Signal reconstruction method and device based on deep learning and electronic equipment

Abstract

The application provides a signal reconstruction method and device based on deep learning and electronic equipment, the method comprises the following steps: acquiring a random incident signal; inputting the random incident signal into a trained signal reconstruction model to obtain a reconstructed signal; wherein the trained signal reconstruction model is obtained through unsupervised training based on a training data set, a cost function and a preset iteration number, and the cost function is established based on the training data set and a reconstruction result of the training data set. The application reduces the complexity of model construction, thereby reducing the complexity of signal reconstruction, and improves the efficiency of signal reconstruction without manual parameter iteration.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and in particular to a signal reconstruction method, apparatus and electronic device based on deep learning. Background Technology

[0002] The study of Finite Rate of Innovation (FRI) signal reconstruction algorithms is a classic problem in the field of signal processing. FRI signals refer to signals where the parameters capable of completely describing the characteristics of the original signal per unit time are finite. FRI signal reconstruction algorithms utilize evenly spaced sampled values ​​at frequencies far lower than the Nyquist sampling frequency to construct a system of linear equations for an annulment filter (AF), thereby achieving the goal of accurately recovering the original signal with a much smaller amount of sampled data than required by Nyquist sampling. This is entirely consistent with the purpose of compressed sensing. With further generalization of FRI signal sampling algorithms, it has become effective even for sampled values ​​on a non-uniform, randomly known set, and this is called a generalized FRI signal reconstruction model.

[0003] Currently, there are many improvements to the sampling algorithms for generalized signal reconstruction models. For example, to make this algorithm applicable to multi-buffer scenarios, the iterative strategy for solving the convex optimization process has been improved, reducing the algorithm's complexity, and the method for determining the initial point of the iteration process has been optimized, making the algorithm more stable. Furthermore, efforts have been made to improve the algorithm for solving bivariate optimization problems with the nullification filter linear equation system as linear constraints. A regularization term is used to replace the linear constraints, transforming an optimization problem with equality constraints into an unconstrained optimization problem, while also avoiding the establishment of the nullification filter linear equation system, thus making it applicable to higher-dimensional generalized FRI signal reconstruction models.

[0004] Sampling algorithms based on the generalized FRI signal reconstruction model require solving a bivariate alternating minimization problem during the reconstruction of the original signal. Currently, commonly used algorithms for solving this problem employ a double-iteration process, continuously updating the coefficients of the nullification filter linear equations and the parameters of the reconstructed signal vector. This ensures that the final reconstructed finite innovation rate signal vector satisfies the nullification filter linear equations while minimizing the reconstruction error function.

[0005] In current generalized FRI signal reconstruction algorithms, the appropriate maximum number of iterations is derived from a large amount of experimental data. This parameter selection method based solely on experimental experience greatly limits the further expansion of generalized FRI signal reconstruction algorithms in practical signal processing applications.

[0006] Therefore, how to reduce the complexity of signal reconstruction and solve the problem of the maximum number of iterations is a technical problem that the field continues to solve. Summary of the Invention

[0007] This invention provides a signal reconstruction method, apparatus, and electronic device based on deep learning, which addresses the aforementioned deficiencies in the prior art, reduces the complexity of signal reconstruction, eliminates the need for manual parameter iteration, and improves signal reconstruction efficiency.

[0008] This invention provides a signal reconstruction method based on deep learning, comprising:

[0009] Obtain random incident signals;

[0010] The random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal;

[0011] The signal reconstruction model that has been trained is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0012] According to a deep learning-based signal reconstruction method provided by the present invention, the signal frequency of the randomly incident signal is within a first preset range and the signal frequency conforms to a uniform distribution; the signal amplitude of the randomly incident signal is within a second preset range and the signal amplitude conforms to a normal distribution; and the phase parameter of the randomly incident signal is within a third preset range and the phase parameter conforms to an exponential distribution.

