A Sparse Signal Reconstruction Method Based on Fuzzy Adaptive Genetic Algorithm

Abstract

The present invention discloses a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm, which relates to the technical field of sparse signal reconstruction; the method comprises the following steps: recovering an original sparse signal based on the compressive sensing theory to determine an optimization problem; improving the genetic algorithm by adding an update strategy for a crossover and mutation operator and a local search strategy to obtain a fuzzy adaptive genetic algorithm; and using the fuzzy adaptive genetic algorithm to obtain an optimal set for the optimization problem to perform sparse signal reconstruction. In the improved algorithm of the present invention, the crossover and mutation probabilities are adaptively controlled by a fuzzy control system, the evolution space of the population is changed at different stages of evolution to improve the evolution efficiency, and a local search strategy is introduced after the crossover and mutation operations, so that each individual in the population has a state of local search and evolution, enabling the individual to search for a better position in the local space most quickly; the present invention does not overly rely on the quality of the measurement matrix and the sparse state of the signal, and has good applicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of sparse signal reconstruction, and particularly relates to a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm. Background Art

[0002] In recent years, research has shown that wireless signals often exhibit sparse characteristics in the propagation process due to multipath effects and the intermittency of mobile communication. Therefore, as another characteristic of the channel, the sparsity of the channel is attracting more and more attention in signal processing for the possibility of using sparsity to solve the channel estimation problem. Traditional linear wireless channel estimation methods need to obtain the statistical characteristics of the channel through the Nyquist sampling theorem, resulting in reduced utilization of spectrum resources. The wireless channel has sparse characteristics, and most of the energy is concentrated on a small number of channel taps. Using the sparse signal reconstruction algorithm in compressive sensing theory can improve the channel estimation accuracy and efficiency to a certain extent and achieve the channel estimation effect.

[0003] The proposal of compressive sensing technology has broken through the early Nyquist-Shannon sampling theorem, and its premise and basis are the sparsity of the signal and the incomplete sampling theorem. Sparsity means that most of the values of the signal in a certain representation domain are zero, the signal has a small number of non-zero elements, and the number of non-zero elements in the signal is also called the sparsity. The incomplete sampling theorem indicates that for a sparse signal, under certain conditions, it can be sampled at a sampling rate far less than that required by the traditional sampling theorem and reconstructed, which has attracted research on the application of CS in multiple fields. At present, compressive sensing technology has been applied to network communication, remote sensing images, image processing, prediction model optimization, microseismic monitoring, etc.

[0004] Compressive sensing technology mainly consists of three parts: sparse representation of the signal, construction of the measurement matrix, and reconstruction of the sparse signal. The sparse signal reconstruction algorithm is the core of compressive sensing. Therefore, the reconstruction algorithm has always been a research hotspot. The research on the reconstruction algorithm mainly includes algorithms based on L1 norm minimization, convex optimization algorithms, greedy algorithms, neural networks and deep learning, and intelligent algorithms. The essential problem of the sparse signal reconstruction algorithm is to solve the norm minimization problem.

[0005] Under the condition of sparse signals, using traditional sparse signal reconstruction algorithms to recover signals has achieved good results. However, the computational efficiency of traditional sparse signal reconstruction algorithms, and the performance of the methods highly depends on the quality of the measurement matrix and the sparsity of the signals. In each iteration recovery process of traditional sparse signal reconstruction algorithms, it is necessary to use the inner product matching criterion to select atoms, and select the atoms most relevant to the observed values in the measurement matrix, which has relatively high requirements for the correlation of each atom in the measurement matrix. When the number of iterations is equal to the channel sparsity, an atom support set is obtained, and finally the signal is recovered using this support set. Therefore, in the atom selection process, once the atom correlation between the observation matrices is poor, errors will be caused during the selection process, ultimately leading to an increase in the reconstruction error.

