distribution. Its magnitude is then scaled back to [r, R], where r = 2 and R = 5. Each element of the random jitter vector τ is independent and identically distributed and follows a uniform distribution U[-λ, λ], where λ ≥ r. The algorithm step size parameter α and momentum parameter β are set, where, for the objective function in the aforementioned sparse signal optimization problem based on random jitter, the square of the minimum and maximum singular values ​​of the perception matrix A is used as its constraint strong convexity parameter ρ. sand the constraint of strong smoothness parameter ξ s The experimental results in this embodiment are the average results of more than 100 independent experiments.

[0090] like Figure 2 The figure shows a comparison of the signal-to-noise ratio (SNR) of the BHIHT-DOCS algorithm with the actual signal sparsity s, where m = 400 and n = 800, compared to existing methods for single-bit signal recovery that rely on solving convex or non-convex optimization problems. As can be seen from the figure, under different sparsity conditions, the BHIHT-DOCS algorithm significantly outperforms other signal recovery methods in signal recovery.

[0091] Table 1 shows a comparison of the average CPU runtime (in seconds) of the BHIHT-DOCS algorithm and existing methods that rely on solving convex or non-convex optimization problems for single-bit signal recovery, with respect to the actual signal sparsity *s*, where *m* = 400 and *n* = 800. The figure shows that, under different sparsity conditions, the average CPU runtime of the BHIHT-DOCS algorithm is at least 50 times faster than other methods, and combined with… Figure 2 As shown, the HBIHT-DOCS algorithm achieves higher signal recovery performance in less time.

[0092] Table 1

[0093]

[0094] See Figure 3 Based on the same inventive concept, embodiments of the present invention also provide an iterative hard threshold sparse signal recovery system 300 based on the heavy ball method, the system comprising:

[0095] Data input module 310 is used to input data, which includes a single-bit observation vector, a sensing matrix, a random jitter vector, and a sparse estimation upper limit.

[0096] The optimization problem construction module 320 establishes a sparse signal optimization problem based on random jitter based on the input data;

[0097] The recovery module 330 uses an iterative hard thresholding algorithm based on the heavy ball method to solve the sparse signal optimization problem and outputs the final sparse signal estimate.

[0098] Therefore, this system uses an iterative hard thresholding algorithm based on the heavy ball method to solve the sparse signal optimization problem, overcoming the shortcomings of traditional single-bit compressed sensing methods in recovering signal amplitude.

[0099] Since this system corresponds to the iterative hard threshold sparse signal recovery method based on the heavy ball method in this embodiment of the invention, and the principle of solving the problem in this system is similar to that of this method, the implementation of this system can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0100] See Figure 4 Based on the same inventive concept, embodiments of the present invention also provide an electronic device, the electronic device including a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, the at least one program, the code set or instruction set being loaded and executed by the processor to realize an iterative hard threshold sparse signal recovery method based on the heavy ball method as described above.

[0101] It is understood that the memory may include random access memory (RAM) or read-only memory. Optionally, the memory may include non-transitory computer-readable storage medium. The memory can be used to store instructions, programs, code, code sets, or instruction sets. The memory may include a stored program area and a stored data area, wherein the stored program area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the various method embodiments described above, etc.; the stored data area may store data created according to the use of the server, etc.

[0102] A processor may include one or more processing cores. The processor connects to various parts of the server via various interfaces and lines, executing instructions, programs, code sets, or instruction sets stored in memory, and accessing data stored in memory to perform various server functions and process data. Optionally, the processor may be implemented using at least one of the following hardware forms: Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), and Programmable Logic Array (PLA). The processor may integrate one or more of the following: Central Processing Unit (CPU) and Modem. The CPU primarily handles the operating system and applications; the modem handles wireless communication. It is understood that the modem may also be implemented as a separate chip without being integrated into the processor.

[0103] Since the electronic device is the electronic device corresponding to the iterative hard threshold sparse signal recovery method based on the heavy ball method in the embodiments of the present invention, and the principle of the electronic device in solving the problem is similar to that of the method, the implementation of the electronic device can refer to the implementation process of the above method embodiments, and the repeated parts will not be described again.

[0104] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or instruction set is loaded and executed by a processor to implement an iterative hard threshold sparse signal recovery method based on the heavy ball method as described above.

[0105] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, including read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0106] Since the storage medium is the storage medium of the iterative hard threshold sparse signal recovery method based on the heavy ball method in the embodiments of the present invention, and the principle of the storage medium in solving the problem is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above method embodiments, and the repeated parts will not be described again.