[0013] According to a deep learning-based signal reconstruction method provided by the present invention, after inputting the randomly incident signal into a trained signal reconstruction model to obtain the reconstructed signal, the method further includes:

[0014] A polynomial is constructed based on the coefficients of the reconstructed signal;

[0015] The signal frequency of the random incident signal is determined based on the zero position of the polynomial, and the signal amplitude of the random incident signal is determined based on the zero position and the least squares method.

[0016] According to a deep learning-based signal reconstruction method provided by the present invention, the training method of the trained signal reconstruction model includes:

[0017] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0018] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0019] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0020] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0021] The signal reconstruction method based on deep learning provided by the present invention further includes:

[0022] The constraint results are obtained based on the cost function, the training data of the target quantity, the reconstructed data, and the null filter coefficients.

[0023] If the constraint result is not within the first preset range, the network parameters of the signal reconstruction network are updated based on the target algorithm, and the linear mapping matrix based on the dual optimization variables is updated until the constraint result is within the first preset range, and the current network parameters are saved.

[0024] According to a deep learning-based signal reconstruction method provided by the present invention, the method for constructing the cost function includes:

[0025] The noise variance is obtained based on the training data, reconstructed data, and nulled filter coefficients of the target quantity.

[0026] The cost function is constructed based on the noise variance, regularization parameter, and constraint function of the linear equation system.

[0027] The linear equations are obtained based on the reconstructed data, the nulled filter coefficients, and the linear mapping matrix.

[0028] According to a deep learning-based signal reconstruction method provided by the present invention, the cost function is constructed based on the noise variance, regularization parameter, and constraint function of the linear equation system, as shown in the following formula:

[0029]

[0030] in, Let r be the noise variance, μ be the regularization parameter, [f1(b,c)+f2(c)] be the constraint function of the linear equation system, r be the sampled data, G be the linear mapping matrix, b be the reconstructed data, and c be the nulling filter coefficients.

[0031] According to a deep learning-based signal reconstruction method provided by the present invention, the constraint function includes a first constraint function and a second constraint function;

[0032] The constraint conditions of the first constraint function are:

[0033]

[0034] Where b is the reconstructed data, c is the nulling filter coefficient, and R(c) is the coefficient matrix.

[0035] According to a deep learning-based signal reconstruction method provided by the present invention, the constraint condition of the second constraint function is:

[0036]

[0037] in, It is the conjugate transpose of a randomly initialized column vector.

[0038] According to a deep learning-based signal reconstruction method provided by the present invention, the trained signal reconstruction model includes a convolutional layer, a fully connected layer, and an output layer;

[0039] The convolutional layer is used to perform convolution operations on the training data of the target amount to obtain convolutional features;

[0040] The fully connected layer is used to downsample the convolutional features to obtain downsampled features;

[0041] The output layer is used to obtain the reconstructed data and nulled filter coefficients based on the downsampling features.

[0042] This invention also provides a training method for a signal reconstruction model, comprising:

[0043] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0044] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0045] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0046] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0047] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a training method for a signal reconstruction model as described above.

[0048] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a training method for a signal reconstruction model as described above.

[0049] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a training method for a signal reconstruction model as described above.

[0050] The signal reconstruction method, apparatus, and electronic device based on deep learning provided by this invention obtain a reconstructed signal by acquiring a random incident signal and then inputting the random incident signal into a trained signal reconstruction model. Since the signal reconstruction model of this invention is obtained through unsupervised training based on a training dataset, a cost function, and a preset number of iterations, and the cost function is established using the reconstruction results of the training dataset and the training dataset, the complexity of model construction is reduced, thus reducing the complexity of signal reconstruction. Furthermore, it eliminates the need for manual parameter iteration, thereby improving the efficiency of signal reconstruction. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0052] Figure 1 This is a flowchart illustrating the signal reconstruction method based on deep learning provided by the present invention;

[0053] Figure 2 This is a schematic diagram of the layer structure of the deep learning-based signal reconstruction model provided by the present invention;

[0054] Figure 3 This is a flowchart illustrating the training method for the signal reconstruction model provided by the present invention;

[0055] Figure 4 This is a schematic diagram of the deep learning-based signal reconstruction device provided by the present invention;

[0056] Figure 5 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0058] First, it should be noted that the execution subject of the deep learning-based signal reconstruction method provided by this invention can be an electronic device, a component within an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. For example, a mobile electronic device can be a mobile phone, tablet computer, laptop computer, PDA, ultra-mobile personal computer (UMPC), netbook, or personal digital assistant (PDA), etc., while a non-mobile electronic device can be a server, network attached storage (NAS), or personal computer (PC), etc. This invention does not impose specific limitations. The following describes the steps of this invention in detail by using a computer to execute the deep learning-based signal reconstruction method provided by this invention.

