Method and device for recovering sparse signal support set

Abstract

The invention discloses a recovery method of a sparse signal support set, which comprises the following steps of: dividing a sparse signal of a signal to be recovered into a plurality of sub-signals, determining a state set, an action set and the number of column vectors in a sensing matrix of each sub-signal according to the number of sparse signals included in the sub-signal, determining a reward value set and an initial Q value set, selecting an action corresponding to the current maximum Q value in the Q value set as a next action, determining a corresponding next state after the next action is executed, determining a corresponding predicted Q value according to the next action and the next state, and updating the current Q value according to the predicted Q value and the current reward value. And taking the predicted Q value as the current Q value until a set cycle index threshold value is reached. The local actions of the sub-signals are summarized to obtain the global action, and the sparse signal support set of the to-be-recovered signal is obtained according to the information of the column position where the column vector selected by the global action is located, so that the intelligence of support set recovery is improved.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to a method for recovering a sparse signal support set. Background Art

[0002] A sparse signal is a discrete signal with very few non-zero elements. If the number of non-zero elements in a signal does not exceed k, then the signal is called a k-sparse signal. In practice, signals are often not sparse. In order to facilitate signal processing, a sparse representation is generated. It uses a sparse basis D to linearly represent a non-sparse signal x with a, that is, x = Da, where the coefficient a is sparse, which is called a sparse representation or sparse signal. There are many ways to represent sparsely, for example, the k-svd algorithm, which constructs a dictionary to represent data sparsely. It is often used in applications such as image compression, encoding, and classification. The coefficient matrix is ​​sparse through dictionary updates and coefficient matrix updates; for another example, for images, they are generally sparsed through wavelet transforms; for another example, the time domain signal is Fourier transformed to obtain a frequency domain signal, and the representation of the frequency domain signal in the frequency domain is sparse.

[0003] The support set represents the index set of the locations of non-zero elements in a sparse signal. In sparse signal processing, accurate recovery of the support set is the basis of signal reconstruction and feature extraction.

[0004] Most of the research on sparse signal support set recovery focuses on solving the sparse support set recovery problem under a given measurement matrix. For example, compressed sensing uses the sparsity of the signal to efficiently recover the signal with only a small amount of observation data by applying specific algorithms.

[0005] Existing sparse signal support set recovery methods are mainly based on signal processing ideas and are implemented using general computing platforms such as digital signal processors. It is difficult to automatically select appropriate parameters according to different data characteristics. Summary of the invention

[0006] The invention provides a method for recovering a sparse signal support set, so as to improve the intelligence of recovering the sparse signal support set.

[0007] A first aspect of the present invention provides a method for recovering a sparse signal support set, the method comprising:

[0008] The sparse signal of the signal to be restored is divided into one or more sub-signals.

[0009] For each sub-signal,

[0010] According to the number of sparse signals included in the sub-signal, a state set, an action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, and the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix.

[0011] Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state.

[0012] The action corresponding to the current maximum Q value in the Q value set is selected as the next action, and the next state corresponding to the next action after being executed is determined, and the corresponding predicted Q value is determined according to the next action and the next state, and the current Q value corresponding to the current action performed in the current state is updated according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, and the predicted Q value is used as the current Q value, and the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action is returned until the set cycle number threshold is reached, and the current action is determined as the local action of the sub-signal.

[0013] Summarize the local actions of each sub-signal to get the global action,

[0014] According to the column position information of the column vector selected by the global action, a sparse signal support set of the signal to be restored is obtained.

[0015] As a possible implementation manner, the sparse signals in the sub-signals are adjacent to each other in sequence in the sparse base domain, the last sparse signal in the front sub-signal and the first sparse signal in the rear sub-signal of two adjacent sub-signals are adjacent to each other in the sparse base domain, and the number of sparse signals included in each sub-signal is the same.

[0016] As a possible implementation manner, the number of column vectors in the perception matrix is ​​the same as the number of sparse signals included in the sub-signals, the number of row vectors in the perception matrix is ​​the same as the number of observations, and the perception matrix is ​​a random Gaussian matrix with a restricted isometry property.

[0017] The combination status includes: a status where no column vector in the perception matrix is ​​selected, and a status where at least one column vector in the perception matrix is ​​selected;

[0018] The number of actions included in the action set is the same as the number of column vectors in the perception matrix, and each action corresponds to a selection operation of a column vector in the perception matrix.

