Iterative hard threshold sparse signal recovery method and system based on heavy ball method

Abstract

The invention discloses an iteration 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 jitter vector and a sparse estimation upper limit; s2, establishing a sparse signal optimization problem based on random jitter based on the input data; and S3, solving the sparse signal optimization problem by using an iterative hard threshold algorithm based on a heavy ball method, and outputting a final sparse signal estimation value. Compared with an existing complex optimization method, the method has the advantages that the calculation complexity is greatly reduced while the high recovery precision is kept, the method has remarkable advantages in a sparse signal recovery task, the amplitude and direction of the sparse signal can be rapidly and accurately recovered, and the method is suitable for large-scale popularization and application. And an efficient sparse signal recovery tool is provided for practical application of single-bit compressed sensing.

Description

Technical Field

[0001] The present invention relates to the technical field of communication signal processing, and in particular to an iterative hard threshold sparse signal recovery method and system based on a heavy sphere method. Background Art

[0002] Compressed sensing (CS) has been widely applied in electronic engineering across multiple technical fields, including communications and signal processing, demonstrating its significant value in signal acquisition and reconstruction. This method exploits the sparsity or compressibility of signals, enabling effective reconstruction of the original signal even at sampling rates far below the Nyquist-Shannon criterion. Unlike the traditional "sample first, compress later" approach, CS compresses data during the sampling process, significantly alleviating the cost, efficiency, and data redundancy bottlenecks of traditional methods. However, in resource-limited systems, measurement data often needs to be quantized due to storage capacity and hardware complexity constraints. Single-bit compressed sensing (1-bit CS) is an extreme form of this quantization strategy, retaining only the sign information (positive or negative) of each measurement, significantly reducing the requirements for storage space and hardware resources.

[0003] In the traditional single-bit compressed sensing framework, a unit modulus normalization constraint is usually imposed on the original signal, so that the recovery process can only obtain the signal's directional information, but cannot accurately recover its amplitude information. Therefore, relying solely on single-bit measurements to simultaneously reconstruct the amplitude and direction of the signal remains a major challenge in current research. To alleviate this problem, some researchers have proposed introducing random dithering technology, which adds carefully designed random dithering to the signal during the measurement phase, thereby improving the ability to characterize the complete structure of the original signal and effectively recovering its amplitude and direction. Despite this, most existing single-bit signal recovery methods still rely on solving complex convex or non-convex optimization problems, and their computational cost increases significantly with the growth of the signal dimension, resulting in not only low computational efficiency in high-dimensional scenarios, but also difficulty in ensuring the recovery quality. Therefore, it is still urgent to study a sparse signal recovery method that combines high recovery accuracy and computational efficiency. Summary of the Invention

[0004] In order to overcome the defects and shortcomings of existing single-bit signal recovery methods, this invention provides an iterative hard threshold sparse signal recovery method and system based on the heavy sphere method, which achieves the purpose of reducing the signal recovery calculation time and improving the sparse signal recovery performance.

[0005] To achieve the above object, the technical solution of the present invention is:

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

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

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

[0009] S3, using an iterative hard threshold algorithm based on the heavy sphere method to solve the sparse signal optimization problem, and outputting a final sparse signal estimation value.

[0010] Optionally, given a sparse estimate signal x k When , the sparse signal optimization problem based on random jitter is expressed as follows:

[0011]

[0012] Where y represents a single-bit observation vector, A represents the perception matrix, τ represents the random jitter vector, s represents the sparse estimation upper limit, ⊙ represents the element-by-element 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, estimate the sparse signal x 1 =x 0 =0

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

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

[0017] S321, calculate the amplitude estimation value b of the current iteration k

[0018] S322, calculate the gradient of the objective function

[0019] S323, update the sparse signal estimation value Among them H s (·) represents a hard threshold operation, which retains the s components with the largest absolute values ​​in the vector and sets the rest to zero;

[0020] S33, repeat step 32 until the stopping condition is met, the iteration stops, and the final sparse signal estimation value x is output 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 estimation value meeting a preset convergence threshold.

[0022] Optionally, the iteration stop 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:

[0025] b k =|Ax k -τ|

[0026] Among them, A is the perception matrix, x k is the signal estimation value of the current iteration, τ is the random jitter vector, and the symbol |·| represents taking the absolute value of each component of the vector.

[0027] Optionally, the step size parameter α and momentum parameter β are selected according to the restricted strong convexity and restricted strong smoothness conditions of the objective function, and are expressed as:

[0028]

[0029] Among them, ξ s and ρ s are the restricted strong smoothness and restricted strong convexity parameters of the objective function respectively.

