A multi-measurement vector deep atomic norm denoising network for line spectrum estimation and a construction method thereof

Abstract

The application discloses a multi-measurement vector deep atom norm denoising network for line spectrum estimation and a construction method thereof, and relates to the field of signal processing. The application solves the problems of low estimation accuracy and slow convergence speed caused by a large number of iterations in the existing line spectrum estimation. The construction method of the denoising network is as follows: T, W and Lambda are selected as auxiliary variables; the auxiliary variables are used to analyze noise measurement values to obtain learning variable values, and then a reconstruction layer is established; the reconstruction layer is used to denoise the noise measurement values to obtain a denoising result, and a piecewise linear mapping function and a mapping grid are used to establish a noise estimation layer; an auxiliary layer is established according to the piecewise linear mapping function and the auxiliary variable matrix; S reconstruction layers, the noise estimation layer and the auxiliary layer are used to obtain a denoising network. A gradient-based back propagation method is used to train the denoising network to complete optimal selection of learnable parameters. The application is suitable for line spectrum estimation in radar detection, sensor array signal processing, medical imaging and communication channel estimation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of signal processing. BACKGROUND

[0002] Line spectrum estimation refers to estimating the frequencies of multiple superimposed complex exponential signals from a small number of noisy samples, which is a fundamental problem in signal processing. Line spectrum estimation problems arise in a variety of application areas, including radar detection, sensor array signal processing, medical imaging, and communication channel estimation.

[0003] Existing subspace methods can be used to estimate signal frequencies from measurement data. However, due to the influence of noise, the estimation accuracy is seriously reduced. The atomic norm soft threshold is a meshless compressive sensing method that can be used to denoise measurement data. Although this method has good theoretical guarantees, its actual algorithm has a large number of iterations, a long convergence time, and its denoising performance depends on the careful selection of hyperparameters, poor accuracy, and is prone to problems.

[0004] Therefore, in summary, the existing line spectrum estimation has the problems of low estimation accuracy and slow convergence speed caused by a large number of iterations. SUMMARY

[0005] The present application solves the problem of low estimation accuracy and slow convergence speed caused by a large number of iterations in the existing line spectrum estimation.

[0006] To achieve the above purpose, the present application provides the following scheme:

[0007] The present application provides a construction method of a deep atomic norm denoising network, the construction method being:

[0008] S1, selecting T, W and Lambda as auxiliary variables, defining the matrices of the auxiliary variables T, W and Lambda as Hermitian matrices, and letting

[0009] S2, collecting noise measurement value M, analyzing the noise measurement value M using the auxiliary variable matrix, and obtaining a learning variable value;

[0010] S3, establishing a reconstruction layer Y according to the auxiliary variable matrix, the noise measurement value M and the learning variable value;

[0011] S4, denoising the noise measurement value M using the reconstruction layer Y to obtain a denoising result;

[0012] S5, establishing a noise estimation layer N according to the denoising result and using a piecewise linear mapping function and a mapping grid;

[0013] S6, establishing an auxiliary layer according to the piecewise linear mapping function and the auxiliary variable matrix;

[0014] S7, obtaining an execution stage layer according to the reconstruction layer, the noise estimation layer and the auxiliary layer;

[0015] S8, obtaining a denoising network by using S execution stage layers,

[0016] S9, training the deep atomic norm denoising network to complete optimal selection of learnable parameters by using a gradient-based back propagation method,

[0017] S10, estimating signal frequencies from the denoising result by using an ESPRIT method.

[0018] Further, there is a preferred embodiment, and the expression of the reconstruction layer Y is:

[0019]

[0020] wherein, and are learnable variables.

[0021] Further, there is a preferred embodiment, and the expression of the noise estimation layer N is:

[0022]

[0023] wherein, is a noise level, P is the number of measurement vectors, is a mapping grid, is a learning parameter.

[0024] Further, there is a preferred embodiment, and the auxiliary layer includes an auxiliary layer W, an auxiliary layer U, an auxiliary layer Lambda and an auxiliary layer T.