[0059] Reference Figure 1 The signal reconstruction method based on deep learning provided by this invention includes the following steps:

[0060] Step 110: Obtain the random incident signal;

[0061] Step 120: Input the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal;

[0062] The signal reconstruction model that has been trained is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0063] It is understood that this invention is the application process of a signal reconstruction model, that is, using the trained signal reconstruction model to verify signal reconstruction.

[0064] First, it should be noted that the signal reconstruction in this embodiment refers to Finite Rate of Innovation (FRI) signal reconstruction. FRI uses equally spaced sample values, which are much lower than the Nyquist sampling frequency, to construct a system of linear equations for an annulment filter (AF), thereby achieving the goal of accurately recovering the original signal with a sample data volume much lower than that required by Nyquist sampling.

[0065] Through step 110 above, a random incident signal is obtained. This random incident signal satisfies a certain number of sampling points by non-uniformly random sampling. For example, 8 random incident signals can be used, and 20 sampling points can be randomly selected non-uniformly.

[0066] Furthermore, the signal frequency of the random incident signal is within a first preset range, the signal frequency conforms to a uniform distribution, the signal amplitude of the random incident signal is within a second preset range, the signal amplitude conforms to a normal distribution, and the phase parameter of the random incident signal is within a third preset range, the phase parameter conforms to an exponential distribution.

[0067] It should be noted that the first, second, and third preset ranges can be set according to actual conditions. For example, the first preset range can be set to (100, 500), meaning the frequency of the randomly incident signal is within the range of 100-500 Hz. The second preset range can be set to (0, 1), meaning the amplitude of the randomly incident signal is within the range of 0-1 Hz. The third preset range can be set to (0, 2π), meaning the phase parameter of the randomly incident signal is within the range of 0-2π Hz.

[0068] Through step 120 above, the random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal.

[0069] The signal reconstruction model trained in this embodiment is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0070] Step 120 above describes the process of reconstructing a signal using the trained signal reconstruction model. Since the signal reconstruction model is obtained through unsupervised training based on the training dataset, cost function, and a preset number of iterations, no iteration parameters are needed; the final model can be obtained simply by iteratively updating the model's parameters. Furthermore, by establishing the cost function using the reconstruction results from the training dataset and the training dataset, the complexity of model construction is reduced, thereby decreasing the complexity of signal reconstruction and improving its efficiency.

[0071] The signal reconstruction method based on deep learning provided by this invention obtains a randomly incident signal and then inputs it into a trained signal reconstruction model to obtain a reconstructed signal. Since the signal reconstruction model of this invention is obtained through unsupervised training based on a training dataset, a cost function, and a preset number of iterations, and the cost function is established using the reconstruction results from the training dataset and the training dataset, the complexity of model construction is reduced, thus reducing the complexity of signal reconstruction. Furthermore, it eliminates the need for manual parameter iteration, thereby improving the efficiency of signal reconstruction.

[0072] In some optional embodiments, after inputting the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal, the method further includes:

[0073] A polynomial is constructed based on the coefficients of the reconstructed signal;

[0074] The signal frequency of the random incident signal is determined based on the zero position of the polynomial, and the signal amplitude of the random incident signal is determined based on the zero position and the least squares method.

[0075] It is understood that this embodiment describes the process of determining the specific parameters of the original signal using the reconstructed signal. A polynomial is constructed based on the coefficients of the reconstructed signal, the signal frequency of the randomly incident signal is determined based on the zero positions of the polynomial, and then the signal amplitude of the randomly incident signal is determined based on the zero positions and a simple least squares method.

