Signal reconstruction method, system and equipment based on dynamic incremental threshold selection strategy

Abstract

The invention relates to a signal reconstruction method, system and equipment based on a dynamic incremental threshold selection strategy, and relates to the technical field of compressed sensing signal processing, the method comprises the following steps: acquiring a low-dimensional observation signal, estimating the low-dimensional observation signal according to the gradient of a loss function to obtain an estimated signal, and then utilizing an incremental function to obtain a reconstructed signal; the method comprises the following steps: performing threshold operation in combination with the number of iterations and preset sparseness to obtain a dynamic threshold related to iteration, applying the dynamic threshold to an algorithm step, performing iteration updating on an estimation signal until an iteration updating termination condition is reached, and obtaining a target signal reconstructed from a low-dimensional observation signal, the target signal being a reconstructed sparse signal. The data processing efficiency and accuracy are improved, the self-adaptive threshold algorithm can be effectively applied to better adapt to the signal structure, and the accuracy and reliability of signal recovery of the algorithm are improved.

Description

Technical Field

[0001] The present application relates to the technical field of compressed sensing signal processing, and in particular to a signal reconstruction method, system and device based on a dynamic increasing threshold selection strategy. Background Art

[0002] In the context of today's technological development, with the continuous emergence of emerging fields such as high-definition video transmission, virtual reality, and the Internet of Things, the accuracy and quality requirements of signal processing are becoming more and more stringent. Taking high-definition video as an example, people have higher and higher expectations for video clarity, smoothness, and color reproduction. This requires that in the process of signal processing, noise and artifacts should be reduced as much as possible, and the quality of the picture should be improved so that the audience can enjoy a better visual experience. In virtual reality technology, users need to interact with the virtual environment in real time, and the accuracy and real-time requirements of the signal are extremely high. Higher-precision signal reconstruction can ensure the authenticity and stability of the virtual scene, reduce delays and freezes, and enable users to interact with virtual objects more naturally and smoothly. The field of the Internet of Things involves a large number of devices and sensors, and the data generated by these devices need to be efficiently and accurately transmitted and processed. For example, in smart homes, various smart devices need to collect and transmit environmental data, user instructions and other information in real time. Improving the accuracy of the algorithm to reconstruct the signal can ensure the accuracy and reliability of these data, so that the smart home system can operate more stably and provide users with better services and experience. In addition, in some professional fields that require extremely high signal quality, such as medical imaging and industrial automation, even a slight deviation in the signal may lead to serious consequences. In medical imaging, more accurate signal reconstruction can help doctors diagnose diseases more accurately and improve treatment effects; in industrial automation, it can ensure accuracy and safety in the production process and improve product quality and production efficiency.

[0003] Existing methods for reconstructing / recovering sparse signals from low-dimensional observation signals mainly use fixed threshold algorithms, such as the Iterative Hard Thresholding (IHT) algorithm, which is a well-known algorithm for solving compression problems. It can effectively recover sparse signals at a low computational cost. However, under the huge amount of data and complex data structure, the use of fixed thresholds has obvious limitations, which seriously affects the performance of the algorithm. It can be seen that with the increasing size and complexity of data, existing signal reconstruction methods are difficult to meet the requirements of efficiency and accuracy. Summary of the invention

[0004] The present application provides a signal reconstruction method, system and device based on a dynamic increasing threshold selection strategy. In the process of reconstructing the signal, as the number of iterations increases, the gradually dynamic increase of the threshold can make the algorithm converge to the final solution more stably, so as to better retain the main features of the signal. Without wasting too much computing time, it effectively accelerates the convergence of the algorithm, improves the efficiency and accuracy of the algorithm in data processing, and solves the problems of low efficiency and insufficient accuracy in existing signal reconstruction methods.

[0005] In a first aspect, the present application provides a signal reconstruction method based on a dynamic increasing threshold selection strategy, comprising:

[0006] Acquire a low-dimensional observation signal and an increasing function, wherein the increasing function is a pre-selected function related to a dynamic threshold;

[0007] According to the gradient of a preset loss function, the low-dimensional observation signal is estimated to obtain an estimated signal;

[0008] Based on the increasing function, a dynamic threshold operation is performed according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold, and the dynamic threshold is applied to the algorithm step to iteratively update the estimated signal until an iterative update termination condition is reached to obtain a reconstructed target signal;

[0009] In which, the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal. During the iterative update process, the dynamic threshold changes incrementally based on the number of iterations. Before the iterative update termination condition is reached, the estimated signal obtained by each iterative update performs a gradient update of the loss function.

[0010] Optionally, obtain low-dimensional observation signals, including:

[0011] Acquire an original sparse signal generated by a sender through data simulation acquisition, wherein the original sparse signal has a sparse structure and is a high-dimensional signal;

[0012] Determine the number of non-zero elements according to the sparse structure of the original sparse signal, and obtain a measurement matrix;

[0013] Performing compression processing on the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal;

[0014] The number of rows of the measurement matrix is ​​smaller than the number of columns.

[0015] Optionally, compressing the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal includes:

[0016] Preset the Gaussian random matrix as the measurement matrix A, and according to aij ~N(0,1 / m), each element of the measurement matrix is ​​independently randomly drawn from a Gaussian distribution;

[0017] Randomly select s indices in the original sparse signal as the positions of non-zero elements, and the non-zero elements obey an independent and identically distributed standard normal distribution;

[0018] The elements at other positions except the non-zero elements in the original sparse signal are set to zero, and the signal is compressed according to y=Ax to obtain a low-dimensional observation signal;

[0019] Among them, x is the original sparse signal, which is an n-dimensional column vector with a sparse structure, y is the low-dimensional observation signal, which is an m-dimensional column vector, A is the measurement matrix used to simulate the compression process, which is an m×n-dimensional matrix, with m<<n, and s is the sparsity.

[0020] Optionally, estimating the low-dimensional observation signal according to the gradient of a preset loss function to obtain an estimated signal includes:

[0021] Perform gradient calculation according to the preset loss function to obtain the loss function gradient;

[0022] According to the gradient of the loss function, the low-dimensional observation signal is updated using the gradient descent method to obtain an estimated signal.

[0023] Optionally, based on the increasing function, a dynamic threshold operation is performed according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold, including:

[0024] According to the characteristics of the problem to be solved, an increasing function with increasing number of iterations is preset as a threshold function;

[0025] According to the threshold function, a function calculation is performed using the number of iterations of the estimated signal and a preset sparsity to obtain a dynamic threshold required for this iteration.

[0026] Optionally, according to the threshold function, function calculation is performed using the number of iterations of the estimated signal and a preset sparsity to obtain a dynamic threshold required for this iteration, including:

[0027] from Select the threshold function and calculate the dynamic threshold for this iteration update;

[0028] Among them, k represents the number of iterations of the current algorithm, is the threshold function, s represents the sparsity of the signal, It means that the integer part is retained. As the number of iterations increases, the dynamic threshold gradually increases.