[0006] In recent years, inspired by the evolutionary laws of organisms, the living habits of animals, and physical phenomena, various new meta-heuristic algorithms have been proposed. With the proposal and improvement of various algorithms, meta-heuristic algorithms already have the ability to solve practical problems creatively and innovatively. Therefore, it is feasible to use meta-heuristic algorithms to solve the sparse signal reconstruction problem. The genetic algorithm is a heuristic algorithm evolved according to the selection and evolution model between the natural environment and organisms, and has a complete theoretical basis and support. In the genetic algorithm, each individual in the population realizes the evolution of the individual and the population through the selection process, the crossover process, and the mutation process.

[0007] Based on the theory of compressive sensing, this invention combines meta-heuristic algorithms to propose a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm. The fuzzy adaptive genetic algorithm (MGA) aims at the deficiencies of the genetic algorithm in sparse signal reconstruction, and proposes to adaptively control the crossover and mutation probabilities through a fuzzy inference system, changing the evolutionary space of the population at different stages of evolution. A local search strategy is introduced in the later stage of the algorithm, enabling individuals to search for better positions in the local space as quickly as possible. Under the basic sparse signal reconstruction test conditions, the fuzzy adaptive genetic sparse reconstruction algorithm can overcome the drawback of over-reliance on the measurement matrix and perform well under the condition of low sparsity. Summary of the Invention

[0008] The purpose of this invention is to provide a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm to solve the problems in the prior art such as the traditional sparse signal reconstruction algorithm in the prior art being overly dependent on the measurement matrix and the reconstruction error being prone to increase when the atom correlation between matrices is poor as mentioned in the above background technology.

[0009] To achieve the above purpose, this invention is implemented by adopting the following technical solutions:

[0010] A sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm includes the following steps:

[0011] S1. Restore the original sparse signal based on the compressive sensing theory and determine the optimization problem;

[0012] S2. Improve the genetic algorithm by adding an update strategy for the crossover and mutation operators and a local search strategy to obtain a fuzzy adaptive genetic algorithm;

[0013] S3. Use the fuzzy adaptive genetic algorithm to obtain the optimal set for the optimization problem and perform sparse signal reconstruction.

[0014] Specifically, it includes the following steps:

[0015] S301. Initialization: Initialize the parameter settings and randomly generate population individuals that meet the signal sparsity condition; each individual represents a selection method for the atomic support set;

[0016] S302. Initial evaluation: Use the error function as the fitness function, calculate the fitness values of the population individuals, and determine the number of individuals in the population for crossover and mutation;

[0017] S303. Main loop: Sequentially perform operations such as population evolution update, local search, and update of the crossover and mutation operators, and repeat the loop operation;

[0018] S304. Stop condition: If the algorithm meets the stop condition, stop the iteration and output the atomic support set corresponding to the optimal individual, and obtain the reconstructed sparse signal through calculation.

[0019] Preferably, the update strategy for the crossover and mutation operators in S2 is as follows:

[0020] Construct a fuzzy control system based on the trapezoidal membership function and the Gaussian membership function, use the fitness value of each generation of population individuals as the input variable of the fuzzy control system, and the output variables of the fuzzy control system are the crossover operator and the mutation operator.

[0021] Preferably, the local search strategy in S2 is as follows:

[0022] The local search strategy assigns step sizes in two directions to each individual after one iteration, and determines whether the individual movement can be closer to the global optimal solution by calculating and comparing the fitness values in different directions; then, move the selected individual in this direction, and the moved individual is more in line with and closer to the global optimal requirements; the specific description is as follows in the formula:

[0023]

[0024] Among them, P l and P r respectively represent the new individuals after the individual moves in two different left and right directions, represents the search step size;

[0025]

[0026] Among them, P t+1 represents the updated next-generation individual; represents the fitness value of the individual after moving to the right, represents the fitness value of the individual after moving to the left, sign(·) is the sign function, and w is the transformation factor.