[0019] As a possible implementation, the reward value is determined in the following manner:

[0020] For each action corresponding to each state in the state set,

[0021] Calculate the dot product between the residual vector of the sub-signal in this state and the column vector selected by the action to obtain the reward value of the action corresponding to the sub-signal in this state.

[0022] As a possible implementation, the residual vector is determined in the following manner:

[0023] For each state in the state set,

[0024] According to the selected column vector in the perception matrix represented by the state, the estimated vector of the sub-signal is calculated,

[0025] The difference between the estimated vector of the sub-signal and the observed vector of the sub-signal is calculated to obtain the residual vector of the sub-signal in this state.

[0026] As a possible implementation manner, the estimated vector of the sub-signal is calculated in the following manner:

[0027] Calculate the product of the current column vector selected in the perception matrix and the sub-signal corresponding to the current column vector to obtain a product result vector.

[0028] The product result vector is added to the noise vector to obtain the estimated vector of the sub-signal.

[0029] As a possible implementation manner, the noise vector is a Gaussian noise vector;

[0030] The updating of the current Q value corresponding to the current action performed in the current state according to the predicted Q value and the current reward value corresponding to the current action performed in the current state includes:

[0031] According to the predicted Q value, the current Q value, the current reward value, the learning rate, and the discount factor, an updated Q value for updating the current Q value is calculated, and the updated Q value replaces the current Q value.

[0032] As a possible implementation, the step of calculating an updated Q value for updating the current Q value according to the predicted Q value, the current Q value, the current reward value, the learning rate, and the discount factor includes:

[0033] Calculate the product of the discount factor and the predicted Q value, subtract the current Q value from the product of the product and the accumulated result of the current reward value, multiply it by the learning rate, and then add it to the current Q value;

[0034] The step of obtaining the sparse signal support set of the signal to be recovered based on the column position information of the column vector selected by the global action includes:

[0035] The sparse signal corresponding to the column position information of the column vector selected by the global action is regarded as a sparse signal with non-zero elements, and the position information of the sparse signal is regarded as an element in the support set.

[0036] As a possible implementation manner, the sub-signal includes two adjacent sparse signals, and when the number of sparse signals of the signal to be restored is an odd number, a zero signal is added to the last sub-signal;

[0037] The perception matrix includes a first column vector and a second column vector;

[0038] The state set includes: a state where neither the first column vector nor the second column vector in the perception matrix is ​​selected, a state where the first column vector in the perception matrix is ​​selected, a state where the second column vector in the perception matrix is ​​selected, and a state where both the first column vector and the second column vector in the perception matrix are selected;

[0039] The action set includes: a selection operation for selecting a first column vector in the perception matrix, and a selection operation for selecting a second column vector in the perception matrix.

[0040] A second aspect of the present application provides a device for recovering a sparse signal support set, the device comprising:

[0041] A segmentation module is used to segment the sparse signal of the signal to be restored into one or more sub-signals,

[0042] A learning module is used for each sub-signal,

[0043] According to the number of sparse signals included in the sub-signal, a state set, an action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, and the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix.

[0044] Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state.

[0045] The action corresponding to the current maximum Q value in the Q value set is selected as the next action, and the next state corresponding to the next action after being executed is determined, and the corresponding predicted Q value is determined according to the next action and the next state, and the current Q value corresponding to the current action performed in the current state is updated according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, and the predicted Q value is used as the current Q value, and the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action is returned until the set cycle number threshold is reached, and the current action is determined as the local action of the sub-signal.

[0046] The recovery module is used to summarize the local actions of each sub-signal to obtain the global action, and obtain the sparse signal support set of the signal to be recovered according to the column position information of the column vector selected by the global action.

[0047] The sparse signal support set recovery method provided by the present invention obtains the sparse signal support set through a Q-value-based learning process, thereby improving the recovery speed and accuracy of the sparse signal, better processing noise and incomplete data, thereby improving robustness and reliability, making it applicable to scenarios with various signal-to-noise ratios, thereby improving the intelligence of sparse signal support set recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flowchart of a sparse signal support set recovery method according to an embodiment of the present application.

[0049] Figure 2 A schematic diagram of a flow chart of the method for recovering a sparse signal support set according to this embodiment.