[0025] The expression of the auxiliary layer W is:

[0026]

[0027] The expression of the auxiliary layer U is:

[0028]

[0029] The expression of the auxiliary layer Lambda is:

[0030]

[0031] The expression of the auxiliary layer T is:

[0032]

[0033] T t+1 = U t diag({lambda t}+ )(U t ) * ;

[0034] wherein, and are learning parameters, is the inverse operator of the Toeplitz projection, ED(·) is the eigenvalue decomposition, diag({λ t} + ) is a diagonal matrix composed of eigenvalues greater than 0, U t is a matrix composed of eigenvectors generated by the eigenvalue decomposition.

[0035] The application provides a deep atomic norm denoising method for line spectrum estimation, which is implemented by using the deep atomic norm denoising network in any one of the above.

[0036] A1, a plurality of sets of measurement data are taken to obtain a measurement vector;

[0037] A2, according to P measurement vectors, and each measurement vector is composed of K frequency components, a complex exponential signal x p (t) is obtained;

[0038] A3, the complex exponential signal is sampled at a sampling rate f s to obtain discrete sampling values;

[0039] A4, according to the discrete sampling values, noiseless measurement data X is obtained;

[0040] A5, the noiseless measurement data X is combined with a Gaussian white noise matrix to obtain noise measurement data;

[0041] A6, the noise measurement data is estimated by using an autocorrelation matrix method to obtain a noise rough estimate N0;

[0042] A7, the denoising network is initially valued, and the denoising network is trained by using a loss function to obtain an optimal denoising network;

[0043] A8, the noise measurement data and the noise rough estimate N0 are respectively input into the optimal denoising network to obtain a denoising result Y out and a noise level estimate σ out ;

[0044] A9, the denoising result Y out and the noise level estimate σ out are estimated by using an ESPRIT method to obtain a signal frequency.

[0045] Furthermore, in a preferred embodiment, the aforementioned complex exponential signal is:

[0046]

[0047] Where P is the number of indices of the measurement vector, P = 1, 2, ..., f k For the signal with the kth frequency component, a p,k Let be the complex amplitude of the Kth frequency component of the Pth measurement vector.

[0048] Furthermore, in a preferred embodiment, the above discrete sampled values ​​are represented as follows:

[0049]

[0050] Where n is the index of the sampled value, and j is the imaginary unit.

[0051] This invention provides a deep atomic norm denoising network system, the system comprising:

[0052] To select T, W, and Λ as auxiliary variables, define the matrices of the auxiliary variables T, W, and Λ as Hermitian matrices, and let... Storage device;

[0053] A storage device for collecting noise measurement values ​​M, analyzing the noise measurement values ​​M using the auxiliary variable matrix, and obtaining learning variable values;

[0054] Storage device for establishing the reconstruction layer Y based on the auxiliary variable matrix, noise measurement value M, and learning variable value;

[0055] Storage device for denoising the noise measurement value M using the reconstruction layer Y to obtain the denoising result;

[0056] Storage device for establishing noise estimation layer N based on the denoising results and using a piecewise linear mapping function and mapping grid;

[0057] Storage device for establishing the auxiliary layer based on the piecewise linear mapping function and the auxiliary variable matrix;

[0058] Storage device for obtaining the execution phase layer based on the reconstruction layer, noise estimation layer, and auxiliary layer;

[0059] A storage device for obtaining a denoising network using S execution stage layers.

[0060] The present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs either the deep atomic norm denoising network implementation described in any one of the preceding claims or the deep atomic norm denoising method for line spectrum estimation described in any one of the preceding claims.

[0061] The present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes either the deep atomic norm denoising network implementation described in any one of the preceding claims or the deep atomic norm denoising method for line spectrum estimation described in any one of the preceding claims.

[0062] The beneficial effects of this invention are as follows:

[0063] This invention provides a method for constructing a deep atomic norm denoising network. The method employs an iterative expansion algorithm to obtain the denoising network, and then uses this denoising network to implement a deep atomic norm denoising method for line spectrum estimation. The denoising method learns the optimal network parameters through backpropagation to obtain the optimal denoising network, which is then used for line spectrum estimation. This approach retains the theoretically guaranteed characteristics of iterative methods while also offering the advantages of fast convergence and high algorithm accuracy.