[0076] In some optional embodiments, the training method for the trained signal reconstruction model includes:

[0077] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0078] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0079] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0080] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0081] It is understood that this embodiment is the training process of the signal reconstruction model, that is, the model acquisition process.

[0082] First, in this embodiment, 20 non-uniform random sampling data points can be used to estimate 8 independent and uncorrelated signals, generating a total of 60,000 training data points. In each training data point, the signal frequency is randomly selected within the range of [100, 500] MHz, conforming to a uniform distribution; the signal amplitude is randomly selected within the range of (0, 1), conforming to a normal distribution; the signal phase parameter is randomly selected within the range of (0, 2π), conforming to an exponential distribution; and the signal-to-noise ratio is fixed at 10 dB.

[0083] It should be noted that the linear mapping matrix in this embodiment is determined by the initialized reconstruction parameters and the ideal sampled data vector, as shown in the following formula:

[0084]

[0085] in, Let b be the ideal sampled data vector, b be the reconstruction parameter, and G be the linear mapping matrix.

[0086] Then, a target amount of training data is selected from the training dataset; for example, 200 data points can be randomly selected from 60,000 training data points each time to input into the network. These 200 training data points are then input into the signal reconstruction network to obtain dual-optimization variables. These dual-optimization variables include the reconstructed data and the nulled filter coefficients, and the linear mapping matrix is ​​continuously updated based on these dual-optimization variables.

[0087] Finally, the cost function is calculated using the network output and 200 randomly selected training data, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the preset number of iterations is reached, the current network parameters are saved, and the trained signal reconstruction model is obtained.

[0088] It should be noted that in this embodiment, the gradient of the cost function is calculated using the Adam optimizer to find the descent direction of the cost function, thereby updating the network parameters.

[0089] It should be further explained that in this embodiment, the maximum number of learning iterations is set to 300. If the current learning iteration has not reached 300, the training data is reshuffled, the model output data is reused, and the network parameters are updated. If the maximum number of iterations has been reached, training is stopped and the current network parameters are saved.

[0090] In some optional embodiments, it also includes:

[0091] The constraint results are obtained based on the cost function, the training data of the target quantity, the reconstructed data, and the null filter coefficients.

[0092] If the constraint result is not within the first preset range, the network parameters of the signal reconstruction network are updated based on the target algorithm, and the linear mapping matrix based on the dual optimization variables is updated until the constraint result is within the first preset range, and the current network parameters are saved.

[0093] Furthermore, the method for constructing the cost function includes:

[0094] The noise variance is obtained based on the training data, reconstructed data, and nulled filter coefficients of the target quantity.

[0095] The cost function is constructed based on the noise variance, regularization parameter, and constraint function of the linear equation system.

[0096] The linear equations are obtained based on the reconstructed data, the nulled filter coefficients, and the linear mapping matrix.

[0097] It is understood that this embodiment describes the process of updating the model using the constraint results.

[0098] First, obtain the constraint results based on the cost function, the training data of the objective quantity, the reconstructed data, and the null filter coefficients. Refer to the following formula:

[0099]

[0100] in, Let r be the noise variance, μ be the regularization parameter, [f1(b,c)+f2(c)] be the constraint function of the linear equation system, r be the sampled data, G be the linear mapping matrix, b be the reconstructed data, and c be the nulling filter coefficients.

[0101] Then, based on the constraint results, it is determined whether to continue updating the model. Specifically:

[0102] When the constraint result is not within the first preset range, i.e., the constraint result is not +∞, the network parameters of the network are reconstructed based on the target algorithm update signal, and the linear mapping matrix is ​​updated based on the dual optimization variables until the constraint result is +∞, at which point the current network parameters are saved.

[0103] In some optional embodiments, the constraint function includes a first constraint function and a second constraint function;

[0104] The constraint conditions of the first constraint function are:

[0105]

[0106] Where b is the reconstructed data, c is the nulling filter coefficient, and R(c) is the coefficient matrix.