[0027] Preferably, the optimization problem is expressed as:

[0028] Y M×1 = Φ M×N x N×1

[0029] Among them, Y ∈ R M×1 is called the observation signal, Φ ∈ R M×N is called the measurement matrix, M << N; the sparse signal x has only k non-zero data, and k is the signal sparsity; the observation signal Y can be understood as a linear combination of k columns of the measurement matrix Φ, and by selecting the best-matching columns in the measurement matrix Φ, the purpose of sparse signal reconstruction is achieved.

[0030] Preferably, in step S301, population individuals that meet the signal sparsity condition are randomly generated as follows:

[0031] A random initial population is generated, and each individual P in the population consists of k integers:

[0032] P = (q1, q2, q3,... q k )

[0033] Among them, 0 < k < x length , x length represents the signal length of the sparse signal x, and the integer q k corresponds to the corresponding column in the measurement matrix Φ and represents the position of the non-zero data in the sparse signal.

[0034] Preferably, in step S302, the fitness value of the population individuals is calculated as follows:

[0035] Each individual P in the population consists of k integers P = (q1, q2, q3,... q k ), and the measurement matrix is expressed as;

[0036]

[0037] Among them, φ ∈ R M×k ;

[0038] After selecting the columns of the measurement matrix, calculate the pseudo-inverse A of the selected columns;

[0039] A = (φ Τ φ) -1 φ Τ

[0040] where A ∈ R k×M ;

[0041] The reconstructed signal is expressed as

[0042]

[0043] After obtaining the estimated value, the estimated value of the observed signal is obtained through calculation;

[0044]

[0045] The measurement matrix is a fixed value during one signal reconstruction iteration process. Therefore, the smaller the error of the Y value, the smaller the error of the x value; then the decision error is obtained through calculation;

[0046]

[0047] Taking the error function as the fitness function, calculate the fitness values of the population individuals:

[0048]

[0049] Preferably, the main loop in S303 specifically includes the following content for looping:

[0050] S3031. Population evolution update: Select a specified number of population individuals, and through the crossover operator and mutation operator, perform crossover and mutation operations to obtain a new generation of individuals;

[0051] S3032. Local search: The individuals after crossover and mutation continue to perform local search with the specified step size in the local search strategy to find the optimal position around;

[0052] S3033. Update the crossover and mutation operators: Take the fitness values of the updated population individuals as the update metric, and obtain the updated crossover operator and mutation operator through the fuzzy control system.

[0053] Compared with the prior art, the beneficial effects of the present invention are:

[0054] (1) The present invention proposes a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm. In the improved algorithm, the crossover and mutation probabilities are adaptively controlled by a fuzzy control system, and the evolutionary space of the population is changed at different stages of evolution to increase the possibility of the evolutionary process, enhance population diversity, improve the evolutionary efficiency, and prevent the algorithm from falling into a local optimum in the later stage of iteration. After the crossover and mutation operations, a local search strategy is introduced to enable each individual in the population to have the state of local search and evolution, so that the individual can quickly search for a better position in the local space. In the algorithm, each individual in the population represents a selection method of an atomic support set. By calculating the reconstruction error, the atomic support set with the minimum reconstruction error is finally evolved, and the reconstructed signal is calculated through the atomic support set.

[0055] (2) The fuzzy adaptive genetic algorithm proposed by the present invention is not overly dependent on the quality of the measurement matrix and the sparse state of the signal compared with the traditional algorithm, and has a unified cost function, showing good applicability. Compared with some existing meta-heuristic signal reconstruction algorithms, the proposed algorithm has higher reconstruction accuracy under the premise of the same number of iterations. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flowchart of a sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm in the present invention;

[0057] Figure 2 is a schematic diagram of the membership function of the input variable of the fuzzy control system in the present invention;

[0058] Figure 3 is a schematic diagram of the membership function of the output variable of the fuzzy control system in the present invention;

[0059] Figure 4 is the average error convergence graph of the MGA, ABC, PSO, and GA algorithms tested under the same conditions of signal length N = 128 and observation matrix M = 64 at 4 different sparsity levels k;

[0060] Figure 5 is the average error convergence graph of the MGA, ABC, PSO, and GA algorithms tested under the same conditions of signal length N = 256 and observation matrix M = 64 at 4 different sparsity levels k. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] Example 1:

[0063] A sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm, comprising the following steps:

[0064] Step 1, recovering the original sparse signal based on the compressive sensing theory.