[0030] In a second aspect, the present invention provides an iterative hard threshold sparse signal recovery system based on a heavy sphere method, comprising:

[0031] A data input module, configured to input data, wherein the data includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit;

[0032] An optimization problem building module, which builds a random jitter-based sparse signal optimization problem based on input data;

[0033] The recovery module solves the sparse signal optimization problem by using an iterative hard threshold algorithm based on the heavy sphere method and outputs a final sparse signal estimation value.

[0034] In a third aspect, 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, 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 sphere method as described in any of the above items.

[0035] In a fourth aspect, the present invention provides a computer-readable storage medium, wherein the storage medium 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 are loaded and executed by a processor to implement the iterative hard threshold sparse signal recovery method based on the heavy sphere method as described in any of the above items.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] In traditional single-bit compressed sensing frameworks, a unit modulus normalization constraint is typically imposed on the original signal, which means that the recovery process can only obtain the signal's directional information, but cannot accurately recover its amplitude information. This limitation severely restricts the effectiveness of single-bit compressed sensing in practical applications, especially in scenarios where accurate recovery of the signal amplitude is required. To alleviate this problem, although some researchers have proposed introducing random dithering technology 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. Their computational cost increases significantly with the growth of the signal dimension, resulting in not only low computational efficiency but also difficulty in ensuring recovery quality in high-dimensional scenarios.

[0038] To address these issues, this paper proposes an iterative hard-threshold sparse signal recovery method based on the heavy-ball method, overcoming the shortcomings of traditional single-bit compressed sensing methods in recovering signal amplitude. Compared with existing complex optimization methods, the iterative hard-threshold algorithm based on the heavy-ball method (HBIHT-DOCS algorithm) significantly reduces computational complexity while maintaining high recovery accuracy. This gives it a significant advantage in sparse signal recovery tasks, enabling it to 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 Schematic diagram of the flow of the iterative hard threshold sparse signal recovery method based on the heavy sphere method according to an embodiment of the present application;

[0041] Figure 2 Schematic diagram of the signal-to-noise ratio (SNR) of signal recovery and the sparsity s of the actual signal in the simulation experiment of this application;

[0042] Figure 3 Schematic diagram of the structure of the iterative hard threshold sparse signal recovery system based on the heavy sphere method in an embodiment of the present application;

[0043] Figure 4 Schematic diagram of an electronic device for implementing iterative hard threshold sparse signal recovery based on the heavy sphere method in an embodiment of the present application. DETAILED DESCRIPTION

[0044] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0045] Example:

[0046] It should be noted that the terms "including" and "having" in the embodiments of the present invention and any variations thereof are intended to cover non-exclusive inclusions. 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 clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or devices.

[0047] The word “exemplary” is used hereinafter to mean “serving as an example, example, or illustration.” Any embodiment described as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0048] The following explains some of the terms used in the embodiments of the present application 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 * is the real sparse signal, that is, the signal to be recovered, and y is the single-bit measurement value. In this model, the real sparse signal is often constrained to a unit modulus, that is: *||2=1. The task of sparse signal recovery is: given a known perceptual matrix A and a single-bit measurement value y, recover the true sparse signal x * .

[0050] Random jitter single-bit compressed sensing: Based on the 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 obeys an independent and identically distributed uniform distribution, that is, τ i ~U[-λ,λ], the selection of the uniform distribution parameter λ is related to the upper limit of the modulus length of the real sparse signal.

[0051] Sparse signal: In the field of compressed sensing, a sparse signal is one 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] Restricted strong convexity: If there exists a constant ρ s >0, so 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 parameter ρ s The restricted strong convexity of , where <·> represents the inner product operation.

[0056] Restricted strong smoothness: If there exists a constant ξ s >0, so 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 parameter ξ s The limitation of strong smoothness.

[0059] In the single-bit compressed sensing problem 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 take a long time to compute and produce suboptimal signal recovery results. To address this issue, this paper proposes an iterative hard-threshold sparse signal recovery method based on the heavy sphere method, which achieves 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 sphere method, which may specifically include the following steps:

[0061] S1, input data, the data includes a single-bit measurement value Perception Matrix Random Jitter Vector Sparse estimation upper bound s;

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

[0063] S3, using an iterative hard threshold algorithm based on the heavy sphere method to solve the sparse signal optimization problem, and outputting a final sparse signal estimation value, so that the sparse signal can be recovered from the single-bit measurement value with the random jitter vector.

[0064] It can be seen that this method uses the iterative hard threshold algorithm based on the heavy sphere method to solve the sparse signal optimization problem, overcoming the shortcomings of the traditional single-bit compressed sensing method in restoring the signal amplitude.