[0107] In some optional embodiments, the constraint conditions of the second constraint function are:

[0108]

[0109] in, It is the conjugate transpose of a randomly initialized column vector.

[0110] In some optional embodiments, the trained signal reconstruction model includes convolutional layers, fully connected layers, and an output layer;

[0111] The convolutional layer is used to perform convolution operations on the training data of the target amount to obtain convolutional features;

[0112] The fully connected layer is used to downsample the convolutional features to obtain downsampled features;

[0113] The output layer is used to obtain the reconstructed data and nulled filter coefficients based on the downsampling features.

[0114] Specifically, please refer to Figure 2 The signal reconstruction model in this embodiment includes three convolutional layers, two fully connected layers, and an output layer;

[0115] A six-layer deep learning network structure is employed. The first three layers are convolutional neural networks, including convolutional layers 211, 212, and 213. These layers use 4, 8, and 16 different random convolutional kernels, respectively, to perform convolution operations with the input data. Each kernel in each layer has a size of 3, and the activation function is tanh. The fourth and fifth layers are fully connected networks, including fully connected layers 221 and 222, with sizes of 800 and 400, respectively. The activation function is tanh, and a 5x downsampling operation is performed after each layer to reduce the dimensionality of the entire network structure and avoid overfitting. The final layer is the output layer 230, also a fully connected network, without an activation function. Its size should be the same as the sum of the dimensions of the reconstructed result b and the coefficients c.

[0116] By using the network's output and input data, the cost function is calculated. Then, the Adam optimizer is used to calculate the gradient of the cost function, find the descent direction of the cost function, and calculate the network parameters for the next training process, thereby ultimately achieving the goal of updating the network parameters.

[0117] This invention also provides a training method for a signal reconstruction model, comprising the following steps:

[0118] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0119] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0120] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0121] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0122] The signal reconstruction device based on deep learning provided by the present invention is described below. The signal reconstruction device based on deep learning described below and the signal reconstruction method based on deep learning described above can be referred to in correspondence.

[0123] Reference Figure 3 The signal reconstruction device based on deep learning provided by the present invention includes the following modules:

[0124] Acquisition module 310 is used to acquire random incident signals;

[0125] The reconstruction module 320 is used to input the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal;

[0126] The signal reconstruction model that has been trained is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0127] The random incident signal is acquired through the acquisition module 310 described above. This random incident signal meets a certain requirement, and sampling points are randomly selected non-uniformly. For example, 8 random incident signals can be used, and 20 sampling points can be randomly selected non-uniformly.

[0128] Furthermore, the signal frequency of the random incident signal is within a first preset range, the signal frequency conforms to a uniform distribution, the signal amplitude of the random incident signal is within a second preset range, the signal amplitude conforms to a normal distribution, and the phase parameter of the random incident signal is within a third preset range, the phase parameter conforms to an exponential distribution.

[0129] It should be noted that the first, second, and third preset ranges can be set according to actual conditions. For example, the first preset range can be set to (100, 500), meaning the frequency of the randomly incident signal is within the range of 100-500 Hz. The second preset range can be set to (0, 1), meaning the amplitude of the randomly incident signal is within the range of 0-1 Hz. The third preset range can be set to (0, 2π), meaning the phase parameter of the randomly incident signal is within the range of 0-2π Hz.

[0130] The random incident signal is input into the trained signal reconstruction model through the reconstruction module 320 to obtain the reconstructed signal.

[0131] The signal reconstruction model trained in this embodiment is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0132] The aforementioned reconstruction module 320 performs signal reconstruction using a trained signal reconstruction model. Since the signal reconstruction model is obtained through unsupervised training based on the training dataset, cost function, and a preset number of iterations, no iteration parameters are needed; the final model is obtained simply by iteratively updating the model's parameters. Furthermore, by establishing the cost function using the reconstruction results from the training dataset and the training dataset, the complexity of model construction is reduced, thereby decreasing the complexity of signal reconstruction and improving its efficiency.