[0050] Figure 3 A schematic diagram showing the performance comparison between the method of the embodiment of the present application and other recovery methods under different numbers of non-zero elements k and high signal-to-noise ratio conditions.

[0051] Figure 4 A schematic diagram showing the performance comparison between the method of the embodiment of the present application and other recovery methods under different numbers of non-zero elements k and high signal-to-noise ratio conditions.

[0052] Figure 5 A schematic diagram of the effect of noise on the false recovery rate in different recovery methods.

[0053] Figure 6 A schematic diagram of a device for recovering a sparse signal support set according to an embodiment of the present application. DETAILED DESCRIPTION

[0054] In order to make the objectives, technical means and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings.

[0055] The applicant's research found that for the support set recovery method of related sparse signals, firstly, although the optimization algorithm can theoretically guarantee a high recovery accuracy, the computational complexity is high and it is difficult to apply to large-scale high-dimensional problems; secondly, the sparse signal support set recovery algorithm is easily interfered in a noisy environment, resulting in a significant decrease in recovery accuracy. For example, noise will mask the weak components of the sparse signal, making it difficult to accurately identify the support set. In order to cope with high-dimensional signal and noise interference, a sparse signal support set recovery method proposed in an embodiment of the present application improves accuracy, robustness and interpretability by introducing reinforcement learning, and can select appropriate parameters according to different data features and environmental conditions.

[0056] See also Figure 1 As shown, Figure 1 A schematic diagram of a flow chart of a sparse signal support set recovery method according to an embodiment of the present application. The method comprises:

[0057] Step 101, dividing the sparse signal of the signal to be restored into one or more sub-signals,

[0058] As an example, the sparse signals of the signal to be recovered are sorted in the sparse base domain to obtain a sparse signal sequence, and the sparse signal sequence is divided into more than one sub-signals, so that the sparse signals in the sub-signals are adjacent to each other in sequence, and the last sparse signal in the front sub-signal and the first sparse signal in the rear sub-signal of two adjacent sub-signals are adjacent in the sparse base domain,

[0059] To reduce complexity, each sub-signal includes the same number of sparse signals.

[0060] Step 102, for each sub-signal,

[0061] According to the number of sparse signals included in the sub-signal, the state set, action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix, and the perception matrix is ​​used to characterize the measurement matrix in the sparse basis domain; for example, if the number of sparse signals included in the sub-signal is p, then the perception matrix has p column vectors, and the state set includes 2 p states, the action set includes p actions, each action corresponds to a selection operation in which a column vector in the perception matrix is ​​selected.

[0062] Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state.

[0063] Select the action corresponding to the current maximum Q value in the Q value set as the next action, and determine the next state corresponding to the next action after being executed, determine the corresponding predicted Q value according to the next action and the next state, and update the current Q value corresponding to the current action performed in the current state according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, use the predicted Q value as the current Q value, return to execute the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action, until the set loop count threshold is reached, and determine the current action as the local action of the sub-signal, wherein the local action is used to characterize that the sparse signal corresponding to the position of the column vector of its selection operation is a non-zero element.

[0064] As an example, the next state can be determined based on the ε-greedy strategy or randomly, and this application does not limit this.

[0065] The reward value is determined as follows:

[0066] For each action corresponding to each state in the state set,

[0067] Calculate the dot product between the residual vector of the sub-signal in this state and the column vector selected by the action to obtain the reward value of the action corresponding to the sub-signal in this state.

[0068] The residual vector is determined as follows:

[0069] For each state in the state set,

[0070] According to the selected column vector in the perception matrix represented by the state, the estimated vector of the sub-signal is calculated,

[0071] The difference between the estimated vector of the sub-signal and the observed vector of the sub-signal is calculated to obtain the residual vector of the sub-signal in this state.

[0072] Step 103, the local actions of each sub-signal are summarized to obtain the global action.

[0073] Step 104: Obtain a sparse signal support set of the signal to be restored according to the column position information of the column vector selected by the global action.

[0074] As an example, the sparse signal corresponding to the column position information of the column vector selected by the global action is taken as a sparse signal with non-zero elements, and the position information of the sparse signal is taken as an element in the support set.