[0065] The prerequisite of the compressive sensing theory is that the signal exhibits sparsity. First, assume a signal x ∈ R of length N N×1 , if the signal under the projection of the transform basis Ψ ∈ R N×N , obtains the transformed vector s ∈ R N×1 , and the number of non-zeros K in the transformed vector << N;

[0066]

[0067] The original signal x is sparse under the action of the orthogonal transform basis Ψ. When the original signal itself is sparse, the transform basis Ψ ∈ R N×N is the identity matrix. After signal processing, the observed signal is expressed as

[0068]

[0069] After simplification

[0070] Y = Φx (3)

[0071] where Y ∈ R M×1 , Φ ∈ R M×N is called the observation matrix M << N. The observation matrix has enough information to process, transmit, and recover the original signal.

[0072] The sparse reconstruction algorithm is to obtain the original sparse signal by finding the optimal solution of an underdetermined equation - formula (3). Under the condition of the existence of noise, formula (3) is expressed as

[0073] Y = Φx + n n ∈ R M×1 (4)

[0074] where the observation matrix Φ ∈ R M×N needs to satisfy the restricted isometry property (RIP). The RIP criterion explains the constraint conditions between the measurement matrix and the sparse signal. It ensures that under different sparse signal conditions, the measurement matrix can accurately map in different sets. The restriction conditions are as follows:

[0075]

[0076] where it is required that δ ∈ (0, 1).

[0077] For an underdetermined equation problem where the equation solution has infinitely many solutions like Equation (3), it is usually transformed into a norm minimization problem that is easier to solve. For example

[0078]

[0079] where ||·||1 represents the 1-norm, and the signal reconstruction solution is obtained by optimizing to obtain the minimum value of the 1-norm.

[0080] Step 2: Improve the genetic algorithm to obtain a fuzzy adaptive genetic algorithm.

[0081] Aiming at the deficiencies of the traditional genetic algorithm in signal reconstruction, a fuzzy genetic algorithm (MGA) is proposed. The improved algorithm adaptively controls the crossover and mutation probabilities through a fuzzy inference system, changes the evolutionary space of the population at different stages of evolution, to increase the possibilities of the evolutionary process and enhance population diversity, while improving the evolutionary efficiency and preventing the algorithm from falling into local optima in the later stage of iteration. After the crossover and mutation operations, a local search strategy is introduced to enable each individual in the population to have the state of local search and evolution, so that the individual can quickly search for a better position in the local space.

[0082] (1). Update strategy of the crossover and mutation operators;

[0083] In the initial stage of iteration of the basic genetic algorithm, a larger crossover operator is needed to search the space to find an approximately globally optimal solution space. In the middle stage of iteration, the population basically determines the optimal region. At this time, it is necessary to reduce the crossover operator to perform local space adjustment, and at the same time, a mutation operator is needed to control the population to avoid falling into local optima. In the later stage of iteration, the population determines the optimal position in the space. At this time, the mutation operator plays a mutation role to continue the possibility of finding the optimal position. When the conditions are met, the population stops iterating. However, for complex engineering problems and multi-peak conditions, premature convergence may occur in each period of iteration. Therefore, the fitness values of each individual in each generation of the population are used as the input variables of the fuzzy control system, and the crossover and mutation operators are used as the output to dynamically adjust the evolutionary operators to improve the exploration and exploitation capabilities of the algorithm.