[0029] Optionally, applying the dynamic threshold to the algorithm step, iteratively updating the estimated signal until an iterative update termination condition is reached to obtain a reconstructed target signal, comprising:

[0030] Applying the dynamic threshold to iteratively update the estimated signal, retaining the maximum absolute value in the estimated signal corresponding to the number of threshold parameters, and setting the remaining elements in the estimated signal to zero;

[0031] Determine the relative reconstruction error between the estimated signal after this iterative update and the original sparse signal;

[0032] Determine whether the relative reconstruction error is less than a preset limit, or whether the number of iterations reaches a preset iteration number threshold;

[0033] When the relative reconstruction error is less than a preset limit and / or the number of iterations reaches a preset iteration number threshold, the iteration is stopped, and the estimated signal obtained by the current iteration is used as the reconstructed target signal;

[0034] When the relative reconstruction error is not less than a preset limit and the number of iterations does not reach a preset iteration number threshold, updating the number of iterations, and performing iterative updating based on the updated number of iterations and a preset sparsity until an iterative updating termination condition is reached to obtain a reconstructed target signal;

[0035] The number of the threshold parameters corresponds to the dynamic threshold.

[0036] Optionally, determining a relative reconstruction error between the estimated signal after the current iteration update and the original sparse signal includes:

[0037] According to relative error = || x k -x * || 2 / ||x * || 2 , calculating the distance between the estimated signal and the original sparse signal, and determining the relative reconstruction error according to the distance, wherein the relative reconstruction error is used to measure the relative distortion degree of the signal;

[0038] Among them, x k represents the estimated signal obtained by the kth iteration update, x * represents the original sparse signal, ||·|| 2 Represents the magnitude of a vector.

[0039] In a second aspect, the present application provides a signal reconstruction system based on a dynamic increasing threshold selection strategy, comprising:

[0040] An observation signal acquisition module, used to acquire a low-dimensional observation signal and an increasing function, wherein the increasing function is a pre-selected function related to a dynamic threshold;

[0041] An estimated signal determination module, used to estimate the low-dimensional observation signal according to the gradient of a preset loss function to obtain an estimated signal;

[0042] A dynamic threshold operation module, used to perform a dynamic threshold operation based on the increasing function and according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold;

[0043] An iterative update module is used to apply the dynamic threshold to the algorithm steps, iteratively update the estimated signal until the iterative update termination condition is reached, and obtain a reconstructed target signal; wherein the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal, and during the iterative update process, the dynamic threshold is incrementally changed based on the number of iterations, and before the iterative update termination condition is reached, the estimated signal obtained by each iterative update is subjected to a gradient update of the loss function.

[0044] In a third aspect, the present application provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus;

[0045] Memory, used to store computer programs;

[0046] The processor is used to implement the steps of the signal reconstruction method based on the dynamic increasing threshold selection strategy as described in any embodiment of the first aspect when executing the program stored in the memory.

[0047] In summary, the embodiment of the present application estimates the acquired low-dimensional observation signal according to the gradient of the loss function to obtain an estimated signal, and then uses the number of iterations selected by the increasing function and the preset sparsity to perform a threshold operation to obtain an iteration-related dynamic threshold, and then iteratively updates the estimated signal according to the dynamic threshold until the iterative update termination condition is reached to obtain a target signal reconstructed from the low-dimensional observation signal, and the target signal is the reconstructed sparse signal. Compared with the fixed threshold solution used in the prior art, the solution provided by the embodiment of the present application, in the process of reconstructing the signal, gradually and dynamically increases the threshold as the number of iterations increases, so that the algorithm can converge to the final solution more stably, so as to better retain the main features of the signal, and effectively accelerate the convergence of the algorithm without spending too much computing time, improve the efficiency and accuracy of the algorithm in data processing, and can effectively apply the adaptive threshold algorithm to better adapt to the signal structure, improve the accuracy and reliability of the algorithm to restore the signal, thereby solving the problems of low efficiency and insufficient accuracy in the existing signal reconstruction methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0049] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0050] Figure 1 A schematic diagram of a flow chart of a signal reconstruction method based on a dynamic increasing threshold selection strategy provided in an embodiment of the present application;

[0051] Figure 2 This is a schematic diagram of the steps of a signal reconstruction method based on a dynamic increasing threshold selection strategy provided by an optional embodiment of the present application;

[0052] Figure 3 It is a schematic diagram of a signal compression process provided by an optional example of the present application;

[0053] Figure 4 is a signal reconstruction flow chart provided by an optional example of the present application;

[0054] Figure 5 This is a schematic diagram of a dynamic increasing threshold selection strategy flow provided by an optional example of the present application;

[0055] Figure 6 A structural block diagram of a signal reconstruction system based on a dynamic increasing threshold selection strategy provided in an embodiment of the present application;

[0056] Figure 7 It is a schematic diagram of an electronic device for implementing sparse signal recovery provided in an embodiment of the present application. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0058] In relevant emerging fields and professional fields, the amount of data is huge and complex, and the requirements for signal processing are getting higher and higher. Improving the accuracy of algorithm reconstruction of signals can better meet the strict requirements of signal processing in these fields, promote the development and application of related technologies, and bring more convenience and progress to people's lives and work. At the same time, with the continuous advancement of technology, the requirements for the accuracy and speed of signal processing will continue to increase, which will prompt researchers to further explore and improve signal processing algorithms to adapt to the ever-changing application scenarios.

[0059] The existing technology mainly adopts the IHT algorithm. Although the sparsity of the signal can be used to effectively restore the signal, it puts forward higher requirements on the efficiency and accuracy of data processing under the situation of increasing data scale and complexity, and it is difficult to meet these requirements. The IHT algorithm mainly performs hard threshold operation on the updated intermediate signal to maintain sparsity. Specifically, the IHT algorithm uses a pre-set threshold parameter s in each iteration, retains the s maximum absolute value elements of the intermediate result obtained in each iteration, and sets the remaining elements to 0, and then repeats the iteration process until the iteration is completed and the estimated signal is output. Therefore, the IHT algorithm is essentially a fixed threshold method. It fails to take into account that different sparse signals have different sparsities and distributions, cannot adapt to diversity, and is prone to over-thresholding (when the fixed threshold is too large), loss of important information, etc. For signals with low sparsity, the fixed threshold may be too small to effectively remove noise and unimportant non-zero elements. In addition, the use of a fixed threshold may affect the convergence speed of the algorithm. If the threshold is not selected properly, the algorithm may require more iterations to converge to a better solution. Moreover, for some complex signals or noisy environments, the fixed threshold may not be able to retain important signal components, resulting in a large error between the restored signal and the original signal.