[0075] The sparse signal support set recovery method provided in the embodiment of the present application applies the iterative process of Q learning to the sparse signal recovery process, and finds the position of non-zero elements (i.e., support set) through continuous learning and adjustment, which can better handle noise and incomplete data, thereby improving the robustness and reliability of the overall method, making it suitable for scenarios with various signal-to-noise ratios, and is conducive to improving the speed and accuracy of sparse signal recovery.

[0076] To facilitate understanding of the embodiments of the present application, a sub-signal including two sparse signals is used as an example for explanation below. It should be understood that the present application is not limited thereto.

[0077] The signal observation model can be expressed as:

[0078] y M×1 =A M×N x N×1 +n M×1

[0079] Among them, y M×1 Represents an observation matrix with M rows and 1 column, also called an observation vector. Each element in the observation matrix represents an observation value, M represents the number of observation values, and x N×1 represents a matrix of signals to be recovered with N rows and 1 column. Each element in the matrix of signals to be recovered represents information of a signal to be recovered. N represents the number of signals to be recovered. M×N represents a measurement matrix with M rows and 1 column, n M×1 It is a noise matrix with M rows and 1 column, also called a noise vector. Each element of the noise matrix represents a noise value, which is Gaussian noise in this embodiment.

[0080] Assume that all signals to be recovered are sparse on the sparse basis Ψ, that is:

[0081] x N×1 =Ψ M×N o N×1 ,

[0082] Among them, N×1 is x N×1 The sparse representation matrix of the signal to be restored is also called the sparse signal of the signal to be restored. Each element in the sparse representation matrix is ​​a sparse representation of the signal to be restored. M×N represents a sparse basis matrix with M rows and 1 column. Each element in the sparse basis matrix is ​​a sparse basis.

[0083] Then we have:

[0084] y M×1 =A M×N x N×1 +n M×1 =A M×N Ψ M×N o N×1+n M×1 =Θ M×N o N×1 +n M×1 (1)

[0085] Among them, A M×N Ψ M×N o N×1 =Θ M×N o N×1 , Θ M×N is a perception matrix with M rows and 1 column, used to represent the measurement matrix in the sparse basis domain.

[0086] Given that the original signal before the sparse representation can be recovered through a small number of linear measurements, this process relies on two key elements:

[0087] 1. Sparsity: The signal to be recovered has a sparse representation under a sparse basis.

[0088] 2. The sensing matrix needs to satisfy the restricted isometry property (RIP) so that the sparse structure of the signal to be recovered is not destroyed during the measurement process. In other words, the measurement matrix A M×N With the sparse basis matrix Ψ M×N Not relevant.

[0089] Assume that the signal matrix to be restored is a k-sparse signal on a sparse basis Ψ, if there exists δ k ∈(0,1) such that

[0090]

[0091] Then the perception matrix satisfies the restricted isometry property.

[0092] See also Figure 2 As shown, Figure 2 FIG. 1 is a flow chart of a method for recovering a sparse signal support set according to an embodiment of the present invention. The method comprises:

[0093] Step 201 : setting constraints on the sparse signal of the signal to be restored, and normalizing the sparse signal.

[0094] The constraints include at least: signal length, sparsity, and noise limitation of the signal to be restored.

[0095] Step 202 , in order to avoid directly processing a high-dimensional signal, the sparse signal is divided into a plurality of sub-signals to ensure that the processing process of each sub-signal can be performed independently, thereby reducing the overall computational complexity.

[0096] In this embodiment, the sparse signals are sorted in the sparse base domain to obtain a sparse signal sequence, which is expressed by a mathematical formula: o1, o2, ... o NWhen the number of sparse signals N is an even number, two adjacent sparse signals are divided into a sub-signal. In this way, when N = 2n, there are n sub-signals, n is a natural number, and the sub-signal set can be expressed mathematically as: {o1, o2}, {o3, o4}, ... {o N-1 , o N}.

[0097] When N is an odd number, two adjacent sparse signals are divided into a sub-signal, and the last sparse signal and a zero signal are combined into a sub-signal.

[0098] For each sub-signal, perform the following steps:

[0099] Step 203, according to the number of sparse signals included in the sub-signal, set the state set, action set, and the number of column vectors in the perception matrix of the sub-signal, and set the reward function,

[0100] As an example, since a sub-signal includes two sparse signals, the perception matrix is ​​composed of a first column vector located in the first column and a second column vector located in the second column. The number of elements contained in each column vector is the same as the number of observations.