[0133] The signal reconstruction device based on deep learning provided by this invention obtains a randomly incident signal and then inputs it into a trained signal reconstruction model to obtain a reconstructed signal. Since the signal reconstruction model of this invention is obtained through unsupervised training based on a training dataset, a cost function, and a preset number of iterations, and the cost function is established using the reconstruction results from the training dataset and the training dataset, the complexity of model construction is reduced, thus reducing the complexity of signal reconstruction. Furthermore, it eliminates the need for manual parameter iteration, thereby improving the efficiency of signal reconstruction.

[0134] In some optional embodiments, after inputting the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal, the method further includes:

[0135] A polynomial is constructed based on the coefficients of the reconstructed signal;

[0136] The signal frequency of the random incident signal is determined based on the zero position of the polynomial, and the signal amplitude of the random incident signal is determined based on the zero position and the least squares method.

[0137] It is understood that this embodiment describes the process of determining the specific parameters of the original signal using the reconstructed signal. A polynomial is constructed based on the coefficients of the reconstructed signal, the signal frequency of the randomly incident signal is determined based on the zero positions of the polynomial, and then the signal amplitude of the randomly incident signal is determined based on the zero positions and a simple least squares method.

[0138] In some optional embodiments, the training method for the trained signal reconstruction model includes:

[0139] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0140] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0141] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0142] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0143] It is understood that this embodiment is the training process of the signal reconstruction model, that is, the model acquisition process.

[0144] First, in this embodiment, 20 non-uniform random sampling data points can be used to estimate 8 independent and uncorrelated signals, generating a total of 60,000 training data points. In each training data point, the signal frequency is randomly selected within the range of [100, 500] MHz, conforming to a uniform distribution; the signal amplitude is randomly selected within the range of (0, 1), conforming to a normal distribution; the signal phase parameter is randomly selected within the range of (0, 2π), conforming to an exponential distribution; and the signal-to-noise ratio is fixed at 10 dB.

[0145] It should be noted that the linear mapping matrix in this embodiment is determined by the initialized reconstruction parameters and the ideal sampled data vector, as shown in the following formula:

[0146]

[0147] in, Let b be the ideal sampled data vector, b be the reconstruction parameter, and G be the linear mapping matrix.

[0148] Then, a target amount of training data is selected from the training dataset; for example, 200 data points can be randomly selected from 60,000 training data points each time to input into the network. These 200 training data points are then input into the signal reconstruction network to obtain dual-optimization variables. These dual-optimization variables include the reconstructed data and the nulled filter coefficients, and the linear mapping matrix is ​​continuously updated based on these dual-optimization variables.

[0149] Finally, the cost function is calculated using the network output and 200 randomly selected training data, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the preset number of iterations is reached, the current network parameters are saved, and the trained signal reconstruction model is obtained.

[0150] It should be noted that in this embodiment, the gradient of the cost function is calculated using the Adam optimizer to find the descent direction of the cost function, thereby updating the network parameters.

[0151] It should be further explained that in this embodiment, the maximum number of learning iterations is set to 300. If the current learning iteration has not reached 300, the training data is reshuffled, the model output data is reused, and the network parameters are updated. If the maximum number of iterations has been reached, training is stopped and the current network parameters are saved.

[0152] In some optional embodiments, it also includes:

[0153] The constraint results are obtained based on the cost function, the training data of the target quantity, the reconstructed data, and the null filter coefficients.

[0154] If the constraint result is not within the first preset range, the network parameters of the signal reconstruction network are updated based on the target algorithm, and the linear mapping matrix based on the dual optimization variables is updated until the constraint result is within the first preset range, and the current network parameters are saved.

[0155] Furthermore, the method for constructing the cost function includes:

[0156] The noise variance is obtained based on the training data, reconstructed data, and nulled filter coefficients of the target quantity.

[0157] The cost function is constructed based on the noise variance, regularization parameter, and constraint function of the linear equation system.

[0158] The linear equations are obtained based on the reconstructed data, the nulled filter coefficients, and the linear mapping matrix.

[0159] It is understood that this embodiment describes the process of updating the model using the constraint results.

