Sparse signal reconstruction method, device and medium based on L0 regularization threshold iteration

Abstract

The present invention discloses a sparse signal reconstruction method based on L0 regularized threshold iteration, comprising: taking parameters from a sparse signal parameter set as input and initializing the sparse signal with a zero vector; constructing an intermediate function using the parameters from the sparse signal parameter set; constructing a sparse signal iterative function based on the intermediate function; and terminating the iteration when two adjacent iteration values ​​of the sparse signal iterative function satisfy an iteration termination condition, and outputting the reconstructed sparse signal. The present invention employs an improved L0 regularized threshold iteration algorithm that reconstructs high-dimensional sparse signals by introducing an intermediate function with a smaller value, resulting in a smaller relaxation gap, significantly improved estimation accuracy, and faster convergence.

Description

Technical Field

[0001] The present invention relates to the technical field of compressed sensing signal processing, and more specifically, to a sparse signal reconstruction method, device, and medium based on L0 regularization threshold iteration. Background Art

[0002] In recent years, compressed sensing (CS) technology has attracted widespread attention in fields such as image processing, 5G communications, and radar detection. For sparse signals, CS can overcome the constraints of the Shannon-Nyquist sampling theorem, compressing samples at a rate far less than twice the Nyquist rate and reconstructing the original signal with high precision using a recovery algorithm.

[0003] However, the applicant found that the existing The regularized threshold iterative algorithm has the problems of large estimation error and low solution accuracy, which to some extent limits its application in various CS scenarios. Summary of the Invention

[0004] In response to at least one deficiency or improvement need in the prior art, the present invention provides a sparse signal reconstruction method, device, and medium based on threshold iteration, so as to reduce the relaxation gap and improve the estimation accuracy of the sparse signal.

[0005] To achieve the above object, according to a first aspect of the present invention, a sparse signal reconstruction method based on threshold iteration is provided, comprising:

[0006] Take the parameters in the sparse signal parameter set as input and initialize the sparse signal with a zero vector;

[0007] constructing an intermediate function using parameters in the sparse signal parameter set;

[0008] Constructing a sparse signal iterative function based on the intermediate function;

[0009] If it is determined that two adjacent iteration values ​​of the sparse signal iterative function meet an iteration termination condition, the iteration is terminated and a reconstructed sparse signal is output;

[0010] Wherein, the expression of the sparse signal iterative function is:

[0011]

[0012] The expression of the iteration termination condition is:

[0013]

[0014] The expression of the intermediate function is:

[0015]

[0016] The parameters in the sparse signal parameter set include: the observation signal y∈R M , measurement matrix The sparsity of the signal to be determined ||x||0, the upper limit of the number of iterations η and the first transition parameter α; λ n is the second transition parameter.

[0017] Furthermore, the expression of the first transition parameter is:

[0018] α=max(eigΦ T Φ)+1;

[0019] Among them, max(eigΦ T Φ) represents the matrix Φ T The maximum eigenvalue of Φ, the expression of the first transition parameter characterizes the exact reconstruction condition of the sparse signal.

[0020] Furthermore, the expression of the second transition parameter is:

[0021] λ n =α|(b α (x n )) k+1 | 2 .

[0022] Furthermore, it also includes:

[0023] If it is determined that the two adjacent iteration values ​​of the sparse signal iterative function do not meet the iteration termination condition, then continue to calculate the value of the intermediate function and the value of the second transition parameter, perform calculation of the next iteration value, and again determine whether the two most recent adjacent iteration values ​​of the sparse signal iterative function meet the iteration termination condition.

[0024] Furthermore, the sparse signal is initialized with a zero vector as follows: 11 =0, n=0.

[0025] According to a second aspect of the present invention, an electronic device is also provided, comprising at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit is enabled to perform the steps of any one of the above methods.

[0026] According to a third aspect of the present invention, a storage medium is provided, which stores a computer program executable by an access authentication device. When the computer program runs on the access authentication device, the access authentication device can perform the steps of any of the above methods.

