A sparse signal reconstruction method based on two-step deep expansion strategy

Abstract

The present invention relates to a sparse signal reconstruction method based on a two-step deep expansion strategy, which belongs to the field of signal reconstruction technology and includes the following steps: S1: sparse input signal; S2: using the TwDU algorithm to improve the deep expansion model of the traditional sparse signal reconstruction algorithm; S3: using the improved sparse signal reconstruction algorithm to reconstruct and restore the original sparse signal. The present invention can make full use of the correlation between signals. Whether it is for a one-dimensional signal in wireless communication or a two-dimensional image signal, the method proposed by the present invention can reconstruct the signal faster and improve the reconstruction accuracy of the signal.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal reconstruction, and relates to a sparse signal reconstruction method based on a two-step depth expansion strategy. Background Art

[0002] Compressed Sensing (CS) refers to using a sampling matrix to obtain discrete samples of the original signal, i.e., sparse signals, under conditions far below the Nyquist sampling rate, and then reconstructing the original signal using the sparse signals through a nonlinear reconstruction algorithm. In order to reconstruct the original signal with high efficiency and high precision, a large number of excellent reconstruction algorithms have been proposed. The method invented in this paper is to reconstruct the original signal with high efficiency and high precision.

[0003] In recent years, deep learning technology has had a significant impact on the research and design of compressed sensing sparse signal reconstruction algorithms due to its powerful feature learning ability. These works can be divided into two categories: the first category is based on data-driven methods, which often adjust the neural network model to adapt to the data structure. Compared with traditional algorithms, data-driven methods have certain advantages, such as: (1) they can reduce the dependence on signal sparsity. (2) they can improve the accuracy of signal reconstruction. However, they mainly use neural network models and have the following disadvantages: (1) the network architecture is often universal, and the model is not interpretable and stable. (2) during network training, these networks often require a large number of signal samples, which has high requirements on the computing power and memory of the platform. The second category is based on model-driven methods. This type of method combines the advantages of traditional algorithms with performance guarantees and neural network models. It has been widely used in wireless communications, image processing and other fields. This type of method is collectively referred to as deep unfolding. Deep unfolding specifically refers to the formation of a new hierarchical structure similar to that in neural networks by unfolding the iterative process in traditional algorithms. These hierarchical structures contain some trainable parameter variables, which are trained by supervised learning and updated by back propagation mechanism based on gradient descent. The deep unfolding method makes full use of the powerful learning ability of deep learning technology and the deterministic internal structure of traditional algorithms, making traditional algorithms have learning ability. Gregor and LeCun first used this method to propose the Learned ISTA (LISTA) network model, which abstracts the threshold value and matrix variables in the ISTA algorithm into network training parameters and achieves better performance than ISTA. Borgerding and Schniter abstracted some parameters and threshold values ​​in the Onsager correction term in AMP into network training parameters and proposed the Learned AMP network model, which performs better than LISTA and AMP. Recently, Ito and Takabe introduced the MMSE estimator into ISTA and proposed the Trainable ISTA (TISTA) deep unfolding model, which achieves faster convergence speed than LISTA and LAMP with a very small number of training parameters. Compared with the first category, the deep unfolding algorithm has the following advantages: (1) It is constrained by traditional algorithms, has high stability and guaranteed performance. (2) Most deep unfolding algorithms require only a small number of parameters to be trained, and therefore require fewer training samples. (3) Deep unfolding algorithms are usually intuitive, interpretable, and have low computational and memory requirements. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a sparse signal reconstruction method based on the two-step deep unfolding strategy (Two Step Deep Unfolding, TwDU), TwDU makes full use of the correlation between signals to assign different weights to the first two estimated values ​​during deep unfolding, and jointly determine the current result. This method can establish a dependency relationship between signals, which is not fixed, but adaptively adjusted as the data changes, thereby improving the accuracy and convergence speed of compressed sensing sparse signal reconstruction.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A sparse signal reconstruction method based on a two-step depth expansion strategy comprises the following steps:

[0007] S1: Sparsification of input signal;

[0008] S2: Using TwDU algorithm to improve the deep unfolding model of traditional sparse signal reconstruction algorithm;

[0009] S3: Use the improved sparse signal reconstruction algorithm to reconstruct and restore the original sparse signal.