[0064] Compared with existing technologies, it has the following advantages:

[0065] 1. Line spectrum estimation refers to estimating the frequencies of multiple superimposed complex exponential signals from a small number of noisy samples. The accuracy of existing line spectrum estimation methods is severely affected by noise, and denoising using atomic norm soft thresholding methods requires a large number of iterations. This invention provides a method for constructing a deep atomic norm denoising network. The method employs an iterative expansion algorithm to obtain the denoising network, and then uses this denoising network to implement a deep atomic norm denoising method for line spectrum estimation. This denoising method learns the optimal network parameters through backpropagation to obtain the optimal denoising network, and then performs line spectrum estimation. Better denoising results are achieved with fewer iterations.

[0066] 2. Line spectrum estimation refers to estimating the frequency of multiple superimposed complex exponential signals from a small number of noise samples. Existing subspace methods can be used to estimate signal frequencies from measurement data M. However, their estimation accuracy is severely reduced due to noise. This invention provides a deep atomic norm denoising method for line spectrum estimation, which uses multi-measurement vector data to estimate frequencies to improve the robustness of frequency estimation, thereby improving estimation accuracy.

[0067] This invention is applicable to line spectrum estimation in radar detection, sensor array signal processing, medical imaging, and communication channel estimation. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of a deep atomic norm denoising network as described in Implementation Method 1;

[0069] Figure 2 This is a comparison chart of the noise reduction effects described in Implementation Method Eleven;

[0070] Wherein, NoiseLevel is the noise level, DAND-Net is the deep atomic norm denoising method, Cadzow is the calzo denoising method, NND is the kernel norm denoising method, AST is the atomic norm soft thresholding method, and AST-MMV is the multi-measurement vector atomic norm soft thresholding method.

[0071] Figure 3 This is a graph showing the frequency parameter estimation results as described in Implementation Method Eleven. Detailed Implementation

[0072] Implementation Method 1. See Figure 1 This embodiment describes a method for constructing a deep atomic norm denoising network. The method is as follows:

[0073] S1. Select T, W, and Λ as auxiliary variables, define the matrices of the auxiliary variables T, W, and Λ as Hermitian matrices, and let...

[0074] S2. Collect noise measurement value M, and analyze the noise measurement value M using the auxiliary variable matrix to obtain the learning variable value;

[0075] S3. Based on the auxiliary variable matrix, noise measurement value M, and learning variable value, establish the reconstruction layer Y;

[0076] S4. The noise measurement value M is denoised using the reconstruction layer Y to obtain the denoising result;

[0077] S5. Based on the denoising results and using a piecewise linear mapping function and a mapping grid, establish a noise estimation layer N;

[0078] S6. Establish an auxiliary layer based on the piecewise linear mapping function and the auxiliary variable matrix;

[0079] S7. Based on the reconstruction layer, noise estimation layer, and auxiliary layer, the execution stage layer is obtained;

[0080] S8. Using S execution stage layers, a denoising network is obtained.

[0081] S9. The deep atomic norm denoising network is trained using a gradient-based backpropagation method to achieve the optimal selection of learnable parameters.

[0082] S10. Use ESPRIT to estimate the signal frequency from the denoising results.

[0083] In practical applications, this implementation defines the auxiliary variable matrices T, W, Λ as Hermitian matrices, and lets A reconstruction layer Y is constructed based on the auxiliary variable matrix, representing the recovery of the denoising result separated from the noise measurement. A noise estimation layer N is established using a piecewise linear mapping function and a mapping grid. This layer estimates the noise measurement data M to obtain the noise level. An auxiliary layer is established based on the noise level, the piecewise linear mapping function, and the auxiliary variable matrix. In application, the auxiliary layer includes auxiliary layer W, auxiliary layer U, auxiliary layer Λ, and auxiliary layer T, representing the update of auxiliary variables during the denoising process. An execution phase layer is obtained based on the reconstruction layer, the noise estimation layer, and the auxiliary layers. Figure 1 As shown, the deep atomic norm denoising network consists of s repetitive execution stages with identical structures. Each execution stage includes a reconstruction layer Y, a noise estimation layer N, an auxiliary layer W, an auxiliary layer U, an auxiliary layer Λ, and an auxiliary layer T. In practical applications, the deep atomic norm denoising network is trained using a gradient-based backpropagation method to achieve the optimal selection of learnable parameters and obtain the optimal denoising network. At the same time, a subspace method is used to estimate the signal frequency from the denoising results.