[0107] In some possible implementations, various aspects of the methods of the embodiments of the present invention can also be implemented as a program product comprising program code that, when run on a computer device, causes the computer device to perform the steps of the sparse signal recovery method according to various exemplary embodiments of the present application described above. The executable computer program code or "code" for performing the various embodiments can be written in high-level programming languages ​​such as C, C++, C#, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0108] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0109] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. An iterative hard-threshold sparse signal recovery method based on the heavy ball method, characterized in that, include: S1, Input data, which includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit; S2, based on the input data, establish a sparse signal optimization problem based on random jitter; S3, The sparse signal optimization problem is solved by using an iterative hard thresholding algorithm based on the heavy ball method, and the final sparse signal estimate is output. Given a sparse estimation signal x k The established optimization problem for sparse signals based on random jitter can be expressed in the following form: Where y represents a single-bit observation vector, A represents the perception matrix, τ represents the random jitter vector, s represents the upper bound of sparse estimation, ⊙ represents the element-wise corresponding multiplication operation, ||x||0 represents the number of non-zero elements in vector x, and ||·||2 represents the l2 norm; Step S3 includes: S30, Initialize the number of iterations k = 1, and estimate the sparse signal x. 1 =x 0 =0 S31, set the iteration stopping condition, step size parameter α, momentum parameter β; S32, for each iteration k, perform the following steps: S321, Calculate the magnitude estimate b for the current iteration. k S322, Calculate the gradient of the objective function. S323, Update the sparse signal estimate Where H s (·) represents a hard thresholding operation, which retains the s components with the largest absolute values ​​in the vector and sets the remaining components to zero. S33, Repeat step 32 until the stopping condition is met, then stop the iteration and output the final sparse signal estimate x. k .

2. The iterative hard-threshold sparse signal recovery method based on the heavy ball method as described in claim 1, characterized in that, The iteration stopping conditions include reaching a preset maximum number of iterations or the difference between two consecutive iterations of the signal estimate satisfying a preset convergence threshold.

3. The iterative hard-threshold sparse signal recovery method based on the heavy ball method as described in claim 2, characterized in that, The iteration stopping condition is expressed as: ||x k -x k-1 ||2≤ε Where ∈ is the preset convergence threshold, and k represents the number of iterations.

4. The iterative hard-threshold sparse signal recovery method based on the heavy ball method as described in claim 1, characterized in that, The amplitude estimate b k The calculation method is as follows: b k =|Ax k -τ| Where A is the perception matrix, x k Let τ be the signal estimate for the current iteration, τ be the random jitter vector, and the symbol |·| denotes taking the absolute value of each component of the vector.

5. The iterative hard-threshold sparse signal recovery method based on the heavy ball method as described in claim 1, characterized in that, The step size parameter α and momentum parameter β are selected based on the constraints of strong convexity and strong smoothness of the objective function, expressed as follows: Where, ξ s and ρ s These are the parameters for restricting strong smoothness and restricting strong convexity of the objective function, respectively.

6. An iterative hard-threshold sparse signal recovery system based on the heavy ball method, characterized in that, include: The data input module is used to input data, which includes a single-bit observation vector, a sensing matrix, a random jitter vector, and a sparse estimation upper limit. The optimization problem construction module establishes a sparse signal optimization problem based on random jitter based on the input data; Given a sparse estimation signal x k The established optimization problem for sparse signals based on random jitter can be expressed in the following form: Where y represents a single-bit observation vector, A represents the perception matrix, τ represents the random jitter vector, s represents the upper bound of sparse estimation, ⊙ represents the element-wise corresponding multiplication operation, ||x||0 represents the number of non-zero elements in vector x, and ||·||2 represents the l2 norm; The recovery module uses an iterative hard thresholding algorithm based on the heavy ball method to solve the sparse signal optimization problem and outputs the final sparse signal estimate, including the following steps: S30, Initialize the number of iterations k = 1, and estimate the sparse signal x. 1 =x 0 =0 S31, set the iteration stopping condition, step size parameter α, momentum parameter β; S32, for each iteration k, perform the following steps: S321, Calculate the magnitude estimate b for the current iteration. k S322, Calculate the gradient of the objective function. S323, Update the sparse signal estimate Where H s (·) represents a hard thresholding operation, which retains the s components with the largest absolute values ​​in the vector and sets the remaining components to zero. S33, Repeat step 32 until the stopping condition is met, then stop the iteration and output the final sparse signal estimate x. k .

7. An electronic device, characterized in that, The electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the iterative hard threshold sparse signal recovery method based on the heavy ball method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the iterative hard threshold sparse signal recovery method based on the heavy ball method as described in any one of claims 1 to 5.

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