[0010] Furthermore, in the step S1, it specifically includes:

[0011] In compressed sensing, is the original signal vector, is the observation matrix, is a Gaussian white noise vector, and y = Φs + n, where is the observed signal vector obtained by sampling s through the observation matrix Φ; assuming that the original signal vector s is in a known standard orthogonal basis It can be sparse, that is, s = Ψx, where It is called the original sparse signal, which is the sparse representation of the original signal vector s in the new transform domain Ψ. Let the sensor matrix So y=Ax+n.

[0012] Furthermore, in step S1, the traditional reconstruction algorithm models the sparse reconstruction problem as the following convex optimization problem:

[0013]

[0014] Further, in step S2, the deep expansion model of the traditional sparse signal reconstruction algorithm includes LISTA, LAMP and TISTA.

[0015] Further, in step S2, the steps of improving the LISTA algorithm using the TwDU algorithm are as follows:

[0016] The ISTA algorithm is deeply expanded, and the symbol Γ(·) is used to represent the ISTA model. The symbol U· represents the deeply expanded model of ISTA. ISTA is re-described as follows:

[0017]

[0018]

[0019] Let βA T =B,I N -BA=S, we get:

[0020]

[0021] Using deep expansion technology to improve ISTA is expressed as

[0022]

[0023] Formula (5) represents the deep expansion of the traditional algorithm ISTA into LISTA, and then obtains the result of the next iteration; in the deep expansion algorithm LISTA, the parameter θ = [B, S, τ] is trained by deep learning technology to input data pairs Minimize the quadratic loss function (6) to achieve self-learning and updating:

[0024]

[0025] Then, the deep expansion algorithm is expanded in two steps; the two-step deep expansion strategy is proposed from The results do not only depend on It also depends on That is, the estimated value of each depth expansion algorithm depends on the estimated values ​​of the previous two depth expansion algorithms, rather than just on the previous one, that is, the existence of correlation between signals, and its formula is expressed as:

[0026]

[0027] In formula (7), UΓ· refers to all deep expansion algorithms, including LISTA, LAMP, and TISTA. The parameters that need to be trained using deep learning technology in (7) are θ=[ω,ψ,θU·], where θU· is the parameter that needs to be trained in each deep expansion algorithm. If it is TwDU-LISTA, then θU·=[B,S,τ]; in formula (7) and A two-step depth expansion strategy was utilized in each evaluation process; and The training parameters of have been trained in their respective two-step depth expansion and no longer participate in the current training, which can reduce the computational burden. The results of the first two calculations are and The influencing factors ω and ψ of the current calculation results will be adjusted adaptively according to the characteristics of the data using the powerful learning ability of deep learning; when ω=ψ=1.0,

[0028]

[0029] and The coefficient term is 0, and the results of the first two iterations have no effect on the current result; at this time, (8) and (5) are both ordinary deep expansion schemes. In fact, the proposed scheme (7) is more universal, and (5) can be regarded as a special case of (7). However, as the number of algorithm iterations increases, the parameters ω and ψ are continuously self-optimized through the back-propagation mechanism in deep learning, and finally stabilize at a small fluctuation around the optimal value. At this time, The coefficient 1-ω is The coefficients ω-ψ of are no longer 0, and the performance of the algorithm has been significantly improved, which indirectly shows that the results of the first two calculations have an important influence on the current result. The two-step deep expansion strategy makes full use of the intrinsic characteristics of the time series signals and uses different weights to jointly influence the current result.

[0030] Furthermore, the incremental training method of parameters. In the method based on the TwDU strategy, the value of the parameter Θ = [ω, ψ, θ(U(·))] will directly affect the reconstruction quality of the sparse signal. Therefore, the training method of Θ is extremely important. In the invention training process, a batch of data is first divided into H small batches of data (batch) and sent to the algorithm network. The network loss value gradually decreases with the training of the batch. When the training of a batch of data is completed, a new batch of data will be sent to the network for training again. After many experiments, it has been verified that the incremental training method is very effective in adjusting Θ and improving network performance. This is because incremental training can not only alleviate the gradient disappearance problem, but also further enhance the generalization ability of the network. The training data is a randomly generated data pair x, y, where y comes from y = Ax + n, which is the feature data after sparse sampling that the two-step expansion network needs to learn, and x is sparse label data. The TwDU algorithm uses the stochastic gradient descent algorithm to learn data features from the batch and reconstruct the original sparse signal x. During the tth gain training process, the optimizer adjusts Θ to promote the objective function of this training. After processing H small batches of data, the optimizer's objective function becomes Although the objective function changes continuously from the first layer to the last layer during the network training process, the parameter θ uses the previous result as the initial value of this training in each training process, which has a certain consistency. In the present invention, in order to control variables, all experiments including control experiments adopt the incremental training method.