[0060] To solve the above problems, the present application aims to increase the threshold dynamically, and gradually increase the threshold parameter as the number of iterations increases without wasting too much computing time, thereby effectively accelerating the convergence of the algorithm, improving the accuracy of the algorithm, and iteratively updating the estimated signal according to the dynamic threshold until the iterative update termination condition is reached, thereby obtaining a sparse signal reconstructed from the low-dimensional observation signal. In the present application, the dynamic threshold selection strategy gradually increases the threshold as the iteration process progresses, better adapting to the characteristics of the estimated signal generated by the current iteration process, promoting the convergence of the algorithm, and improving the accuracy of the algorithm recovery signal.

[0061] To facilitate the understanding of the embodiments of the present application, further explanation will be given below in conjunction with the drawings and specific embodiments. The embodiments do not constitute a limitation on the embodiments of the present application.

[0062] The following is an explanation of some of the terms used in the various embodiments of the present application to facilitate understanding by those skilled in the art:

[0063] Sparse signal: In the field of compressed sensing, a sparse signal refers to a signal in which most elements are zero and only a few elements are non-zero, that is, the number of non-zero elements is much smaller than the dimension of the signal, which can be represented by x in the embodiments of the present application.

[0064] The observation signal refers to a low-dimensional signal obtained after the high-dimensional original signal is transformed by the measurement matrix. It is a known quantity and can be represented by y in each embodiment of the present application.

[0065] Sparse is a special structure, which means that the number of non-zero elements of a signal is much smaller than the signal dimension. The present invention considers that the signal has sparseness, that is, most of the elements in the original signal generated by the algorithm are zero, and only a very small number of elements are non-zero.

[0066] Sparsity: In the field of compressed sensing, the number of non-zero elements is used to measure the sparsity of a signal. If an n-dimensional signal has at most s non-zero elements, then the sparsity of the signal is s.

[0067] Loss function: The loss function is a function used to measure the difference between the model prediction result and the true value. In the field of compressed sensing, the loss function is The goal of the algorithm is to find the independent variable x that makes the function value as small as possible. Among them, x is the high-dimensional original signal, that is, the sparse signal, y is the observed signal, and A is the measurement matrix.

[0068] Gradient: Gradient refers to the vector of partial derivatives of a function in the direction of each variable. For function f(x), its gradient is From a geometric point of view, the gradient direction is the direction in which the function grows fastest at that point.

[0069] Index: A number used to identify the position of an element in a vector. For a one-dimensional vector, the index is usually an integer starting from 0. In a one-dimensional vector, an integer is used as the position information. In a multidimensional vector, an integer array is usually used to describe the position of the element, and each integer corresponds to the position of a dimension.

[0070] Support set: In the field of compressed sensing, due to the sparsity of the signal, the signal contains only a small number of non-zero elements. The index of all non-zero elements is used as a set of elements, which is called the support set.

[0071] Threshold operator: In the iterative hard thresholding algorithm (IHT), the threshold operator is usually represented by the symbol Indicates that, where x is the input vector and s is the threshold parameter, for a given vector x=(x 1,x 2 ,...,x n ), the role of the threshold operator is to retain the s largest absolute value elements of the vector x and set the remaining elements to 0. The threshold operator is the core component of the IHT algorithm. It implements sparse approximation of the signal by performing hard threshold processing on the signal, controls the sparsity of the restored signal, and promotes the convergence of the algorithm.

[0072] Figure 1 The flowchart of a signal reconstruction method based on a dynamic increasing threshold selection strategy provided by an embodiment of the present application is as follows. Figure 1 As shown, the signal reconstruction method based on the dynamic increasing threshold selection strategy provided in the embodiment of the present application may specifically include the following steps:

[0073] Step 110, obtaining a low-dimensional observation signal and an increasing function.

[0074] The increasing function is a pre-selected function related to the dynamic threshold.

[0075] In this embodiment, the low-dimensional observation signal (referred to as the observation signal) is usually obtained by compressing the high-dimensional signal (i.e., the original sparse signal, referred to as the sparse signal). Specifically, in the field of communication, after the sender compresses the high-dimensional signal into a low-dimensional signal and transmits it to the receiver, the receiver receives the low-dimensional observation signal and then reconstructs the original signal through the low-dimensional observation signal.

[0076] In a specific implementation, reconstructing a sparse signal from a low-dimensional observation signal requires multiple iterations and updates. To accurately reconstruct a sparse signal from a low-dimensional observation signal, this embodiment uses a dynamic increasing threshold selection strategy. The dynamic increasing threshold selection strategy can select an increasing function about the number of iterations in advance, and the increasing function can be used to update the dynamic threshold based on the number of iterations. For example, after each iteration, the number of iterations increases once. As the number of iterations increases, the dynamic threshold will also increase according to the increasing function.

[0077] Step 120, estimating the low-dimensional observation signal according to the gradient of a preset loss function to obtain an estimated signal.

[0078] Step 130, based on the increasing function, a dynamic threshold operation is performed according to the number of iterations of the estimated signal and the preset sparsity to obtain an iteration-related dynamic threshold, and the dynamic threshold is applied to the algorithm step to iteratively update the estimated signal until the iterative update termination condition is reached to obtain a reconstructed target signal.

[0079] In which, the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal. During the iterative update process, the dynamic threshold changes incrementally based on the number of iterations. Before the iterative update termination condition is reached, the estimated signal obtained by each iterative update performs a gradient update of the loss function.

[0080] A unified description of steps 120 to 130 is given as follows:

[0081] In this embodiment, each time the iteration is updated, the gradient of the loss function can be calculated according to the preset loss function, and then the current signal can be updated according to the calculated gradient to obtain an updated estimated signal. The estimated signal is then used as an intermediate signal to perform a dynamic threshold operation, specifically, based on an increasing function, the number of iterations and / or sparsity are used as parameters, the dynamic threshold is calculated, and then the estimated signal is iteratively updated using the dynamic threshold.

[0082] In the related technology, the existing technology also uses an adaptive threshold method to achieve iterative updates. However, the existing adaptive threshold method usually calculates the threshold based on the statistical characteristics of the signal. This method may require continuous adjustment of parameter settings during the iteration process according to the characteristics of the signal, which increases the computing resources required for the algorithm. In addition, improper parameter selection may cause the algorithm performance to deteriorate or even fail to converge.