[0084] The population diversity as an input variable is discrete data, and its influence on the output variable is also non-linear. The present invention uses a trapezoidal membership function to represent the mapping relationship between the population diversity and the set as Figure 2 shown. The crossover and mutation operators, as the output variables of the system, monitor the changes in each generation of the population and dynamically adjust the crossover and mutation operators. According to the change in the population quality, the crossover and mutation operators show a basic linear change. Therefore, a Gaussian membership function is used to describe the mapping relationship between the crossover and mutation operators and the set as Figure 3 shown in (a)-(b) therein to prevent the algorithm from falling into the trap of local optima. It should be noted that Figure 2-3The configuration of all membership functions is fixed and only extended according to the new upper limit value.

[0085] The single-input fuzzy rules of the linear system are shown in Table 1, and the cross-mutation adaptive fuzzy rules are shown in Table 2.

[0086] Table 1 Single-Input Fuzzy Rule System

[0087]

[0088] Table 2 Cross-Mutation Rate Adaptive Fuzzy Rules

[0089] <![CDATA[p m > ND ZD PD <![CDATA[p c > ND ZD PD

[0090] (2). Local Search Strategy;

[0091] After the cross-mutation operation, a local search strategy is introduced to search around the current position of individuals in the population, and the search step size is added to control the process of local search, thereby improving the calculation efficiency. Each individual undergoes local search and enters the next generation population through update, and a better position than the current position can be found faster in each iteration, thereby improving the quality of each generation of population. During the optimization process, local search can assist the global search process, thereby finding the global optimal solution more efficiently.

[0092] The local search strategy assigns step sizes in two directions to each individual after one iteration. By calculating and comparing the fitness values in different directions, it is determined in which direction the individual should move to be closer to the global optimal solution. Then, the selected individual is moved in that direction, and the moved individual should be more in line with and closer to the requirements of the global optimum. Finally, after meeting the iteration requirements, the ideal global optimal solution is obtained. The specific description is as follows:

[0093]

[0094] Equations (7) and (8) represent the new individuals after the individual moves in two different directions, left and right, represents the search step size.

[0095]

[0096] In Equation (9), P t+1 represents the updated individual in the next generation.

[0097] Among them, represents the fitness value of the individual after moving to the right, represents the fitness value of the individual after moving to the left, and sign(·) is the sign function.

[0098] To prevent the step size from being set too small, a random transformation factor w is set to avoid "overfitting" and "underfitting" in the search and improve the algorithm efficiency.

[0099] Step 3: Use the fuzzy adaptive genetic algorithm for sparse signal reconstruction.

[0100] An improved genetic algorithm is used to recover the sparse signal, making full use of the relationship among the sparsity, the observation vector, and the measurement matrix.

[0101] The problem optimized by the present invention is as shown in the following formula (10), which is a problem of solving an underdetermined linear equation. By selecting the best-matched columns in the measurement matrix Φ, the purpose of signal reconstruction is achieved.

[0102] Y M×1 =Φ M×N x N×1 (10)

[0103] The sparse signal x has only k non-zero data, which is understood as the observation vector Y being a linear combination of k columns of the measurement matrix Φ.

[0104] First, a random initial population is generated. Each individual P in the population consists of k (signal sparsity) integers P = (q1, q2, q3,... q k ), where the integer q k corresponds to the corresponding column in the measurement matrix and represents the position of the non-zero data in the sparse signal.

[0105]

[0106] φ∈R M×k , after selecting the columns of the measurement matrix, the pseudo-inverse A of the selected columns is calculated through formula (12), and A∈R k×M .

[0107] A = (φ Τ φ) -1 φ Τ (12)

[0108] Then the reconstructed signal can be expressed as (13)

[0109]

[0110] After obtaining the estimated value, the estimated value of the observed signal is obtained by calculating (14). Then the error is determined by calculating (15).

[0111]

[0112] When the correct set of the observation matrix is found, the reconstructed signal is equal to the original sparse signal.