[0031] Further, in step S2, the steps of improving the LAMP algorithm using the TwDU algorithm are as follows:

[0032] The AMP algorithm is a signal processing algorithm proposed in recent years. It has attracted widespread attention due to its fast convergence speed. Its mathematical iteration formula is expressed as

[0033]

[0034]

[0035] Where v t For the signal tt=0,1,2,…T-1th iteration Estimate residuals, initialize v_1 = 0, and

[0036] The deep expansion algorithm LAMP simplifies AMP into the following form:

[0037]

[0038]

[0039] Equations (10a) and (10b) are based on the generalization of AMP algorithms (9a) and (9b), where matrices A, A T At iteration t, it behaves as A t ,B t In order to reduce the training parameters required by the LAMP network and speed up the signal processing, without changing the algorithm characteristics, A t =β t A, at this time, A t There is only scalar β t Changes with the number of iterations t. LAMP network parameters Through the training input data Minimize the loss function L(θ) in formula (6) to achieve self-learning and update;

[0040] In the TwDU method, TwDU-LAMP The iterative process is

[0041]

[0042] Based on the original training parameters of LAMP, trainable parameters ω and ψ are added to establish the connection between signals; ω and ψ convert the estimated values ​​of the first two steps into and Adaptive and current signal estimation through deep learning technology Establishing connections between signals speeds up the speed and accuracy of signal reconstruction.

[0043] Further, in step S2, the steps of improving the TISTA algorithm using the TwDU algorithm are as follows:

[0044] TISTA is another deep expansion form of the ISTA algorithm, and its mathematical representation is

[0045]

[0046]

[0047]

[0048]

[0049] Where the matrix W = A T (AA T ) -1 is the pseudo-inverse matrix of matrix A, σ 2 is the noise variance, η MMSE is the minimum mean square error (MMSE) estimator:

[0050]

[0051] in is the variance of non-zero elements of the input signal, is the error variance, p is the probability of a non-zero element in the input signal, and

[0052]

[0053] From (12), we can see that the signal error variance estimate in the depth expansion algorithm TISTA is and The influence of the final sparse signal estimate is crucial. is the step size parameter, which is used to control the error variance. It is also a parameter that needs to be trained for deep learning technology. Its number is equal to the number of network layers. TISTA algorithm training parameter θ = [γ t ];

[0054] In the TwDU method, TwDU-TISTA The iterative process is

[0055]

[0056] The trainable parameters are Θ = [ω, ψ, γ t ], in TwDU-TISTA, ω and ψ also use the estimated values ​​of the first two steps of the signal and Adaptive and signal The connection is established, which improves the convergence speed of the depth expansion algorithm TISTA.

[0057] Further, in step S3, the signal is reconstructed through the signal sparseness in step S1 and the signal algorithm processing in step S2. The estimated value of the signal output in step S2 is Input to the mean square error loss function In the present invention, the algorithm parameters are updated by using the back propagation mechanism based on the gradient descent method through deep learning technology, and the signal is reconstructed and restored by combining the incremental training method.

[0058] The beneficial effect of the present invention is that the sparse signal reconstruction method based on the two-step depth expansion strategy can make full use of the correlation between signals. Whether it is for one-dimensional signals in wireless communications or for two-dimensional image signals, the method proposed by the present invention can reconstruct signals faster and improve the reconstruction accuracy of signals.

[0059] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0061] Figure 1 It is the tth iteration of the deep expansion network LAMP;

[0062] Figure 2 It is the block diagram of TwDU-LAMP algorithm;

[0063] Figure 3 The tth iteration of the deep expansion network TISA;

[0064] Figure 4 It is the block diagram of TwDU-TISTA algorithm;

[0065] Figure 5 NMSE comparison of each deep expansion algorithm, SNR = 40dB;

[0066] Figure 6 NMSE comparison of each deep expansion algorithm, SNR = 30dB;

[0067] Figure 7 NMSE comparison of each deep expansion algorithm, SNR = 20dB. DETAILED DESCRIPTION

[0068] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0069] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0070] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0071] The present invention provides a sparse signal reconstruction method based on a two-step depth expansion strategy, comprising the following steps:

[0072] Step 1: Sparsification of input signal.