[0083] To solve the above problems, the present application uses a dynamic increasing threshold selection strategy. The dynamic threshold can better adapt to the signal structure and improve the accuracy and stability of the algorithm to restore the signal. Specifically, each time the iteration is updated, the dynamic threshold can change incrementally with the number of iterations, that is, as the number of iterations increases, the threshold gradually increases. Therefore, the scheme of this embodiment will determine a threshold function before the algorithm starts. During the algorithm iteration process, the function is used to calculate the threshold required for each iteration without adjusting the function parameters, thereby solving the problem of increased computing resource consumption caused by the use of the adaptive threshold method in the prior art.

[0084] In actual processing, when performing the first iterative update, the observation signal can be updated according to the calculated gradient to obtain an estimated signal for threshold operation. When performing subsequent iterative updates, the gradient update can be performed first according to the estimated signal obtained in the previous iterative update to obtain the estimated signal after the current iterative update, and then the threshold operation can be performed. During the iterative update process, if the algorithm stop condition is met, the algorithm is terminated, and the above result is the output of the algorithm. Otherwise, the next iteration is performed until the algorithm termination condition is met. Therefore, after the iterative update is completed in this embodiment, the reconstructed target signal can be obtained, and the target signal is the original sparse signal recovered from the received low-dimensional observation signal.

[0085] It should be noted that the dynamic increasing threshold selection strategy involved in this embodiment is different from the previous adaptive threshold method in that the previous adaptive threshold method usually calculates the threshold based on the statistical characteristics of the signal. This method may need to continuously adjust the parameter settings during the iteration process according to the characteristics of the signal, thereby increasing the computing resources required for the algorithm, and improper parameter selection may cause the algorithm performance to decline or even fail to converge. To solve this problem, the dynamic increasing threshold selection strategy used in this embodiment determines a threshold function before the algorithm starts. During the algorithm iteration process, the function is used to calculate the threshold required for each iteration without adjusting the parameters of the function. This embodiment adjusts the threshold according to the advancement of the iterative process. In the early stage of the algorithm, a smaller threshold is conducive to quickly finding the approximate support set of the signal. As the number of iterations increases, gradually increasing the threshold can make the algorithm converge to the final solution more stably. In addition, thanks to the adaptive threshold selection method, the signal reconstruction scheme provided by this application can better retain the main features of the signal, so that there is no need for too many complex calculations, and it does not consume too much computing time, so as to achieve higher reconstruction accuracy.

[0086] It can be seen that the embodiment of the present application estimates the acquired low-dimensional observation signal according to the gradient of the loss function to obtain an estimated signal, and then uses the number of iterations and the preset sparsity as parameters to perform a threshold operation using an increasing function to obtain an iteration-related dynamic threshold, and then iteratively updates the estimated signal according to the dynamic threshold until the iterative update termination condition is reached to obtain a target signal reconstructed from the low-dimensional observation signal, and the target signal is the reconstructed sparse signal. This embodiment increases the threshold dynamically, and gradually increases the threshold parameter as the number of iterations increases without wasting too much computing time, thereby reducing the probability of selecting an erroneous index to join the support set, thereby effectively accelerating the convergence of the algorithm and improving the accuracy of the algorithm. In the case of increasing the size and complexity of the data, it is also possible to quickly and accurately achieve signal reconstruction, solving the existing accuracy problem of sparse signal reconstruction in the field of compressed sensing.

[0087] Reference Figure 2 , shows a schematic flow chart of a signal reconstruction method based on a dynamic increasing threshold selection strategy provided by an optional embodiment of the present application. The method may specifically include the following steps:

[0088] Step 210, obtaining a low-dimensional observation signal and an increasing function.

[0089] The increasing function is a pre-selected function related to the dynamic threshold.

[0090] In an alternative embodiment, obtaining the low-dimensional observation signal may include: acquiring, through data simulation, the original sparse signal generated by the sender, where the original sparse signal has a sparse structure and is a high-dimensional signal; determining the number of non-zero elements according to the sparse structure of the original sparse signal, and obtaining a measurement matrix; performing compression processing on the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal; where the number of rows of the measurement matrix is less than the number of columns.

[0091] In a specific implementation, this embodiment may use an algorithm to simulate the process of signal acquisition, that is, the process of generating a measurement matrix, an original signal, and finally obtaining an observation signal. In the communication field, the sender has a high-dimensional original signal, but the bandwidth is limited. In order to transmit information under limited bandwidth, the signal needs to be compressed to obtain a low-dimensional observation signal before it can be sent to the receiver. Specifically, in nature, signals often have certain special structural characteristics. The original sparse signal is converted into a signal containing only a few elements through a specific coding rule. Compared with the original signal, the signal dimension is greatly reduced, but a small number of elements in the observation signal reflect the main characteristics of the original signal.

[0092] In this embodiment, the process of compressing a high-dimensional signal into a low-dimensional signal can be implemented using a measurement matrix. Since the measurement matrix is an operator that projects a high dimension to a low dimension, the number of rows of the measurement matrix should be much less than the number of columns. In addition, in order to better capture the sparse characteristics of the original signal, each element of the measurement matrix in this embodiment independently follows a standard normal distribution. Finally, the measurement matrix is applied to the original signal to obtain a low-dimensional observation vector.

[0093] Optionally, performing compression processing on the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal may include: presetting a Gaussian random matrix as the measurement matrix A, and according to a ij ~N(0, 1 / m), randomly extracting each element of the measurement matrix from a Gaussian distribution independently; randomly selecting s indices in the original sparse signal as the positions of non-zero elements, and the non-zero elements follow an independent and identically distributed standard normal distribution; setting the elements at the remaining positions in the original sparse signal except for the non-zero elements to zero, and performing signal compression according to y = Ax to obtain a low-dimensional observation signal; where x is the original sparse signal, which is an n-dimensional column vector and has a sparse structure, y is the low-dimensional observation signal, which is an m-dimensional column vector, A is the measurement matrix, used to simulate the compression process, which is an m×n-dimensional matrix, and m << n, and s is the sparsity.

[0094] Since the measurement matrix simulates the compression process from the high-dimensional original signal to the low-dimensional observation signal, the matrix needs to satisfy the requirement that its number of rows is much smaller than the number of columns. n is the dimension of the high-dimensional original signal, and m is the dimension of the low-dimensional observation signal. Therefore, the number of rows and columns of the matrix are m and n respectively, and m< <n。

[0095] In the specific implementation, this implementation multiplies the generated measurement matrix A with the real signal x, simulates the process of compressing the high-dimensional signal into a low-dimensional signal, and obtains the observed signal: y = Ax, thereby obtaining the parameters required by the algorithm: measurement matrix, observed signal and sparsity s. The subsequent operation of the algorithm can obtain the estimated signal x k , then we can use the real signal x to measure the estimated signal x k The accuracy of the restoration. The signal compression process can be referred to Figure 3 shown.

[0096] Step 220, performing gradient calculation according to a preset loss function to obtain a loss function gradient.