[0113] When the algorithm meets the maximum number of iterations, the algorithm stops.

[0114] The steps of the proposed method for reconstructing sparse signals using the MGA algorithm are as follows:

[0115]

[0116]

[0117] Simulation experiment:

[0118] The sparse signals with different sparsity levels randomly generated by the sparse signal reconstruction method (MGA) based on the fuzzy adaptive genetic algorithm proposed in the present invention and the random Gaussian measurement matrix are evaluated and tested.

[0119] The line graph calculated by Equation (16) shows that the MGA algorithm in the present invention can effectively reconstruct random signals with different sparsity levels.

[0120]

[0121] Table 3 gives the control parameters of each swarm intelligence algorithm in the simulation experiment, and the traditional sparse reconstruction algorithms are implemented in standard form on MATLAB. These experiments were carried out on a PC with 4GB RAM and a 2.40GHz CPU using MATLAB.

[0122] Table 3 Parameter settings of each algorithm

[0123]

[0124] (1). Compare the performance of the MGA algorithm in the present invention with that of other swarm intelligence algorithms, namely the GA, PSO, and ABC algorithms.

[0125] This part of the experiment studies the influence of different sparsity levels on the performance of the algorithm under the condition of the same signal length. Under the premise that the signal length N = 128, N = 256, and the observation matrix M = 64, and a random Gaussian measurement matrix is uniformly used. The MGA, GA, PSO, and ABC algorithms are tested. Among them, the MGA algorithm is basically better than the PSO and ABC algorithms proposed by Murat Emre Erkoc in "Sparse signal reconstruction by swarm intelligence algorithms". Since an intelligent algorithm based on population iteration is used, it is difficult to conduct a complexity analysis of the algorithm. The complexity of the proposed algorithm basically depends on the population size, number of iterations, signal sparsity, and calculation of matrix pseudo-inverse in the initialization settings.

[0126] By randomly generating sparse signals under different conditions, the applicability of the proposed method to sparse signal reconstruction is examined. In this part of the experiment, the present invention will be compared with the existing swarm intelligence-based sparse signal reconstruction algorithms. The MGA, ABC, PSO, and GA algorithms are run multiple times under the same conditions, and each run has different signals and measurement matrices. Through comparative analysis, the following conclusions can be obtained.

[0127] Table 4 compares the average convergence values of each algorithm under the condition of N = 128

[0128] K MGA GA ABC PSO 8 5.471e-2 3.917e-1 6.148e-2 3.507e-1 16 7.323e-4 5.719e-1 3.172e-1 3.578e-1 28 3.517e-2 6.633e-1 5.609e-1 5.079e-1 32 3.717e-2 7.789e-1 5.331e-1 6.615e-1

[0129] Table 5 compares the average convergence values of each algorithm under the condition of N = 256

[0130] K MGA GA ABC PSO 8 8.449e-2 4.245e-1 1.905e-1 1.403e-1 16 3.175e-3 5.660e-1 2.533e-1 4.625e-1 28 1.847e-1 7.407e-1 6.072e-1 5.405e-1 32 2.045e-1 7.408e-1 6.309e-1 6.275e-1

[0131] Refer to Figure 4 and compare Figure 4 the error values under the four sparsity conditions of (a)-(d) therein. Under the condition of the same 2000 iterations, the proposed MGA algorithm is superior to other algorithms in terms of reconstruction error. Under the condition of the same number of iterations, other algorithms may be more likely to fall into local states. In addition, when comparing the same algorithm alone, as the sparsity increases, the final error of the algorithm also gradually increases. This is because, under the condition of constant signal length, an increase in sparsity means an increase in the number of positions of non-zero entries to be searched, which increases the algorithm difficulty. Therefore, without increasing the number of iterations, the reconstruction error will increase. Table 4 gives Figure 4 the final error convergence values of each algorithm in (a)-(d) therein. From the data, it can be seen that under different sparsity conditions, the final error value of the MGA algorithm is always the smallest.