[0027] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0028] The present invention adopts an improved method of reconstructing high-dimensional sparse signals by introducing an intermediate function with a smaller value and a reconstruction function with a smaller relaxation gap. The regularized threshold iterative algorithm makes the relaxation gap smaller, significantly reduces the mean square error, significantly improves the estimation accuracy, and converges faster. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] 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 invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0030] Figure 1 An improved embodiment of the present invention provides Flowchart of the regularized threshold iteration algorithm;

[0031] Figure 2 Improved embodiment of the present invention Comparison of the curves of the regularized threshold iterative algorithm and the original algorithm showing the changes in the number of iterations; Figure 2 middle:

[0032] Number of Iteration n:Number of iterations n;

[0033] Iteration Error (log-scale): Iteration error (logarithmic scale);

[0034] M-hard regularization: Improved Regularization;

[0035] hard regularization: conventional type Regularization;

[0036] Figure 3 Improved embodiment of the present invention Comparison of the mean square error of the regularized threshold iteration algorithm and the original algorithm as the signal-to-noise ratio changes; Figure 3 middle:

[0037] M-hard regularization: Improved Regularization;

[0038] hard regularization: conventional type Regularization;

[0039] SNR: signal-to-noise ratio;

[0040] MSE: mean square error;

[0041] Figure 4 A block diagram of an electronic device suitable for implementing the above-described method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0043] The terms "first," "second," or "third" in the specification, claims, or drawings of this application are used to distinguish different objects, not to describe a specific order. In addition, the terms "including," "having," and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to the process, method, product, or apparatus.

[0044] As mentioned in the background technology section, the applicant found that the existing The regularized threshold iteration algorithm has the problem of large estimation error and low solution accuracy, which limits its application in various CS scenarios to a certain extent. Faced with this technical status quo, the applicant found through research that The main reason for the large estimation error of the regularized threshold iteration algorithm is that the relaxation gap is too large, which leads to low accuracy of the solution. Based on this, an embodiment of the present invention proposes an improved Regularized threshold iteration algorithm, the overall idea of ​​the algorithm includes: first, initialize the sparse signal x1 with a zero vector; second, calculate the iteration value through the iterative formula, that is, the solution and regularization parameter in the nth iteration of the reconstruction function; finally, when the iteration termination condition is met, the calculation is terminated and the estimated signal is obtained, otherwise the iteration continues. Figure 1 , a more specific implementation method includes the following steps:

[0045] Step 1. Input: Observation signal y∈R M , the measurement matrix The sparsity of the signal to be determined ||x||0, the upper limit of the number of iterations η and the parameter α=max(eigΦ T Φ)+1;max(eigΦ T Φ) represents the matrix Φ T The maximum eigenvalue of Φ, α=max(eigΦ T Φ)+1 characterizes the exact reconstruction condition of sparse signals;

[0046] Initialization: x1=0, n=0.

[0047] Step 2: According to the Minimization Maximum Theorem (MM), a non-negative intermediate function is introduced for the objective function. The result of this operation can be obtained by the function To characterize.

[0048] Step 3: Calculate λ n , according to the formula λ n =α|(b α (x n )) k+1 | 2 ,α and (b α (x n )) can be obtained from steps one and two.

[0049] Step 4: Based on the intermediate function b α (x n ) and some of the aforementioned parameters to construct a sparse signal iterative function, the expression of the sparse signal iterative function is:

[0050]

[0051] Step 5: Compare the two adjacent iteration values ​​of the sparse signal iterative function. If Then terminate the iteration and obtain the estimated reconstructed sparse signal x n+1 ; Otherwise, repeat steps 2 to 4.

[0052] Figure 2 It is a graph showing the iterative error changing with the number of iterations. The convergence characteristics of the regularized threshold iteration algorithm are compared with the original algorithm. It can be found that the iteration error decreases monotonically with the number of iterations. When the number of iterations n = 200, the improved The regularized threshold iterative algorithm can recover the sparse signal.

[0053] Figure 3 is a curve of mean square error changing with signal-to-noise ratio. The performance of the regularized threshold iteration algorithm is significantly better than the original algorithm. 5When the mean square error can be reduced to MSE=10 -8 , while the mean square error of the original algorithm is always around 1.

[0054] The present invention adopts an improved method of reconstructing high-dimensional sparse signals by introducing an intermediate function with a smaller value and a reconstruction function with a smaller relaxation gap. The regularized threshold iteration algorithm makes the relaxation gap smaller, the mean square error significantly reduced, the estimation accuracy significantly improved, and the convergence speed faster. Regularized threshold iterative algorithm, according to The measurement relationship can more accurately reconstruct high-dimensional sparse signals from low-dimensional linear measurements, thus solving the existing The regularized threshold iteration algorithm has a technical problem that limits its application in various CS scenarios due to its large estimation error.