[0097] Step 230: According to the gradient of the loss function, the low-dimensional observation signal is updated using a gradient descent method to obtain an estimated signal.

[0098] A unified description of steps 220 to 230 is given as follows:

[0099] In the specific implementation, the signal compression process mainly involves the original sparse signal, the measurement matrix and the observation signal. According to the above expression formula of compressing the high-dimensional sparse signal into the low-dimensional observation signal, the loss function can be obtained as follows: Considering the difference between the model prediction result and the true value, and the dynamic increasing threshold selection strategy needs to select an increasing function about the number of iterations in advance, therefore, in each iteration update, this embodiment first calculates the gradient of the loss function, and then uses the gradient descent method to update the estimated signal according to the calculated gradient, and performs the threshold operation on the updated intermediate signal. The specific execution process can be referred to Figure 4 The algorithm flow chart and Figure 5 The flowchart of the dynamic increasing threshold selection strategy is shown.

[0100] Step 240: preset an increasing function with increasing number of iterations according to the characteristics of the problem to be solved as a threshold function.

[0101] Step 250: According to the threshold function, function calculation is performed using the number of iterations of the estimated signal and a preset sparsity to obtain a dynamic threshold required for this iteration.

[0102] A unified description of steps 240 to 250 is given as follows:

[0103] In this embodiment, the increasing function is essentially a threshold function about the number of iterations. For example, the number of iterations can be directly used as a parameter to calculate the dynamic threshold in the increasing function, or the number of iterations and the sparsity can be combined and used together in the increasing function to calculate the dynamic threshold. Therefore, there are many ways to select the increasing function in this embodiment. Before determining the dynamic threshold of this iteration, this embodiment can select a threshold function according to the characteristics of the problem to be solved (the threshold function may be only related to the number of iterations, or related to the number of iterations and the preset sparsity at the same time), and use the threshold function to calculate with the number of iterations and the preset sparsity as parameters to obtain the dynamic threshold.

[0104] In the specific implementation, this embodiment is improved on the basis of the IHT algorithm used in the prior art, with the IHT algorithm as the framework, and the fixed threshold method for realizing signal sparsity is changed, and a dynamic increasing threshold selection strategy is applied to replace it, so that the algorithm no longer selects the same threshold parameter in each iteration process, but calculates the threshold required for this iteration according to the current number of iterations and the preset sparsity. The dynamic increasing threshold selection strategy used in this embodiment is intended to dynamically adjust the threshold according to the iteration process, and effectively retain important signal components using the dynamic threshold, thereby effectively reducing the error between the restored signal and the original signal.

[0105] In actual implementation, in order to better adapt to the complexity and variability of the problem, the convergence speed and accuracy of the algorithm are improved. In each iteration process, this embodiment calculates a threshold value according to the threshold function. The difference between the scheme of this embodiment and other schemes in threshold selection is that the dynamic increasing threshold selection strategy does not retain the same number of non-zero elements each time, but gradually increases the number of retained non-zero elements as the number of iterations increases, until the algorithm reaches the maximum number of iterations or the error precision reaches a certain standard.

[0106] In actual implementation, the dynamic increasing threshold selection method refers to the process of gradually increasing the threshold parameter with the number of iterations to finally obtain the optimal solution when the algorithm retains the main features of the signal through the threshold operator. The present invention aims to increase the threshold parameter gradually with the increase of the number of iterations without consuming too much computing time by dynamically increasing the threshold. The number of iterations is calculated by the increasing function, and then the threshold of the iteration is calculated in combination with the threshold function, so that the algorithm has different thresholds at different iteration stages, and as the number of iterations increases, the corresponding threshold is also increasing. In each iteration, the threshold is calculated according to the current number of iterations, and the calculated threshold is applied to the corresponding steps of the algorithm until the number of iterations of the algorithm reaches the maximum preset number of iterations, or the relative error between the estimated value and the original signal is less than a specific limit, and the estimated value at this time is used as the result of the entire algorithm operation to obtain the output of the algorithm. Since the threshold is small in the initial stage, the number of wrong indexes selected into the support set will also be reduced accordingly, reducing the probability of selecting wrong indexes to join the support set.

[0107] Furthermore, according to the above, the signal reconstruction process is often simulated as solving an underdetermined linear system of equations, and the number of rows of the measurement matrix of the simulated signal compression process is much smaller than its number of columns. Recovering a high-dimensional signal from a low-dimensional signal is equivalent to solving a system of equations with fewer equations than unknowns. From basic mathematical knowledge, it can be known that this system of equations has infinite solutions, and it is difficult to determine the solution that meets the requirements of the problem. That is, recovering a sparse signal from an underdetermined linear system means finding the true signal x given the measurement matrix A and the measurement vector y. That is, the process is equivalent to solving an optimization problem, which can be expressed as: Among them, ||·|| 0 represents the number of non-zero elements in the signal x, ||·|| 2 represents the two-norm.

[0108] To solve this problem, this embodiment replaces the existing fixed threshold solution with a dynamic increasing threshold during the algorithm iteration process. A function for increasing the number of iterations is determined according to the characteristics and requirements of the problem to be solved. The increasing function is used to determine the current number of iterations during each iteration. Then, based on the threshold function, the threshold parameters required for the current iteration are calculated using the calculated number of iterations and the preset sparsity.

[0109] Optionally, this embodiment performs function calculation according to the threshold function using the number of iterations of the estimated signal and a preset sparsity to obtain the dynamic threshold required for this iteration, which may specifically include: Select the threshold function and calculate the dynamic threshold for this iteration update; where k represents the number of iterations of the current algorithm, is the threshold function, s represents the sparsity of the signal, It means that the integer part is retained. As the number of iterations increases, the dynamic threshold gradually increases.

[0110] In the specific implementation, combined with Figure 5 As shown, this embodiment uses Represents the increasing function of dynamic threshold selection, that is, the threshold function. When updating the dynamic threshold, the threshold parameter required for the current iteration is calculated according to the threshold function The intermediate signal (i.e. the estimated signal updated in the current iteration) The elements with the largest absolute value are retained, and the remaining elements are set to 0. In order to reasonably obtain the dynamic threshold and reduce the computing resources required by the algorithm, this embodiment provides three threshold functions for determining the dynamic threshold. For example, ①, or ②, or ③, any formula is used to calculate the dynamic threshold for this iteration update.

[0111] It should be noted that the above threshold function is only used for illustration, and it does not mean that only one can be selected from these three functions. There are many other ways to select the threshold function, which is mainly related to the number of iterations. This embodiment does not limit the specific threshold function.

[0112] Step 260: Apply the dynamic threshold to the algorithm step, iteratively update the estimated signal until an iterative update termination condition is reached to obtain a reconstructed target signal.