[0132] Finally, the present invention increases the signal length, which means increasing the search space. Refer to Figure 5 , Figure 5 and (a)-(d) therein show the reconstruction effects of each algorithm under the condition of N = 256. The results show that under different sparsity conditions, the MGA algorithm still has the best convergence. However, compared with the convergence accuracy of N = 128, the accuracy has decreased. To achieve the same convergence accuracy, the number of iterations of the algorithm can be increased. Table 5 shows the final convergence effects of each algorithm after 2000 iterations.

[0133] (2) Compare the performance of the MGA algorithm in the present invention with that of the traditional algorithms MP, OMP, StOMP, and IHT algorithms.

[0134] This part of the experiment studies different situations and their impacts on the performance of the algorithm. Under different signal lengths and observation matrix conditions, a random Gaussian measurement matrix is uniformly adopted. The performances of the MGA, MP, OMP, StOMP, and IHT algorithms are compared. The MGA algorithm and other traditional classical reconstruction algorithms are run 10 times for the same problem to obtain the optimal value. Table 6 shows the running results of all algorithms.

[0135] Table 6 Reconstruction Error Results under Different Conditions

[0136] N M k MGA GA MP OMP StOMP IHT 64 24 8 1.260e-2 2.409e-1 2.200e-3 5.323e-1 2.971e-1 5.6831 64 24 16 1.810e-2 5.195e-1 9.260e-2 8.584e-1 3.163e-1 6.2035 128 64 12 2.608e-16 3.993e-1 1.200e-3 7.075e-1 3.580e-16 9.4838 128 64 16 3.289e-16 5.377e-1 2.500e-3 8.664e-1 5.277e-16 10.0758 256 64 32 1.746e-1 8.570e-1 9.263e-1 1.485e-0 8.761e-1 11.0716

[0137] From the experimental data results in Table 6, it can be seen that under the same conditions, the MGA algorithm is basically superior to other traditional classical algorithms. Especially when the sparse signal length is 128 and the observed signal length is 64, the MGA algorithm is the best. Comparing the two conditions of N = 128, M = 64 and N = 64, M = 24, there is a large contrast between the MGA algorithm and StOMP. After multiple experiments, it is concluded that StOMP has certain requirements for the selection of the number of iterations and the threshold value under different signal conditions. Once the threshold setting is unreasonable, this situation will occur. The search difficulty of the MGA algorithm is different under different search space conditions. By increasing the number of iterations, the ideal reconstruction accuracy can be achieved. Similarly, other algorithms can meet the reconstruction requirements only under suitable threshold values and better measurement matrix conditions.

[0138] Conclusion: The present invention proposes a new sparse signal reconstruction algorithm MGA. Different from the traditional reconstruction algorithms based on the compressed sensing theory, the method proposed in the present invention obtains the parameters of all non-zero signals at one time, and then tests the feasibility of the algorithm on the test function of basic sparse signal reconstruction. The results show that the proposed algorithm is basically superior to the traditional algorithms and other swarm intelligence algorithms used for sparse signal reconstruction.