[0073] In compressed sensing, It is the original signal vector, which can be a signal collected by sensors in the Internet of Things environment, a signal in wireless communication, or a two-dimensional image signal collected by various electronic devices. is the observation matrix, is a Gaussian white noise vector, and y = Φs + n, where is the observed signal vector obtained by sampling s through the observation matrix Φ. Assume that the original signal vector s is in a known standard orthogonal basis It can be sparse, that is, s = Ψx, where It is called the original sparse signal, which is the sparse representation of the original signal vector s in the new transform domain Ψ. Let the sensor matrix So y = Ax + n. The purpose of the compressed sensing reconstruction algorithm is to reconstruct the estimated value of the original sparse signal x through the observed signal y in such an underdetermined linear system. And then by Reconstruct the original signal. Common reconstruction algorithms model the above sparse reconstruction problem as the following convex optimization problem:

[0074]

[0075] The implementation case provided by the present invention is a solution to (1).

[0076] Step 2: The TwDU algorithm processes the input signal. The sparse signal y is input into the algorithm for processing.

[0077] The traditional reconstruction algorithm is deeply expanded. The symbol Γ(·) is used to represent the traditional reconstruction algorithm model, and the symbol U· represents the deep expansion model of the traditional reconstruction algorithm. Taking ISTA as an example, ISTA is re-described as

[0078]

[0079]

[0080] Let βA T =B,I N -BA=S, we can get:

[0081]

[0082] The above is the traditional ISTA algorithm. The improved ISTA algorithm using the deep expansion technology is expressed as

[0083]

[0084] Formula (5) represents the deep expansion of the traditional algorithm ISTA into LISTA, and then obtains the result of the next iteration. In the deep expansion algorithm LISTA, the parameter θ = [B, S, τ] is trained by deep learning technology to train the input data pair Minimize the quadratic loss function (6) to achieve self-learning and updating.

[0085]

[0086] Then, the depth expansion algorithm is expanded in two steps. The two-step depth expansion strategy is proposed from The results do not only depend on It also depends on That is, the estimated value of each depth expansion algorithm depends on the estimated values ​​of the previous two depth expansion algorithms, rather than just on the previous one, that is, the existence of correlation between signals, and its formula is expressed as:

[0087]

[0088] In formula (7), UΓ· does not refer specifically to LISTA, but generally refers to various deep expansion algorithms, such as LAMP, TISTA, etc. The parameters that need to be trained using deep learning technology in (7) are θ=[ω,ψ,θU·], where θU· is the parameter that needs to be trained in each deep expansion algorithm. If it is TwDU-LISTA, then θU·=[B,S,τ]. In formula (7) and A two-step depth expansion strategy is used in each evaluation process. In addition, and The training parameters of have also been trained in their respective two-step depth expansions and no longer participate in the current training, which can reduce the computational burden. The results of the first two calculations ( and ) The influencing factors ω and ψ of the current calculation results will be adjusted adaptively according to the characteristics of the data using the powerful learning ability of deep learning. When ω=ψ=1.0,

[0089]

[0090] and The coefficient term is 0, and the results of the first two iterations have no effect on the current result. At this point, (8) and (5) are both ordinary depth expansion schemes. In fact, the proposed scheme (7) is more universal, and (5) can be regarded as a special case of (7). However, as the number of algorithm iterations increases, the parameters ω and ψ are continuously self-optimized through the back-propagation mechanism in deep learning, and finally stabilize at a small fluctuation above and below the optimal value. At this point, The coefficient 1-ω is The coefficients ω-ψ of are no longer 0, and the performance of the algorithm has been significantly improved, which indirectly shows that the results of the first two calculations have an important influence on the current result. The two-step deep expansion strategy makes full use of the intrinsic characteristics of the time series signals and uses different weights to jointly influence the current result.