[0065] In a specific embodiment, given a sparse estimation signal x k When , the sparse signal optimization problem based on random jitter can be expressed as follows:

[0066]

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

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

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

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

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

[0072] S321, calculate the amplitude estimation value b of the current iteration k

[0073] S322, calculate the gradient of the objective function

[0074] S333, update the sparse signal estimation value Among them H s (·) represents a hard threshold operation, which retains the s components with the largest absolute values ​​in the vector and sets the rest to zero; the momentum term β(x k -x k -1 ) uses the information from the previous iteration to speed up the convergence and significantly improve the computational efficiency of the algorithm.

[0075] S33, repeat step 32 until the stopping condition is met, the iteration stops, and the final sparse signal estimation value x is output k .

[0076] In this way, through the above steps, the final sparse signal estimation value x can be output quickly and accurately. k , recovering the amplitude and direction of the sparse signal.

[0077] Exemplarily, the stopping condition includes reaching a preset maximum number of iterations or the difference between two consecutive iterations of the signal estimation value meets a preset convergence threshold, which is 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, the amplitude estimate b k The calculation method is:

[0081] b k =|Ax k -τ|

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

[0083] Thus, the amplitude estimate b k =|Ax k-τ| provides key amplitude information for the recovery process, so that the complete structure of the signal can be accurately characterized.

[0084] For example, the step size parameter α and the momentum parameter β are selected according to the restricted strong convexity and restricted strong smoothness conditions of the objective function, which can be expressed as:

[0085]

[0086] Among them, ξ s and ρ s are the restricted strong smoothness and restricted strong convexity parameters of the objective function respectively.

[0087] In this way, the step size parameter α and momentum parameter β are selected in the above way. The selection of the step size parameter α and momentum parameter β is based on the restricted strong convexity and restricted strong smoothness conditions of the objective function, ensuring the stability and efficiency of the algorithm under different signal dimensions and sparsity.

[0088] In summary, the amplitude estimation b of the HBIHT-DOCS algorithm provided in this embodiment is k =|Ax k -τ| provides key amplitude information for the recovery process, so that the complete structure of the signal can be accurately described. At the same time, the momentum term β(x k -x k-1 ) uses the information of the previous iteration to accelerate the convergence speed and significantly improve the computational efficiency of the algorithm. In addition, this embodiment also provides an optimal selection method for the step size parameter α and the momentum parameter β. The selection of these parameters is based on the restricted strong convexity and restricted strong smoothness conditions 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 the 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.

[0089] In the above embodiment, it is assumed that each element in the perception matrix A is independent and identically distributed and obeys the standard normal distribution; the real s sparse signal x * Each element of is independent and identically distributed and obeys the standard normal distribution, and then its modulus is rescaled to [r, R], where r = 2, R = 5; each element of the random jitter vector τ is independent and identically distributed and obeys the uniform distribution U[-λ, λ], where λ ≥ r; set the algorithm step size parameter α and momentum parameter β, where for the objective function in the 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 restricted strong convexity parameter ρ sand constrained strong smoothness parameter ξ s The experimental results of this embodiment are the average results of more than 100 independent experiments.

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

[0091] As shown in Table 1, the average CPU running time (in seconds) of the above-mentioned BHIHT-DOCS algorithm and the existing single-bit signal recovery methods that rely on solving convex or non-convex optimization problems are compared with the actual signal sparsity s, where m = 400 and n = 800. As can be seen from the figure, under different sparsity conditions, the average CPU running time of the BHIHT-DOCS algorithm is at least 50 times faster than that of the other methods, and combined with Figure 2 As shown in Figure 3, the HBIHT-DOCS algorithm achieves higher signal recovery performance in less time.

[0092] Table 1

[0093]

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

[0095] A data input module 310 is configured to input data, wherein the data includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit;

[0096] An optimization problem building module 320 builds a random jitter-based sparse signal optimization problem based on the input data;

[0097] The recovery module 330 solves the sparse signal optimization problem using an iterative hard threshold algorithm based on the heavy sphere method and outputs a final sparse signal estimation value.

[0098] It can be seen that the system uses the iterative hard threshold algorithm based on the heavy sphere method to solve the sparse signal optimization problem, overcoming the shortcomings of the traditional single-bit compressed sensing method in restoring the signal amplitude.

[0099] Since this system is a system corresponding to the iterative hard threshold sparse signal recovery method based on the heavy sphere method in an embodiment of the present invention, and the principle of solving the problem by this system is similar to that of this method, the implementation of this system can refer to the implementation process of the above-mentioned method embodiment, and the repeated parts will not be repeated.