[0139] As described above, it is only used to help understand the method of the present invention and its core essence, but the protection scope of the present invention is not limited thereto. For those of ordinary skill in the art in the technical field of the present invention, any equivalent replacement or change made within the technical scope disclosed by the present invention according to the technical solution and inventive concept of the present invention should be covered within the protection scope of the present invention. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm, characterized in that, It includes the following steps: S1. Based on the compressed sensing theory, recover the original sparse signal and determine the optimization problem; S2. Improve the genetic algorithm by adding an update strategy for the crossover and mutation operators and a local search strategy to obtain a fuzzy adaptive genetic algorithm; The update strategy for the crossover and mutation operators is as follows: Construct a fuzzy control system based on the trapezoidal membership function and the Gaussian membership function. Take the fitness value of each individual in each generation of the population as the input variable of the fuzzy control system, and the output variables of the fuzzy control system are the crossover operator and the mutation operator; S3. Use the fuzzy adaptive genetic algorithm to obtain the optimal set for the optimization problem and perform sparse signal reconstruction; Specifically, it includes the following steps: S301. Initialization: Set the initial parameters and randomly generate population individuals that meet the signal sparsity condition; each individual represents a selection method of an atomic support set; S302. Initial evaluation: Use the error function as the fitness function, calculate the fitness values of the population individuals, and determine the number of individuals in the population for crossover and mutation; S303. Main loop: Sequentially perform operations of population evolution update, local search, and update of the crossover and mutation operators, and repeat the loop operation; S304. Stop condition: If the algorithm meets the stop condition, stop the iteration and output the atomic support set corresponding to the optimal individual, and obtain the reconstructed sparse signal through calculation.

2. The sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm according to claim 1, characterized in that, In S1, the optimization problem is expressed as: where Y ∈ R M×1 is called the observation signal, Φ ∈ R M×N is called the measurement matrix, M << N; the sparse signal x has only k non-zero data, and k is the signal sparsity; the observation signal Y can be understood as a linear combination of k columns of the measurement matrix Φ, and by selecting the best-matching columns in the measurement matrix Φ, the purpose of sparse signal reconstruction is achieved.

3. The sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm according to claim 1, characterized in that, The local search strategy in S2 is as follows: The local search strategy assigns step sizes in two directions to each individual after one iteration. By calculating and comparing the fitness values in different directions, it is judged whether the individual movement is closer to the global optimal solution; then, the selected individual is moved in this direction, and the moved individual is more in line with and closer to the global optimal requirements. The specific description is as follows in the formula: Among them, P l , P r respectively represent the new individuals after the individual moves in two different directions, represents the search step size; Among them, P t+1 represents the updated next-generation individuals; represents the fitness value of the individual after moving to the right, represents the fitness value of the individual after moving to the left, sign(·) is the sign function, and w is the transformation factor.

4. The sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm according to any one of claims 1-3, characterized in that, In S301, randomly generating population individuals that meet the signal sparsity condition is as follows: Randomly generate an initial population, and each individual P in the population consists of k integers as follows: P = (q1, q2, q3,... q k ) where \(0 \lt k \lt x\) length , \(x\) length denotes the signal length of the sparse signal \(x\), and the integer \(q\) k corresponds to the corresponding column in the measurement matrix \(\varPhi\) and represents the positions of the non - zero data in the sparse signal.

5. The sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm according to claim 4, characterized in that, In S302, calculating the fitness values of the population individuals is as follows: Each individual P in the population consists of k integers P = (q1, q2, q3,... q k ), and the measurement matrix is represented as; where φ ∈ R M×k ; After selecting the columns of the measurement matrix, calculate the pseudo-inverse A of the selected columns; A = (φ Τ φ) -1 φ Τ where A ∈ R k×M ; The reconstructed signal is expressed as After obtaining the estimated value, calculate the estimated value of the observed signal through calculation; The measurement matrix is a fixed value during one signal reconstruction iteration process. Therefore, the smaller the error of the Y value, the smaller the error of the x value; then calculate to obtain the judgment error; Use the error function as the fitness function and calculate the fitness values of the population individuals:

6. The sparse signal reconstruction method based on a fuzzy adaptive genetic algorithm according to claim 5, wherein, The main loop in S303 specifically includes the following content for looping: S3031. Population evolution update: Select a specified number of population individuals, and perform crossover and mutation operations through the crossover operator and the mutation operator to obtain a new generation of individuals; S3032. Local search: The individuals after crossover and mutation continue to perform local search at the specified step size in the local search strategy to find the optimal position around; S3033. Update the crossover and mutation operators: Take the fitness values of the updated population individuals as the update metric, and obtain the updated crossover operator and mutation operator through the fuzzy control system.

Images