[0091] Incremental training method of parameters. In the method based on the TwDU strategy, the value of the parameter Θ = [ω, ψ, θ(U(·))] will directly affect the reconstruction quality of the sparse signal. Therefore, the training method of Θ is extremely important. In the invention training process, a batch of data is first divided into H small batches of data (batch) and sent to the algorithm network. The network loss value gradually decreases with the training of the batch. When the training of a batch of data is completed, a new batch of data will be sent to the network for training again. After many experiments, it has been verified that the incremental training method is very effective in adjusting Θ and improving network performance. This is because incremental training can not only alleviate the gradient disappearance problem, but also further enhance the generalization ability of the network. The training data is a randomly generated data pair x, y, where y comes from y = Ax + n, which is the feature data after sparse sampling that the two-step expansion network needs to learn, and x is sparse label data. The TwDU algorithm uses the stochastic gradient descent algorithm to learn data features from the batch and reconstruct the original sparse signal x. During the tth gain training process, the optimizer adjusts Θ to promote the objective function of this training. After processing H small batches of data, the optimizer's objective function becomes Although the objective function changes from the first layer to the last layer during the network training process, the parameter Θ uses the previous result as the initial value of this training in each training process, which has a certain consistency. In this paper, in order to control variables, all experiments including control experiments use the incremental training method.

[0092] The TwDU-LAMP and TwDU-TISTA algorithms are used as examples for further processing.

[0093] 1) TwDU-LAMP. The AMP algorithm is a signal processing algorithm proposed in recent years. It has attracted widespread attention due to its fast convergence speed. Its mathematical iterative formula is expressed as

[0094]

[0095]

[0096] Where v t is the signal for the t0,1,2,T-1th iteration Estimate residuals, initialize v -1 = 0, and

[0097] The deep expansion algorithm LAMP simplifies AMP into the following form:

[0098]

[0099]

[0100] (10) is based on the generalization of AMP algorithm (9), where the matrices A, A T At iteration t, it behaves as A t ,B t In order to reduce the training parameters required for the LAMP network and speed up the signal processing, Borgerding and Schniter set A t =β t A, at this time, A t There is only scalar β t Changes with the number of iterations t. LAMP network parameters Through the training input data Minimize the loss function L(θ) in (6) to achieve self-learning and updating. Expand the iterative process in (10) in depth as follows Figure 1 shown.

[0101] In the TwDU method, TwDU-LAMP The iterative process is

[0102]

[0103] The trainable parameters are only increased by two, ω and ψ, based on the original training parameters of LAMP, to establish the connection between signals. Figure 2 As shown. ω and ψ are the estimated values ​​of the first two steps of the signal and Adaptive and current signal estimation through deep learning technology Establishing connections between signals speeds up the speed and accuracy of signal reconstruction.

[0104] 2) TwDU-TISTA. TISTA is another deep expansion form of the ISTA algorithm, and its mathematical expression is:

[0105]

[0106]

[0107]

[0108]

[0109] Where the matrix W = A T (AA T ) -1 is the pseudo-inverse matrix of matrix A, σ 2 is the noise variance.MMSE is the minimum mean square error (MMSE) estimator,

[0110]

[0111] in is the variance of non-zero elements of the input signal, is the error variance, p is the probability of a non-zero element in the input signal, and

[0112]

[0113] From (12), we can see that the signal error variance estimate in the depth expansion algorithm TISTA is and The influence of the final sparse signal estimate is crucial. It is the step size parameter, which is used to control the error variance. It is also the parameter that needs to be trained for deep learning technology. Its number is equal to the number of network layers. TISTA algorithm training parameter θ = [γ t ]. The iterative process in (12) is expanded in depth as follows Figure 3 shown.

[0114] In the TwDU method, TwDU-TISTA The iterative process is

[0115]

[0116] The trainable parameters are Θ = [ω, ψ, γt]. The block diagram of TwDU-TISTA is shown in Figure 4 In TwDU-TISTA, ω and ψ are also the estimated values ​​of the first two steps of the signal. and Adaptive and signal The connection is established, which improves the convergence speed of the depth expansion algorithm TISTA.

[0117] Step three: signal reconstruction and recovery.

[0118] Through the signal sparseness in step 1 and the signal algorithm processing in step 2, this step will reconstruct the signal. The estimated value of the output signal in step 2 Input to the mean square error loss function In this paper, deep learning technology is used to update the algorithm parameters using the back propagation mechanism based on the gradient descent method, and the incremental training method introduced above is combined to reconstruct and restore the signal.

[0119] The present invention is not only applicable to the above cases, but also applicable to other depth expansion algorithms. The pseudo code of the algorithm of the present invention is shown in Table 1.