[0160] First, obtain the constraint results based on the cost function, the training data of the objective quantity, the reconstructed data, and the null filter coefficients. Refer to the following formula:

[0161]

[0162] in, Let r be the noise variance, μ be the regularization parameter, [f1(b,c)+f2(c)] be the constraint function of the linear equation system, r be the sampled data, G be the linear mapping matrix, b be the reconstructed data, and c be the nulling filter coefficients.

[0163] Then, based on the constraint results, it is determined whether to continue updating the model. Specifically:

[0164] When the constraint result is not within the first preset range, i.e., the constraint result is not +∞, the network parameters of the network are reconstructed based on the target algorithm update signal, and the linear mapping matrix is ​​updated based on the dual optimization variables until the constraint result is +∞, at which point the current network parameters are saved.

[0165] In some optional embodiments, the constraint function includes a first constraint function and a second constraint function;

[0166] The constraint conditions of the first constraint function are:

[0167]

[0168] Where b is the reconstructed data, c is the nulling filter coefficient, and R(c) is the coefficient matrix.

[0169] In some optional embodiments, the constraint conditions of the second constraint function are:

[0170]

[0171] in, It is the conjugate transpose of a randomly initialized column vector.

[0172] In some optional embodiments, the trained signal reconstruction model includes convolutional layers, fully connected layers, and an output layer;

[0173] The convolutional layer is used to perform convolution operations on the training data of the target amount to obtain convolutional features;

[0174] The fully connected layer is used to downsample the convolutional features to obtain downsampled features;

[0175] The output layer is used to obtain the reconstructed data and nulled filter coefficients based on the downsampling features.

[0176] Specifically, the signal reconstruction model in this embodiment employs a 6-layer deep learning network structure. The first three layers are convolutional neural networks, using 4, 8, and 16 different random convolutional kernels respectively to convolve with the input data of that layer. Each kernel in each layer has a size of 3, and the activation function is tanh. The fourth and fifth layers are fully connected networks with sizes of 800 and 400 respectively, both using tanh activation. A 5x downsampling operation is performed after each layer to reduce the dimensionality of the entire network structure and avoid overfitting. The last layer is the output layer, also a fully connected network, without an activation function, and its size should be the same as the sum of the dimensions of the reconstructed result b and the coefficients c.

[0177] By using the network's output and input data, the cost function is calculated. Then, the Adam optimizer is used to calculate the gradient of the cost function, find the descent direction of the cost function, and calculate the network parameters for the next training process, thereby ultimately achieving the goal of updating the network parameters.

[0178] Figure 4 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 4 As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute a deep learning-based signal reconstruction method, which includes:

[0179] Obtain random incident signals;

[0180] The random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal;

[0181] The trained signal reconstruction model is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0182] Alternatively, a method for training a signal reconstruction model may be implemented, the method comprising:

[0183] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0184] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0185] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0186] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0187] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0188] On the other hand, the present invention also provides a computer program product, the computer program product comprising a computer program that can be stored on a non-transitory computer-readable storage medium, wherein when the computer program is executed by a processor, the computer is able to execute the signal reconstruction method based on deep learning provided by the above methods, the method comprising:

[0189] Obtain random incident signals;

[0190] The random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal;

[0191] The trained signal reconstruction model is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0192] Alternatively, a method for training a signal reconstruction model may be implemented, the method comprising:

[0193] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0194] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0195] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0196] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0197] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the signal reconstruction method based on deep learning provided by the methods described above, the method comprising:

[0198] Obtain random incident signals;

[0199] The random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal;

[0200] The trained signal reconstruction model is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

[0201] Alternatively, a method for training a signal reconstruction model may be implemented, the method comprising:

[0202] Obtain a training dataset, which includes sampled data and a linear mapping matrix;

[0203] Select training data of the target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables, which include reconstructed data and nulled filter coefficients.

[0204] The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables;

[0205] A cost function is constructed, and the network parameters of the signal reconstruction network are updated based on the descent direction of the cost function. Training is stopped when the number of iterations reaches a preset number of iterations, and the current network parameters are saved to obtain the trained signal reconstruction model.