[0101] As an example, the state set is a set of state spaces, and the state space is used to characterize the state combination of each column in the selected perception matrix. In this embodiment, the state set includes: the state of not selecting any column of the perception matrix, the state of selecting the second column in the perception matrix, the state of selecting the first column in the perception matrix, and the state of selecting the first and second columns in the perception matrix; each state is represented by a state sequence composed of 0 and 1, and the state sequence corresponds to the sequence position of the sparse signal sequence. 0 indicates that there is no non-zero element in the sparse signal at its sequence position, and 1 indicates that there may be a non-zero element. In this way, each state indicates whether the current sub-signal is selected for recovery. It can be expressed as:

[0102] S={s0=(0,0), s1=(0,1), s2=(1,0), s3=(1,1)}.

[0103] Among them, S represents the state set,

[0104] s0 represents the state where no column vector of the perception matrix is ​​selected, indicating that there are no non-zero elements in the two sparse signals in the sub-signal;

[0105] s1 indicates the state where the second column vector is selected, indicating that the first sparse signal in the sub-signal does not have non-zero elements, but the second sparse signal may have non-zero elements;

[0106] s2 indicates the state where the first column vector is selected, indicating that the first sparse signal in the sub-signal may have non-zero elements, while the second sparse signal does not have non-zero elements;

[0107] s3 indicates the state where the first column vector and the second column vector are selected, indicating that both the first sparse signal and the second sparse signal in the sub-signal may have non-zero elements.

[0108] The action set is a set of action spaces, which are used to represent the selectable column vectors in the perception matrix. Each action represents the selection operation of a column vector in the perception matrix. Through this action selection mechanism, the position of the non-zero elements of the sub-signal can be gradually restored, and the Q value update of each step of the action can be recorded.

[0109] In this embodiment, the action space includes: selecting the first column vector in the perception matrix and selecting the second column vector in the perception matrix, which is expressed by a mathematical formula:

[0110] A={a0=0,a1=1}.

[0111] Among them, A represents the action set, a0 represents the operation of selecting the first column vector of the perception matrix, and a1 represents the operation of selecting the second column vector.

[0112] The reward function is used to calculate the reward value corresponding to selecting an action in any state. The higher the reward value, the higher the probability of non-zero elements in the sub-signal. The reward function can be set according to the recovery accuracy of the signal. In this embodiment, the reward function is the dot product between the residual vector and the column vector selected by the perception matrix action. It can be expressed as:

[0113]

[0114] Among them, R(s, a) represents the reward value under the condition of state s and action a, and residual is the residual vector. It is the column vector of the i-th column in the perception matrix selected for action a, and dot represents the dot product operation.

[0115] Step 204, respectively set the learning rate and discount factor, initialize the perception matrix and Q table, establish the residual table and the reward table,

[0116] As an example, a random Gaussian matrix is ​​used as the perception matrix.

[0117] The residual table, as a form of residual set, is used to characterize the residual vector corresponding to each state, as shown in Table 1.

[0118] Table 1

[0119] state Residual vector s0 Residual vector 1 s1 Residual vector 2 s2 Residual vector 3 s3 Residual vector 4

[0120] The residual vector is used to characterize the difference between the estimated vector and the observed vector of the sub-signal, wherein the estimated vector is estimated based on the selected column vector corresponding to the state, the vector composed of the sub-signals, and the noise vector. In this embodiment,

[0121] When the state is s0, the column vectors in the perception matrix are not selected, and the estimated vector of the sub-signal is:

[0122]

[0123] in, is the estimated vector, o 2×1 is the column vector composed of the sparse signal sequence in the sub-signal, n M×1 is the noise vector, I M×1 is a unit column vector;

[0124] When the state is s1, the second column vector in the perception matrix is ​​selected, and the estimated vector of the sub-signal is:

[0125]

[0126] Among them, Θ M×1 is the second column vector in the perception matrix, o 1×1 is the sparse signal corresponding to the second column vector in the perception matrix, that is, the second sparse signal in the sparse signal sequence;

[0127] When the state is state s2, the first column vector in the perception matrix is ​​selected, and the estimated vector of the sub-signal is:

[0128]

[0129] Among them, Θ M×1 is the first column vector in the perception matrix, o 1×1 is the sparse signal corresponding to the first column vector in the perception matrix, that is, the first sparse signal in the sparse signal sequence;

[0130] When the state is state s3, the first column vector and the second column vector in the perception matrix are both selected, and the estimated vector of the sub-signal is:

[0131]

[0132] Among them, Θ M×2 is the perception matrix, o 2×1 is a column vector composed of sparse signals corresponding to the perception matrix, that is, a column vector composed of sparse signal sequences;

[0133] According to the estimated vector of each state, the residual vector of each state can be obtained, which can be expressed as follows:

[0134]

[0135] Among them, residual M×1 is the residual vector, y M×1 is the observation vector, is the estimated vector.