[0100] See also Figure 4 Based on the same inventive concept, an embodiment of the present invention also provides an electronic device, which 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 sphere method as described above.

[0101] It is understood that the memory may include random access memory (RAM) or read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory may be used to store instructions, programs, codes, code sets, or instruction sets. The memory may include a program storage area and a data storage area, wherein the program storage 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 data storage area may store data created based on the use of the server, etc.

[0102] The processor may include one or more processing cores. The processor utilizes various interfaces and circuits to connect various components within the server. It executes various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory, as well as accessing data stored in memory. 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 a combination of a central processing unit (CPU) and a modem. The CPU primarily processes the operating system and application programs, while the modem handles wireless communications. It is understood that the modem may not be integrated into the processor and may be implemented separately via a single chip.

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

[0104] Based on the same inventive concept, an embodiment of the present invention also provides a computer-readable storage medium, which stores at least one instruction, at least one program, a code set or an instruction set. 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 sphere method as described above.

[0105] Those skilled in the art will appreciate that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program. The program can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, magnetic 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 sphere method in an embodiment of the present invention, and the principle of solving the problem by the storage medium is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above-mentioned method embodiment, and the repeated parts will not be repeated.

[0107] In some possible implementations, various aspects of the methods of the embodiments of the present invention may also be implemented in the form of a program product, which includes program code. When the program product is run on a computer device, the program code is used to cause the computer device to perform the steps of the sparse signal recovery method according to various exemplary embodiments of the present application described above in this specification. The executable computer program code or "code" for performing each embodiment may be written in a high-level programming language 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 reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0109] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made based on the essence of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. An iterative hard threshold sparse signal recovery method based on the heavy sphere method, characterized in that: include: S1, input data, the data includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit; S2, establishing a random jitter-based sparse signal optimization problem based on the input data; S3, using an iterative hard threshold algorithm based on the heavy sphere method to solve the sparse signal optimization problem, and outputting a final sparse signal estimation value.

2. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 1, characterized in that: Given a sparse estimated signal x k When , the sparse signal optimization problem based on random jitter is expressed as follows: Where y represents a single-bit observation vector, A represents the perception matrix, τ represents the random jitter vector, s represents the sparse estimation upper limit, ⊙ represents the element-by-element multiplication operation, ‖x‖0 represents the number of non-zero elements in vector x, and ||·||2 represents norm.

3. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 2, characterized in that: The step S3 comprises: S30, initialize the number of iterations k = 1, estimate the sparse signal x 1 =x 0 =0 S31, set the iteration stop condition, step size parameter a, momentum parameter β; S32, for each iteration k, perform the following steps: S321, calculate the amplitude estimation value b of the current iteration k S322, calculate the gradient of the objective function S323, update the sparse signal estimation value Among them H s (·) represents a hard threshold operation, which retains the s components with the largest absolute values ​​in the vector and sets the rest to zero; S33, repeat step 32 until the stopping condition is met, the iteration stops, and the final sparse signal estimation value x is output k .

4. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 3, characterized in that: The iteration stopping condition includes reaching a preset maximum number of iterations or the difference between two consecutive iterations of the signal estimation value meeting a preset convergence threshold.

5. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 4, characterized in that: The iteration stop condition is expressed as: ||x k -x k-1 ||2≤∈ Where ∈ is the preset convergence threshold, and k represents the number of iterations.

6. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 3, characterized in that: The amplitude estimate b k The calculation method is: b k =|Ax k -τ| Among them, A is the perception matrix, x k is the signal estimation value of the current iteration, τ is the random jitter vector, and the symbol |·| represents taking the absolute value of each component of the vector.

7. The iterative hard threshold sparse signal recovery method based on the heavy sphere method according to claim 3, characterized in that: The step size parameter α and momentum parameter β are selected according to the restricted strong convexity and restricted strong smoothness conditions of the objective function, which can be expressed as: Among them, ξ s and ρ s are the restricted strong smoothness and restricted strong convexity parameters of the objective function respectively.

8. An iterative hard threshold sparse signal recovery system based on the heavy sphere method, characterized in that: include: A data input module, configured to input data, wherein the data includes a single-bit observation vector, a perception matrix, a random jitter vector, and a sparse estimation upper limit; An optimization problem building module, which builds a random jitter-based sparse signal optimization problem based on input data; The recovery module solves the sparse signal optimization problem by using an iterative hard threshold algorithm based on the heavy sphere method and outputs a final sparse signal estimation value.

9. 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 sphere method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The storage medium 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 are loaded and executed by the processor to implement the iterative hard threshold sparse signal recovery method based on the heavy sphere method as described in any one of claims 1 to 7.

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