[0206] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0207] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0208] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A signal reconstruction method based on deep learning, characterized in that, include: Obtain random incident signals; The random incident signal is input into the trained signal reconstruction model to obtain the reconstructed signal; The trained signal reconstruction model is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset. The training method for the completed signal reconstruction model includes: Obtain a training dataset, which includes sampled data and a linear mapping matrix; Select training data of a target quantity from the training dataset, and input the training data of the target quantity into the signal reconstruction network to obtain dual optimization variables. The dual optimization variables include reconstructed data and null filter coefficients. The size of the output layer of the signal reconstruction network is the same as the sum of the dimensions of the reconstructed data and the null filter coefficients. The linear mapping matrix is ​​updated based on the aforementioned dual optimization variables; Construct a cost function and update the network parameters of the signal reconstruction network based on the descent direction of the cost function. Stop training when the number of iterations reaches a preset number of iterations, save the current network parameters, and obtain the trained signal reconstruction model. The method for constructing the cost function includes: The noise variance is obtained based on the training data, reconstructed data, and nulled filter coefficients of the target quantity. Based on the noise variance, regularization parameter, and constraint function of the linear equation system, the cost function is constructed; the cost function is shown in the following formula: ； in, Let V be the noise variance. The regularization parameter is... Let be the constraint function of the linear equation system. The sampled data, Let be the linear mapping matrix. For the reconstructed data, These are the nulled filter coefficients; The linear equations are obtained based on the reconstructed data, the nulled filter coefficients, and the linear mapping matrix.

2. The signal reconstruction method based on deep learning according to claim 1, characterized in that, The frequency of the randomly incident signal is within a first preset range and the frequency conforms to a uniform distribution. The amplitude of the randomly incident signal is within a second preset range and the amplitude conforms to a normal distribution. The phase parameter of the randomly incident signal is within a third preset range and the phase parameter conforms to an exponential distribution.

3. The signal reconstruction method based on deep learning according to claim 1, characterized in that, After inputting the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal, the process further includes: A polynomial is constructed based on the coefficients of the reconstructed signal; The signal frequency of the random incident signal is determined based on the zero position of the polynomial, and the signal amplitude of the random incident signal is determined based on the zero position and the least squares method.

4. The signal reconstruction method based on deep learning according to claim 1, characterized in that, Also includes: The constraint results are obtained based on the cost function, the training data of the target quantity, the reconstructed data, and the null filter coefficients. If the constraint result is not within the first preset range, the network parameters of the signal reconstruction network are updated based on the target algorithm, and the linear mapping matrix based on the dual optimization variables is updated until the constraint result is within the first preset range, and the current network parameters are saved.

5. The signal reconstruction method based on deep learning according to claim 1, characterized in that, The constraint function includes a first constraint function and a second constraint function; The constraint conditions of the first constraint function are: Where b is the reconstructed data, and c is the nulling filter coefficient. It is a coefficient matrix.

6. The signal reconstruction method based on deep learning according to claim 5, characterized in that, The constraint conditions of the second constraint function are: in, It is the conjugate transpose of a randomly initialized column vector.

7. The signal reconstruction method based on deep learning according to claim 1, characterized in that, The trained signal reconstruction model includes convolutional layers, fully connected layers, and an output layer; The convolutional layer is used to perform convolution operations on the training data of the target amount to obtain convolutional features; The fully connected layer is used to downsample the convolutional features to obtain downsampled features; The output layer is used to obtain the reconstructed data and nulled filter coefficients based on the downsampling features.

8. A deep learning-based signal reconstruction apparatus for performing the deep learning-based signal reconstruction method as described in claim 1, characterized in that, include: The acquisition module is used to acquire random incident signals; The reconstruction module is used to input the random incident signal into the trained signal reconstruction model to obtain the reconstructed signal; The signal reconstruction model that has been trained is obtained through unsupervised training based on the training dataset, the cost function, and a preset number of iterations. The cost function is established based on the training dataset and the reconstruction results of the training dataset.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the deep learning-based signal reconstruction method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the deep learning-based signal reconstruction method as described in any one of claims 1 to 7.

Images