[0113] In which, the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal. During the iterative update process, the dynamic threshold changes incrementally based on the number of iterations. Before the iterative update termination condition is reached, the estimated signal obtained by each iterative update performs a gradient update of the loss function.

[0114] In the specific implementation, in the iterative update process, this embodiment iteratively updates the estimated signal based on the dynamic threshold, and tries to ensure that the maximum s absolute value elements in each result are in the support set. When the algorithm termination (stop) condition is reached, the algorithm is terminated, and the above result is the output of the algorithm, and finally the reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal is obtained.

[0115] Optionally, the above-mentioned step of applying the dynamic threshold to the algorithm step, iteratively updating the estimated signal until an iterative update termination condition is reached to obtain a reconstructed target signal may include the following sub-steps:

[0116] Sub-step 2601, applying the dynamic threshold to iteratively update the estimated signal, retaining the maximum absolute value in the estimated signal corresponding to the number of threshold parameters, and setting the remaining elements in the estimated signal to zero.

[0117] The number of the threshold parameters corresponds to the dynamic threshold.

[0118] Sub-step 2602, determining the relative reconstruction error between the estimated signal after this iteration update and the original sparse signal.

[0119] Sub-step 2603, determining whether the relative reconstruction error is less than a preset limit, or whether the number of iterations reaches a preset iteration number threshold.

[0120] Sub-step 2604, when the relative reconstruction error is less than a preset limit and / or the number of iterations reaches a preset iteration number threshold, the iteration is stopped, and the estimated signal obtained by the current iteration is used as the reconstructed target signal.

[0121] Sub-step 2605, when the relative reconstruction error is not less than a preset limit and the number of iterations has not reached a preset iteration threshold, the number of iterations is updated, and iterative update is performed based on the updated number of iterations and the preset sparsity until the iterative update termination condition is reached to obtain a reconstructed target signal.

[0122] Sub-steps 2601 to 2605 are described uniformly:

[0123] In the specific implementation, the method of calculating the dynamic threshold by function is used so that the algorithm has different thresholds at different iteration stages, and the corresponding threshold increases with the increase of the number of iterations. In each iteration, the threshold is calculated according to the current number of iterations, and the calculated threshold is applied to the corresponding step of the algorithm until the number of iterations of the algorithm reaches the maximum preset number of iterations, or it is determined that the relative error between the estimated value of the estimated signal and the original signal is less than a specific limit, and the estimated value at this time is used as the result of the entire algorithm operation to obtain the output of the algorithm. Since the threshold is small in the initial stage, the number of wrong indexes selected into the support set will also be reduced accordingly.

[0124] During the iterative update process, in order to verify whether the support set obtained each time is correct, this embodiment can compare the original sparse signal with the estimated signal obtained by running the algorithm. The specific comparison method includes but is not limited to: calculating the distance between the estimated signal and the original signal, dividing the distance by the modulus of the original signal, and the resulting ratio is the relative error of the reconstructed signal (that is, the relative reconstruction error). For the improvement of the recovery accuracy of the dynamic threshold selection strategy, the relative error obtained at each iteration of the IHT algorithm is compared with the relative error at each iteration of the IHT algorithm to which the dynamic increasing threshold selection strategy is applied through the same data, the same equipment, and the same settings. In other words, the verification of the recovery effect in this embodiment is mainly to compare the difference between the output signal obtained by the algorithm and the original signal, so as to compare the quality of the estimated solution obtained by the dynamic increasing threshold selection strategy.

[0125] Furthermore, since the dynamic increasing threshold selection strategy does not select a fixed value as the threshold, the number of support set elements selected each time may be different. This embodiment compares whether the estimated value obtained by this method will affect the final result of the algorithm. Specifically, this embodiment calculates the distance between the algorithm estimated signal and the original signal, divides the distance by the modulus of the original signal, and the obtained ratio is the relative reconstruction error of the restored signal. This value can measure the relative degree of distortion of the signal. Compared with the simple distance, it takes into account the strength of the original signal itself. The smaller the value, the higher the accuracy of the recovery. Conversely, it means that the distortion of the signal after reconstruction is more serious relative to the original signal.

[0126] Furthermore, this embodiment uses a normalized reconstruction error to take into account the strength of the original signal itself, which can more accurately determine the relative reconstruction effect of the algorithm on each signal, and then analyze the adaptability of the algorithm to signals of different strengths. In this embodiment, the dynamic threshold selection strategy gradually increases the threshold as the iteration process progresses, better adapts to the characteristics of the estimated signal generated by the current iteration process, promotes algorithm convergence, and improves the accuracy of the algorithm to restore the signal. Therefore, by comparing the relative reconstruction errors of the IHT algorithm and the IHT algorithm that applies the dynamic increasing threshold selection strategy at the end of each iteration under the same settings, the improvement of the algorithm recovery performance of this method can be measured.

[0127] It can be seen that this embodiment uses the relative reconstruction error to measure the effectiveness of the dynamic increasing threshold selection strategy, which can more accurately determine the reconstruction effect of the algorithm.

[0128] Optionally, the embodiment determines the relative reconstruction error between the estimated signal after the current iteration update and the original sparse signal, including: according to relative error = || x k -x * || 2 / ||x* || 2 , calculate the distance between the estimated signal and the original sparse signal, and determine the relative reconstruction error based on the distance. The relative reconstruction error is used to measure the relative distortion of the signal; where x k represents the estimated signal obtained by the kth iteration update, x * represents the original sparse signal, ||·|| 2 Represents the magnitude of a vector.

[0129] Specifically, in order to more accurately judge the reconstruction effect of the algorithm, this embodiment provides a criterion for judging the relative reconstruction error. The criterion can be written as: relative error = || x k -x * || 2 / ||x * || 2 .

[0130] In summary, in the iterative update process of the low-dimensional observation signal, the embodiment of the present application performs gradient calculation according to the loss function to obtain the gradient of the loss function, and then uses the gradient descent method to update the iteratively updated signal according to the gradient of the loss function to obtain an updated estimated signal, and then uses the number of iterations of the estimated signal and the preset sparsity as parameters to perform function calculation using the selected threshold function to obtain the dynamic threshold required for this iteration, and applies the dynamic threshold to the iterative update of the algorithm to iteratively update the estimated signal until the iterative update termination condition set by the algorithm is reached, and the target signal corresponding to the reconstructed low-dimensional observation signal is obtained. The embodiment of the present application can effectively apply the dynamic increasing threshold algorithm to better adapt to the signal structure, improve the accuracy and reliability of the algorithm to restore the signal, and solve the problems of low efficiency and insufficient accuracy of the existing signal reconstruction method.

[0131] It should be noted that, for the purpose of simple description, the method embodiments are expressed as a series of action combinations, but those skilled in the art should be aware that the embodiments of the present application are not limited to the described order of actions, because according to the embodiments of the present application, certain steps may be performed in other orders or simultaneously.