[0120] Table 1 Two-step depth expansion strategy reconstruction algorithm flow

[0121]

[0122] In order to illustrate the feasibility and superiority of the present invention, a simulation experiment will be conducted below. This experimental system is deployed on the Linux platform, using the PyTorch1.5.1 deep learning framework and the Adam optimizer. In the experiment, a one-dimensional sparse signal that obeys the Bernoulli-Gaussian distribution is used as the simulation input signal. At the same time, the normalized mean square error (NMSE) is used as the judgment criterion to measure the performance of each deep reconstruction algorithm. The length of the simulated sparse signal used in this experiment is N=500, and the dimension of the observation matrix A is M=250, N=500. Each element in the matrix A obeys a Gaussian distribution with a mean of 0 and a variance of 1 / M, that is, A i,j ~N(0,1 / M).

[0123] Figure 5 The normalized minimum mean square error (NMSE) of LISTA, TwDU-LISTA, TISTA, TwDU-TISTA, LAMP and TwDU-LAMP after 12 iterations is shown when SNR = 40dB. The NMSE calculation formula is as follows:

[0124]

[0125] from Figure 5 It can be observed that the reconstruction algorithm based on the two-step deep expansion strategy can better reconstruct sparse signals than the ordinary deep expansion algorithm. TwDU-LISTA and LISTA have similar NMSE in the initial stage. As the number of iterations increases, TwDU-LISTA has about 9dB and 6dB gains compared to LISTA at t=9 and t=12, respectively. TISTA converges in the first 12 iterations, with NMSE=-42dB at convergence, while TwDU-TISTA has reached NMSE-42dB at t=8. Compared with TISTA convergence at t=10, TwDU-TISTA has a faster convergence speed. At the same time, in the first 12 iterations, the NMSE performance of TwDU-LAMP has always been better than that of LAMP, and it is also 2 cycles ahead of LAMP in convergence speed.

[0126] Figure 6 and Figure 7The NMSE comparison of each deep expansion algorithm when the signal-to-noise ratio is 30dB and 20dB is shown respectively. It can be clearly observed from the figure that as the signal-to-noise ratio decreases, the reconstruction ability of each deep expansion algorithm becomes worse. Even so, the reconstruction algorithm based on the TwDU strategy can still reconstruct sparse signals better than the ordinary deep expansion algorithm. When the signal-to-noise ratio is 30dB, TwDU-LISTA has a maximum gain of 0.6dB compared to LISTA, TwDU-TISTA has a maximum gain of 4.6dB compared to TISTA, and TwDU-LAMP has a maximum gain of 3.9dB compared to LAMP. When the signal-to-noise ratio is 20dB, due to the serious noise "pollution", the performance gap between each deep expansion reconstruction algorithm becomes smaller, and the deep expansion algorithm based on the two-step deep expansion strategy has a gain of less than 1dB compared to its ordinary deep expansion algorithm.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A sparse signal reconstruction method based on a two-step deep expansion strategy, characterized in that: Includes the following step: S1: Sparsification of input signals, including: In compressed sensing, is the original signal vector, is the observation matrix, N>M, is a Gaussian white noise vector, and y = Φs + n, where is the observed signal vector obtained by sampling s through the observation matrix Φ; assuming that the original signal vector s is in a known standard orthogonal basis It can be sparse, that is, s = Ψx, where It is called the original sparse signal, which is the sparse representation of the original signal vector s in the new transform domain Ψ. Let the sensor matrix So y=Ax+n; The traditional reconstruction algorithm models the sparse reconstruction problem as the following convex optimization problem: S2: using the two-step deep expansion strategy TwDU algorithm to improve the deep expansion model of the traditional sparse signal reconstruction algorithm; the deep expansion model of the traditional sparse signal reconstruction algorithm includes LISTA, LAMP and TISTA; The steps to improve the LISTA algorithm using the TwDU algorithm are as follows: The ISTA algorithm is deeply expanded, and the symbol Γ(·) is used to represent the ISTA model. The symbol U(·) represents the deeply expanded model of ISTA. The ISTA is re-described as follows: Let βA T =B,I N -BA=S, we get: Using deep expansion technology to improve ISTA is expressed as Formula (5) represents the deep expansion of the traditional algorithm ISTA into LISTA, and then obtains the result of the next iteration; in the deep expansion algorithm LISTA, the parameter θ = [B, S, τ] is trained by deep learning technology to input data pairs Minimize the quadratic loss function (6) to achieve self-learning and updating: Then, the depth expansion algorithm is expanded in two steps, and its formula is expressed as: In formula (7), U(Γ(·)) refers to all deep expansion algorithms, including LISTA, LAMP, and TISTA. The parameters that need to be trained using deep learning technology in formula (7) are θ=[ω,ψ,θ(U(·))], where θ(U(·)) is the parameter that needs to be trained in each deep expansion algorithm. If it is TwDU-LISTA, then θ(U(·))=[B,S,τ]; in formula (7) and A two-step depth expansion strategy was utilized in each evaluation process; and The training parameters of have been trained in their respective two-step depth expansion and are no longer involved in the current training. The results of the first two calculations and The influencing factors ω and ψ of the current calculation results will be adaptively adjusted according to the characteristics of the data using the powerful learning ability of deep learning; when ω=ψ=1.0, and The coefficient term is 0, and the results of the first two iterations have no effect on the current result. At this time, both equation (8) and equation (5) are ordinary depth expansion schemes, and equation (5) is regarded as a special case of equation (7). As the number of algorithm iterations increases, the parameters ω and ψ are continuously self-optimized through the back propagation mechanism in deep learning, and finally stabilize at the optimal value with a small fluctuation. At this time, The coefficient 1-ω is The coefficients ω-ψ of are no longer 0; Incremental training of the parameter Θ: During the training process, a batch of data is first divided into H small batches of data batches and sent to the algorithm network. The network loss value gradually decreases with the training of the batch; when the training of a batch of data is completed, a new batch of data will be sent to the network for training again; the training data is a randomly generated data pair (x, y), where y comes from y = Ax + n, which is the feature data after sparse sampling that the two-step expansion network needs to learn, and x is the sparse label data; the TwDU algorithm uses the stochastic gradient descent algorithm to learn data features from the batch and reconstruct the original sparse signal x; during the tth gain training process, the optimizer adjusts Θ to promote the objective function of this training Minimize; after processing H small batches of data, the optimizer's objective function becomes The parameter Θ uses the previous result as the initial value of this training in each training process; S3: Reconstruct and restore the original sparse signal using the improved sparse signal reconstruction algorithm; through the signal sparseness in step S1 and the signal algorithm processing in step S2, this step will reconstruct the signal, and the estimated value of the output signal in step S2 Input to the mean square error loss function In the present invention, the algorithm parameters are updated by using the back propagation mechanism based on the gradient descent method through deep learning technology, and the signal is reconstructed and restored by combining the incremental training method.