[0136] The reward table is a form of reward value set, which is used to establish the reward value corresponding to each state and each action. See Table 2.

[0137] Table 2

[0138]

[0139] The reward values ​​in the reward table can be determined as follows:

[0140] For each action corresponding to each state,

[0141] According to the state, the residual vector corresponding to the state is determined, and according to the action, the column vector in the perception matrix selected by the action is determined.

[0142] The reward value in this state is calculated according to formula (2).

[0143] The Q table is a form of Q value set, which is used to establish the Q value corresponding to each action and each state. See Table 3. Each Q value is set to an initial value.

[0144] Table 3

[0145]

[0146]

[0147] Step 205, select any Q value from the Q table as the current Q value,

[0148] Step 206, according to the current state and current action corresponding to the current Q value, determine the current reward value in the reward table.

[0149] Step 207, according to the current maximum Q value in the Q table, select the action corresponding to the current maximum Q value in the Q table as the next action, determine the next state after the next action is executed according to the ε-greedy strategy, and determine the Q value corresponding to the next state as the predicted Q value, based on the predicted Q value, the current reward value, and the current Q value, calculate the updated Q value for updating the current Q value, replace the current Q value with the updated Q value, so as to update the current Q value.

[0150] The updated Q value is calculated as follows:

[0151] Calculate the product of the discount factor and the predicted Q value, subtract the current Q value from the product and the accumulated result of the current reward value, multiply it by the learning rate, and then add it to the current Q value. It can be expressed as:

[0152]

[0153] Among them, Q(s,a) represents the current Q value at the current state s and the current action a; R(s,a) represents the current reward value at the current state s and the current action a, α is the learning rate, γ is the discount factor, Q(s′,a′) represents the predicted Q value of the next action a′ and the next state s′ corresponding to the current maximum Q value, and Q′(s,a) is the updated Q value at the current state s and the current action a.

[0154] Step 208, taking the predicted Q value corresponding to the selected next action and next state as the current Q value, returning to execute step 206, until the set loop number threshold is reached, taking the current action as the local action of the sub-signal, which represents that the sparse signal corresponding to the position of the column vector of the currently selected perception matrix is ​​a non-zero element.

[0155] For example, in this embodiment, if the column vector of the currently selected perception matrix is ​​the second column vector in the perception matrix, the second sparse signal in the sparse sequence is a non-zero element; if the column vector of the currently selected perception matrix is ​​the first column vector in the perception matrix, the first sparse signal in the sparse sequence is a non-zero element.

[0156] The local motion acquisition process of the above-mentioned sub-signals can be executed in parallel, so as to improve the computational efficiency and prevent the dimensionality disaster caused by too high a dimension.

[0157] Step 209: Summarize the local actions of each sub-signal to obtain the global action.

[0158] For example, in this embodiment, for n sub-signals, n local actions can be obtained, and the global action can be obtained by sequentially integrating the n local actions.

[0159] Step 210: Obtain a sparse signal support set of the signal to be restored according to the column position information of the column vector selected by the global action.

[0160] For example, in this embodiment, the sparse signals corresponding to the global action are o2, o3, o5, ... a total of n sparse signals, and the set of sequence position information of these sparse signals is the sparse signal support set of the signal to be restored.

[0161] This embodiment achieves the divide-and-conquer method for sparse signals, significantly reduces the complexity of the problem, and at the same time ensures the accuracy of sparse signal recovery.

[0162] In order to illustrate the technical effect of the sparse signal support set recovery method proposed in this patent, a simulation verification of this method was carried out.