[0132] like Figure 6 As shown, the embodiment of the present application further provides a signal reconstruction system 600 based on a dynamic increasing threshold selection strategy, including:

[0133] An observation signal acquisition module 610 is used to acquire a low-dimensional observation signal and an increasing function, where the increasing function is a pre-selected function related to a dynamic threshold;

[0134] An estimated signal determination module 620, configured to estimate the low-dimensional observation signal according to a gradient of a preset loss function to obtain an estimated signal;

[0135] A dynamic threshold operation module 630 is used to perform a dynamic threshold operation based on the increasing function and according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold;

[0136] The iterative update module 640 is used to apply the dynamic threshold to the algorithm steps, iteratively update the estimated signal until the iterative update termination condition is reached, and obtain a reconstructed target signal; wherein, the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal, and during the iterative update process, the dynamic threshold is incrementally changed based on the number of iterations, and before the iterative update termination condition is reached, the estimated signal obtained by each iterative update is subjected to a gradient update of the loss function.

[0137] Optionally, the observation signal acquisition module 610 includes:

[0138] An original sparse signal generation submodule, used for acquiring an original sparse signal generated by a sender through data simulation acquisition, wherein the original sparse signal has a sparse structure and is a high-dimensional signal;

[0139] A submodule for determining the number of non-zero elements and a measurement matrix, used to determine the number of non-zero elements according to the sparse structure of the original sparse signal and obtain a measurement matrix;

[0140] The compression processing submodule is used to compress the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal; wherein the number of rows of the measurement matrix is ​​less than the number of columns.

[0141] Optionally, the compression processing submodule is specifically used to: preset a Gaussian random matrix as a measurement matrix A, and according to a ij ~N(0,1 / m), each element of the measurement matrix is ​​randomly extracted independently from the Gaussian distribution; s indexes are randomly selected in the original sparse signal as the positions of non-zero elements, and the non-zero elements obey the standard normal distribution of independent and identical distribution; the elements of the remaining positions except the non-zero elements in the original sparse signal are set to zero, and the signal is compressed according to y=Ax to obtain a low-dimensional observation signal; wherein x is the original sparse signal, which is an n-dimensional column vector and has a sparse structure, y is the low-dimensional observation signal, which is an m-dimensional column vector, A is the measurement matrix, which is used to simulate the compression process, which is an m×n-dimensional matrix, and m<<n, s is the sparsity.

[0142] Optionally, the estimated signal determination module 620 includes:

[0143] The gradient calculation submodule is used to perform gradient calculation according to the preset loss function to obtain the loss function gradient;

[0144] The signal updating submodule is used to update the low-dimensional observation signal using the gradient descent method according to the gradient of the loss function to obtain an estimated signal.

[0145] Optionally, the dynamic threshold operation module 630 includes:

[0146] The threshold function selection submodule is used to preset an increasing function with increasing number of iterations according to the characteristics of the problem to be solved as the threshold function;

[0147] The function calculation submodule is used to perform function calculation based on the threshold function, using the number of iterations of the estimated signal and the preset sparsity to obtain the dynamic threshold required for this iteration.

[0148] Optionally, the function calculation submodule is specifically used to:

[0149] from Select the threshold function and calculate the dynamic threshold for this iteration update; where k represents the number of iterations of the current algorithm, is the threshold function, s represents the sparsity of the signal, such as the sparsity of the original signal, It means that the integer part is retained. As the number of iterations increases, the dynamic threshold gradually increases.

[0150] Optionally, the iterative update module 640 includes:

[0151] A first iterative updating submodule, configured to apply the dynamic threshold to iteratively update the estimated signal;

[0152] a retaining and zero-setting submodule, configured to retain the maximum absolute value corresponding to the number of threshold parameters in the estimated signal, and to set the remaining elements in the estimated signal to zero, wherein the number of threshold parameters corresponds to the dynamic threshold;

[0153] A relative reconstruction error determination submodule is used to determine the relative reconstruction error between the estimated signal after this iteration update and the original sparse signal;

[0154] A judgment submodule, used to judge whether the relative reconstruction error is less than a preset limit, or whether the number of iterations reaches a preset iteration number threshold;

[0155] A second iterative update submodule is used to stop the iteration when the relative reconstruction error is less than a preset limit and / or the number of iterations reaches a preset iteration number threshold, and use the estimated signal obtained in the current iteration as the reconstructed target signal; when the relative reconstruction error is not less than the preset limit and the number of iterations does not reach the preset iteration number threshold, update the number of iterations, and perform iterative update based on the updated number of iterations and a preset sparsity until the iterative update termination condition is reached to obtain the reconstructed target signal;

[0156] Optionally, the relative reconstruction error determination submodule is specifically used to:

[0157] According to relative error = || x k -x * || 2 / ||x * || 2 , calculating the distance between the estimated signal and the original sparse signal, and determining the relative reconstruction error according to the distance, wherein the relative reconstruction error is used to measure the relative distortion degree of the signal;

[0158] Among them, x k represents the estimated signal obtained by the kth iteration update, x * represents the original sparse signal, ||·|| 2 Represents the magnitude of a vector.

[0159] It should be noted that the signal reconstruction system based on the dynamic increasing threshold selection strategy provided in the embodiment of the present application can execute the signal reconstruction method based on the dynamic increasing threshold selection strategy provided in any embodiment of the present application, and has the corresponding functions and beneficial effects of the execution method.

[0160] In a specific implementation, the signal reconstruction system based on the dynamic increasing threshold selection strategy can be integrated into a device, so that the device can dynamically increase the threshold value as the number of iterations increases during the signal reconstruction process to retain the characteristics of the signal and accurately reconstruct the sparse signal. As an electronic device, it can effectively accelerate the convergence of the algorithm without wasting too much computing time, and improve the efficiency and accuracy of the algorithm in data processing. The electronic device can be composed of two or more physical entities, or it can be composed of one physical entity. For example, the electronic device can be a personal computer (PC), a computer, a server, etc., and the embodiments of the present application do not impose specific restrictions on this.

[0161] like Figure 7As shown, an embodiment of the present application provides an electronic device, including a processor 111, a communication interface 112, a memory 113 and a communication bus 114, wherein the processor 111, the communication interface 112, and the memory 113 communicate with each other through the communication bus 114; the memory 113 is used to store computer programs; the processor 111 is used to implement the steps of the signal reconstruction method based on the dynamic increasing threshold selection strategy provided by any of the aforementioned method embodiments when executing the program stored in the memory 113. Exemplarily, the steps of the signal reconstruction method based on the dynamic increasing threshold selection strategy may include the following steps: obtaining a low-dimensional observation signal and an increasing function, wherein the increasing function is a pre-selected function related to the dynamic threshold; estimating the low-dimensional observation signal according to the gradient of a preset loss function to obtain an estimated signal; based on the increasing function, performing a dynamic threshold operation according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold, and applying the dynamic threshold to the algorithm steps to iteratively update the estimated signal until the iterative update termination condition is reached to obtain a reconstructed target signal; wherein the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal, and during the iterative update process, the dynamic threshold changes incrementally based on the number of iterations.