2. The sparse signal reconstruction method based on the two-step depth expansion strategy according to claim 1 is characterized in that: In step S2, the steps of improving the LAMP algorithm using the TwDU algorithm are as follows: The mathematical iteration formula of the AMP algorithm is expressed as Where v t is the signal for the tth iteration Estimated residual, t=0,1,2,…T-1, initialize v -1 = 0, and The deep expansion algorithm LAMP simplifies AMP into the following form: Equations (10a) and (10b) are based on the generalization of AMP algorithm equations (9a) and (9b), where the matrix (A, A T ) is expressed as (A t ,B t ), let A t =β t A, at this time, A t There is only scalar β t Changes with the number of iterations t; LAMP network parameters Through the training input data Minimize the loss function L(θ) in formula (6) to achieve self-learning and update; In the TwDU method, TwDU-LAMP The iterative process is Add trainable parameters ω and ψ to the original training parameters of LAMP to establish the connection between signals; ω and ψ are the estimated values ​​of the first two steps of the signal and Adaptive and current signal estimation through deep learning technology Establish a connection.

3. The sparse signal reconstruction method based on the two-step depth expansion strategy according to claim 1 is characterized in that: In step S2, the steps of improving the TISTA algorithm using the TwDU algorithm are as follows: TISTA is another deep expansion form of the ISTA algorithm, and its mathematical representation is Where the matrix W = A T (AA T ) -1 is the pseudo-inverse matrix of matrix A, σ 2 is the noise variance, η MMSE is the minimum mean square error MMSE estimator: in α 2 is the variance of non-zero elements of the input signal, is the error variance, p is the probability of a non-zero element in the input signal, and Scalar variables is the step size parameter, which is used to control the size of the error variance. It is also a parameter that needs to be trained for deep learning technology. Its number is equal to the number of network layers, where t = 0, 1, ... T-1; TISTA algorithm training parameter θ = [γ t ]; In the TwDU method, TwDU-TISTA The iterative process is The trainable parameters are Θ = [ω, ψ, γ t ], in TwDU-TISTA, ω and ψ are the estimated values ​​of the signal two steps ahead and Adaptive and signal Establish a connection.

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