[0163] See also Figure 3 As shown, Figure 3 It is a schematic diagram for comparing the performance of the method of the embodiment of the present application with other recovery methods under different numbers of non-zero elements k and high signal-to-noise ratio conditions. It can be seen from the figure that under high signal-to-noise ratio conditions, the performance of the embodiment of the present application (the curve corresponding to QSR in the figure) for high-sparseness signals is comparable to other algorithms, and the performance for low-sparseness signals is better than other algorithms.

[0164] See also Figure 4 As shown, Figure 4 It is a schematic diagram for comparing the performance of the method of the embodiment of the present application with other recovery methods under different non-zero element numbers k and high signal-to-noise ratio conditions. It can be seen from the figure that under low signal-to-noise ratio conditions, the processing performance of the QSR of the present embodiment for high-sparseness level signals is lower than that of other algorithms, while the processing performance for low-sparseness level signals is comparable to that of other algorithms.

[0165] See also Figure 5 As shown, Figure 5 A schematic diagram of the effect of noise on the false recovery rate in different recovery methods.

[0166] In the figure, the number of non-zero elements k = 2. As can be seen from the figure, as the noise power increases, the performance of the embodiment of the present application is better than that of other algorithms.

[0167] Figure 3 to Figure 5 In the figure, FCB (Federated Consensus Based Algorithm) is a federated consensus algorithm, OMP (Orthogonal Matching Pursuit) is an orthogonal matching pursuit, StOMP (Stagewise Orthogonal Matching Pursuit) is a stage-wise orthogonal matching pursuit, SP (Subspace Pursuit) is a subspace pursuit, CoSaMP (Compressed Sampling Matching Pursuit) is a compressed sampling matching pursuit, and QSR is a recovery method of an embodiment of the present application.

[0168] See also Figure 6 As shown, Figure 6 A schematic diagram of a device for recovering a sparse signal support set according to an embodiment of the present application. The device includes:

[0169] A segmentation module is used to segment the sparse signal of the signal to be restored into one or more sub-signals,

[0170] A learning module is used for each sub-signal,

[0171] According to the number of sparse signals included in the sub-signal, a state set, an action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, and the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix.

[0172] Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state.

[0173] The action corresponding to the current maximum Q value in the Q value set is selected as the next action, and the next state corresponding to the next action after being executed is determined, and the corresponding predicted Q value is determined according to the next action and the next state, and the current Q value corresponding to the current action performed in the current state is updated according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, and the predicted Q value is used as the current Q value, and the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action is returned until the set cycle number threshold is reached, and the current action is determined as the local action of the sub-signal.

[0174] The recovery module is used to summarize the local actions of each sub-signal to obtain the global action, and obtain the sparse signal support set of the signal to be recovered according to the column position information of the column vector selected by the global action.

[0175] An embodiment of the present invention further provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the steps of the method for recovering a sparse signal support set described in the embodiment of the present application are implemented.

[0176] As for the apparatus / network-side device / storage medium embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0177] In this article, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0178] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for recovering a sparse signal support set, characterized in that: The method includes: The sparse signal of the signal to be restored is divided into one or more sub-signals. For each sub-signal, According to the number of sparse signals included in the sub-signal, a state set, an action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, and the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix. Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state. The action corresponding to the current maximum Q value in the Q value set is selected as the next action, and the next state corresponding to the next action after being executed is determined, and the corresponding predicted Q value is determined according to the next action and the next state, and the current Q value corresponding to the current action performed in the current state is updated according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, and the predicted Q value is used as the current Q value, and the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action is returned until the set cycle number threshold is reached, and the current action is determined as the local action of the sub-signal. Summarize the local actions of each sub-signal to get the global action, According to the column position information of the column vector selected by the global action, a sparse signal support set of the signal to be restored is obtained.

2. The recovery method according to claim 1, characterized in that: The sparse signals in the sub-signals are adjacent to each other in the sparse base domain, the last sparse signal in the previous sub-signal and the first sparse signal in the next sub-signal of two adjacent sub-signals are adjacent to each other in the sparse base domain, and the number of sparse signals included in each sub-signal is the same.

3. The recovery method according to claim 2, characterized in that: The number of column vectors in the perception matrix is ​​the same as the number of sparse signals included in the sub-signals, the number of row vectors in the perception matrix is ​​the same as the number of observations, the perception matrix is ​​a random Gaussian matrix, and has a restricted isometry property, The combination status includes: a status where no column vector in the perception matrix is ​​selected, and a status where at least one column vector in the perception matrix is ​​selected; The number of actions included in the action set is the same as the number of column vectors in the perception matrix, and each action corresponds to a selection operation of a column vector in the perception matrix.