[0162] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of a signal reconstruction method based on a dynamic increasing threshold selection strategy as provided in any of the aforementioned method embodiments are implemented.

[0163] It should be noted that, in this article, relational terms such as "first" and "second" are only used 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 "include", "comprise" 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 sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0164] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A signal reconstruction method based on a dynamic increasing threshold selection strategy, characterized in that: include: Acquire a low-dimensional observation signal and an increasing function, wherein the increasing function is a pre-selected function related to a dynamic threshold; According to the gradient of a preset loss function, the low-dimensional observation signal is estimated to obtain an estimated signal; Based on the increasing function, a dynamic threshold operation is performed according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold, and the dynamic threshold is applied to the algorithm step to iteratively update the estimated signal until an iterative update termination condition is reached to obtain a reconstructed target signal; In which, the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal. During the iterative update process, the dynamic threshold changes incrementally based on the number of iterations. Before the iterative update termination condition is reached, the estimated signal obtained by each iterative update performs a gradient update of the loss function.

2. The method according to claim 1, characterized in that Obtain low-dimensional observation signals, including: Acquire an original sparse signal generated by a sender through data simulation acquisition, wherein the original sparse signal has a sparse structure and is a high-dimensional signal; Determine the number of non-zero elements according to the sparse structure of the original sparse signal, and obtain a measurement matrix; Performing compression processing on the original sparse signal according to the measurement matrix to obtain a low-dimensional observation signal; The number of rows of the measurement matrix is ​​smaller than the number of columns.

3. The method according to claim 2, characterized in that The original sparse signal is compressed according to the measurement matrix to obtain a low-dimensional observation signal, including: Preset the Gaussian random matrix as the measurement matrix A, and according to a ij ~N(0,1 / m), each element of the measurement matrix is ​​independently randomly drawn from a Gaussian distribution; Randomly select s indices in the original sparse signal as the positions of non-zero elements, and the non-zero elements obey an independent and identically distributed standard normal distribution; The elements at other positions except the non-zero elements in the original sparse signal are set to zero, and the signal is compressed according to y=Ax to obtain a low-dimensional observation signal; Among them, x is the original sparse signal, which is an n-dimensional column vector with a sparse structure, y is the low-dimensional observation signal, which is an m-dimensional column vector, A is the measurement matrix used to simulate the compression process, which is an m×n-dimensional matrix, with m<<n, and s is the sparsity.

4. The method according to claim 1, characterized in that: According to the gradient of the preset loss function, the low-dimensional observation signal is estimated to obtain an estimated signal, including: Perform gradient calculation according to the preset loss function to obtain the loss function gradient; According to the gradient of the loss function, the low-dimensional observation signal is updated using the gradient descent method to obtain an estimated signal.

5. The method according to claim 1, characterized in that: Based on the increasing function, a dynamic threshold operation is performed according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold, including: According to the characteristics of the problem to be solved, an increasing function with increasing number of iterations is preset as a threshold function; According to the threshold function, a function calculation is performed using the number of iterations of the estimated signal and a preset sparsity to obtain a dynamic threshold required for this iteration.

6. The method according to claim 5, characterized in that According to the threshold function, the function calculation is performed using the number of iterations of the estimated signal and the preset sparsity to obtain the dynamic threshold required for this iteration, including: from Select the threshold function and calculate the dynamic threshold for this iteration update; Among them, k represents the number of iterations of the current algorithm, is the threshold function, s represents the sparsity of the signal, It means that the integer part is retained. As the number of iterations increases, the dynamic threshold gradually increases.

7. The method according to claim 1, characterized in that Applying the dynamic threshold to the algorithm step, iteratively updating the estimated signal until an iterative update termination condition is reached, and obtaining a reconstructed target signal, including: Applying the dynamic threshold to iteratively update the estimated signal, retaining the maximum absolute value in the estimated signal corresponding to the number of threshold parameters, and setting the remaining elements in the estimated signal to zero; Determine the relative reconstruction error between the estimated signal after this iterative update and the original sparse signal; Determine whether the relative reconstruction error is less than a preset limit, or whether the number of iterations reaches a preset iteration number threshold; When the relative reconstruction error is less than a preset limit and / or the number of iterations reaches a preset iteration number threshold, the iteration is stopped, and the estimated signal obtained by the current iteration is used as the reconstructed target signal; When the relative reconstruction error is not less than a preset limit and the number of iterations does not reach a preset iteration number threshold, updating the number of iterations, and performing iterative updating based on the updated number of iterations and a preset sparsity until an iterative updating termination condition is reached to obtain a reconstructed target signal; The number of the threshold parameters corresponds to the dynamic threshold.

8. The method according to claim 7, characterized in that Determine the relative reconstruction error between the estimated signal after this iteration update and the original sparse signal, including: According to relative error = || x k -x * ||2 / ||x * ||2, calculate the distance between the estimated signal and the original sparse signal, and determine the relative reconstruction error based on the distance, wherein the relative reconstruction error is used to measure the relative distortion degree of the signal; Among them, x k represents the estimated signal obtained by the kth iteration update, x * represents the original sparse signal, and ||·||2 represents the modulus of the vector.

9. A signal reconstruction system based on a dynamic increasing threshold selection strategy, characterized in that: include: An observation signal acquisition module, used to acquire a low-dimensional observation signal and an increasing function, wherein the increasing function is a pre-selected function related to a dynamic threshold; An estimated signal determination module, used to estimate the low-dimensional observation signal according to the gradient of a preset loss function to obtain an estimated signal; A dynamic threshold operation module, used to perform a dynamic threshold operation based on the increasing function and according to the number of iterations of the estimated signal and a preset sparsity to obtain an iteration-related dynamic threshold; An iterative update module is used to apply the dynamic threshold to the algorithm steps, iteratively update the estimated signal until the iterative update termination condition is reached, and obtain a reconstructed target signal; wherein the target signal is a reconstructed signal of the original sparse signal corresponding to the low-dimensional observation signal, and during the iterative update process, the dynamic threshold is incrementally changed based on the number of iterations, and before the iterative update termination condition is reached, the estimated signal obtained by each iterative update is subjected to a gradient update of the loss function.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the signal reconstruction method based on a dynamic increasing threshold selection strategy as described in any one of claims 1 to 8 are implemented.

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