[0055] Figure 4 The block diagram schematically shows an electronic device suitable for implementing the method described above according to an embodiment of the present invention. Figure 4 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0056] like Figure 4 As shown, the electronic device 1000 described in this embodiment includes: a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage part 1008 into a random access memory (RAM) 1003. The processor 1001 may, for example, include a general-purpose microprocessor (such as a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (such as an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include an onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0057] Various programs and data required for the operation of the system 1000 are stored in the RAM 1003. The processor 1001, ROM 1002, and RAM 1003 are connected to each other via a bus 1004. The processor 1001 executes the various operations of the method flow according to the embodiment of the present disclosure by executing the programs in the ROM 1002 and / or RAM 1003. It should be noted that the programs may also be stored in one or more memories other than the ROM 1002 and RAM 1003. The processor 1001 may also execute the various operations of the method flow according to the embodiment of the present disclosure by executing the programs stored in the one or more memories.

[0058] According to an embodiment of the present disclosure, electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to bus 1004. System 1000 may also include one or more of the following components connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and speakers; a storage section 1008 including a hard disk; and a communication section 1009 including a network interface card such as a LAN card or a modem. Communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. Removable media 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed in drive 1010 as needed, so that computer programs read therefrom can be installed into storage section 1008 as needed.

[0059] The method flow according to the embodiment of the present disclosure can be implemented as a computer software program. For example, the embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1009, and / or installed from the removable medium 1011. When the computer program is executed by the processor 1001, the above-mentioned functions defined in the system of the embodiment of the present disclosure are executed. According to the embodiment of the present disclosure, the system, equipment, device, module, unit, etc. described above can be implemented by a computer program module.

[0060] Embodiments of the present invention further provide a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments, or may exist independently and not incorporated into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the methods according to the embodiments of the present disclosure.

[0061] According to an embodiment of the present disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium, for example, may include but is not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In an embodiment of the present disclosure, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, apparatus, or device. For example, according to an embodiment of the present disclosure, the computer-readable storage medium may include one or more memories other than the ROM 1002 and / or RAM 1003 described above.

[0062] It should be noted that the functional modules in the various embodiments of the present invention can be integrated into a processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The above-mentioned integrated modules can be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product.

[0063] The flowcharts or block diagrams in the accompanying drawings illustrate the possible architectures, functions and operations of the systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, program segment or part of code, and the above-mentioned module, program segment, or part of code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the boxes can also occur in an order different from that marked in the accompanying drawings. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0064] Those skilled in the art will appreciate that the features described in the various embodiments and / or claims of the present disclosure may be combined and / or coupled in various ways, even if such combinations and / or couplings are not explicitly described in the present disclosure. In particular, the features described in the various embodiments and / or claims of the present disclosure may be combined and / or coupled in various ways without departing from the spirit and teachings of the present disclosure, and all such combinations and / or couplings fall within the scope of the present disclosure.

[0065] Although the present disclosure has been shown and described with reference to certain exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made to the present disclosure without departing from the spirit and scope of the present disclosure as defined by the appended claims and their equivalents. Therefore, the scope of the present disclosure should not be limited to the above-described embodiments, but should be determined not only by the appended claims but also by the equivalents of the appended claims.

Claims

1. A sparse signal reconstruction method based on L0 regularization threshold iteration, characterized in that: include: Take the parameters in the sparse signal parameter set as input and initialize the sparse signal with a zero vector; constructing an intermediate function using parameters in the sparse signal parameter set; Constructing a sparse signal iterative function based on the intermediate function; If it is determined that two adjacent iteration values ​​of the sparse signal iterative function meet the iteration termination condition, the iteration is terminated and the reconstructed sparse signal is output; Wherein, the expression of the sparse signal iterative function is: ； The expression of the iteration termination condition is: ； The expression of the intermediate function is: ； The parameters in the sparse signal parameter set include: observation signal , measurement matrix , the sparsity of the signal to be determined , the upper limit of the number of iterations and the first transition parameter ; is the second transition parameter; the expression of the first transition parameter is: ； in, Representation matrix The maximum eigenvalue of the first transition parameter characterizes the accurate reconstruction condition of the sparse signal, and the expression of the second transition parameter is: 。 2. The sparse signal reconstruction method according to claim 1, wherein: Also includes: If it is determined that the two adjacent iteration values ​​of the sparse signal iterative function do not meet the iteration termination condition, then continue to calculate the value of the intermediate function and the value of the second transition parameter, perform calculation of the next iteration value, and again determine whether the two most recent adjacent iteration values ​​of the sparse signal iterative function meet the iteration termination condition.

3. The sparse signal reconstruction method according to claim 1, wherein: The specific method of initializing the sparse signal with a zero vector is: , .

4. An electronic device, characterized in that: The method comprises at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit is enabled to perform the steps of the method according to any one of claims 1 to 3.

5. A storage medium, characterized in that It stores a computer program executable by an access authentication device. When the computer program runs on the access authentication device, the access authentication device is enabled to execute the steps of the method according to any one of claims 1 to 3.

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