4. The recovery method according to claim 3, characterized in that: The reward value is determined as follows: For each action corresponding to each state in the state set, Calculate the dot product between the residual vector of the sub-signal in this state and the column vector selected by the action to obtain the reward value of the action corresponding to the sub-signal in this state.

5. The recovery method according to claim 4, characterized in that: The residual vector is determined as follows: For each state in the state set, According to the selected column vector in the perception matrix represented by the state, the estimated vector of the sub-signal is calculated, The difference between the estimated vector of the sub-signal and the observed vector of the sub-signal is calculated to obtain the residual vector of the sub-signal in this state.

6. The recovery method according to claim 5, characterized in that: The estimated vector of the sub-signal is calculated as follows: Calculate the product of the current column vector selected in the perception matrix and the sub-signal corresponding to the current column vector to obtain a product result vector. The product result vector is added to the noise vector to obtain the estimated vector of the sub-signal.

7. The recovery method according to claim 6, characterized in that: The noise vector is a Gaussian noise vector; The updating of the current Q value corresponding to the current action performed in the current state according to the predicted Q value and the current reward value corresponding to the current action performed in the current state includes: According to the predicted Q value, the current Q value, the current reward value, the learning rate, and the discount factor, an updated Q value for updating the current Q value is calculated, and the updated Q value replaces the current Q value.

8. The recovery method according to claim 7, characterized in that: The step of calculating an updated Q value for updating the current Q value according to the predicted Q value, the current Q value, the current reward value, the learning rate, and the discount factor includes: Calculate the product of the discount factor and the predicted Q value, subtract the current Q value from the product of the product and the accumulated result of the current reward value, multiply it by the learning rate, and then add it to the current Q value; The step of obtaining the sparse signal support set of the signal to be recovered based on the column position information of the column vector selected by the global action includes: The sparse signal corresponding to the column position information of the column vector selected by the global action is regarded as a sparse signal with non-zero elements, and the position information of the sparse signal is regarded as an element in the support set.

9. The recovery method according to claim 8, characterized in that: The sub-signal includes two adjacent sparse signals, and when the number of sparse signals of the signal to be restored is an odd number, a zero signal is added to the last sub-signal; The perception matrix includes a first column vector and a second column vector; The state set includes: a state where neither the first column vector nor the second column vector in the perception matrix is ​​selected, a state where the first column vector in the perception matrix is ​​selected, a state where the second column vector in the perception matrix is ​​selected, and a state where both the first column vector and the second column vector in the perception matrix are selected; The action set includes: a selection operation for selecting a first column vector in the perception matrix, and a selection operation for selecting a second column vector in the perception matrix.

10. A device for recovering a sparse signal support set, characterized in that: The device includes: A segmentation module is used to segment the sparse signal of the signal to be restored into one or more sub-signals, A learning module is used for each sub-signal, According to the number of sparse signals included in the sub-signal, a state set, an action set, and the number of column vectors in the perception matrix of the sub-signal are determined, wherein the state in the state set is used to characterize the combination of the column vectors in the selected perception matrix, and the action in the action set is used to characterize the selection operation of the column vectors in the selected perception matrix. Determine a reward value set and an initial Q value set, wherein the reward value in the reward value set is used to represent the probability that the sub-signal is a non-zero element when each action is performed in each state, and the Q value in the Q value set is used to represent the degree of reward obtained when each action is performed in each state. The action corresponding to the current maximum Q value in the Q value set is selected as the next action, and the next state corresponding to the next action after being executed is determined, and the corresponding predicted Q value is determined according to the next action and the next state, and the current Q value corresponding to the current action performed in the current state is updated according to the predicted Q value and the current reward value corresponding to the current action performed in the current state, and the predicted Q value is used as the current Q value, and the step of selecting the action corresponding to the current maximum Q value in the Q value set as the next action is returned until the set cycle number threshold is reached, and the current action is determined as the local action of the sub-signal. The recovery module is used to summarize the local actions of each sub-signal to obtain the global action, and obtain the sparse signal support set of the signal to be recovered according to the column position information of the column vector selected by the global action.

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