[0084] This embodiment provides a method for constructing a deep atomic norm denoising network. The method employs an iterative expansion algorithm to obtain the denoising network, and then uses this denoising network to implement a deep atomic norm denoising method for line spectrum estimation. The denoising method learns the optimal network parameters through backpropagation to obtain the optimal denoising network. This approach retains the theoretically guaranteed characteristics of iterative methods while also offering the advantages of fast convergence speed and high algorithm accuracy.

[0085] Implementation Method 2. This implementation method illustrates the reconstruction layer Y in the construction method of a deep atomic norm denoising network described in Implementation Method 1. The expression for the reconstruction layer Y is:

[0086]

[0087] in, and It is a learnable variable, and M is the noise measurement data.

[0088] In practical applications, the reconstruction layer Y in this embodiment represents the recovery of the denoising result separated from the noise measurement.

[0089] Implementation Method 3. This implementation method illustrates the noise estimation layer N in the construction method of a deep atomic norm denoising network described in Implementation Method 1. The expression for the noise estimation layer N is:

[0090]

[0091] in, Where P represents the noise level and P is the number of measurement vectors. For mapping grid, These are the learning parameters.

[0092] In practical applications, the noise estimation layer N uses the denoising results to estimate the noise level in this embodiment.

[0093] Implementation Method 4. This implementation method illustrates the auxiliary layer in the construction method of a deep atomic norm denoising network described in Implementation Method 1. The auxiliary layer includes auxiliary layer W, auxiliary layer U, auxiliary layer Λ, and auxiliary layer T.

[0094] The expression for the auxiliary layer W is:

[0095]

[0096] The expression for the auxiliary layer U is:

[0097]

[0098] The expression for the auxiliary layer Λ is:

[0099]

[0100] The expression for the auxiliary layer T is:

[0101]

[0102] T t+1 =U t diag({λ t} + (U) t ) * ;

[0103] in, and For learning parameters, Let ED(·) be the inverse operator of the Toplitz projection, and let diag({λ) be the eigenvalue decomposition. t} + U is a diagonal matrix composed of eigenvalues ​​greater than 0. t It is a matrix composed of eigenvectors generated by eigenvalue decomposition.

[0104] In practical applications, the auxiliary layers in this embodiment include auxiliary layer W, auxiliary layer U, auxiliary layer Λ, and auxiliary layer T. These four auxiliary layers represent the updates of auxiliary variables during the denoising process.

[0105] Implementation Method 5. This implementation method provides a deep atomic norm denoising method for line spectrum estimation. The denoising method is implemented using a deep atomic norm denoising network as described in any one of Implementation Methods 1 to 4. The denoising method is as follows:

[0106] A1. Obtain the measurement vector by collecting multiple sets of measurement data;

[0107] A2. Based on P measurement vectors, and each measurement vector consists of K frequency components, obtain the complex exponential signal x. p (t);

[0108] A3. The complex exponential signal is sampled at a rate f. s Sampling is performed to obtain discrete sampled values;

[0109] A4. Based on the discrete sampled values, obtain noise-free measurement data X;

[0110] A5. Combine the noise-free measurement data X with a Gaussian white noise matrix to obtain the noise measurement data M;

[0111] A6. Estimate the noise measurement data M using the autocorrelation matrix method to obtain a rough noise estimate N0;

[0112] A7. Initialize the denoising network and train it using a loss function to obtain the optimal denoising network;

[0113] A8. Input the noise measurement data M and the coarse noise estimate N0 into the optimal denoising network to obtain the denoising result Y. out and noise level estimate σ out ;

[0114] A9. The denoising result Y is processed using the ESPRIT method. out and noise level estimate σ out The signal frequency is estimated.

[0115] In practical applications, the measurement vector in this embodiment refers to multiple sets of measurement data, which have the same frequency support but different amplitudes. Based on P measurement vectors, and each measurement vector consisting of K frequency components, a complex exponential signal x is obtained. p (t); the complex exponential signal is sampled at a rate f s Sampling is performed to obtain discrete sampled values; noise-free measurement data X is derived from the discrete sampled values; noise measurement data is obtained from the noise-free measurement data X, and the noise measurement data is written in matrix form, specifically as follows: Where X represents noise-free measurement data. Let M be the Gaussian white noise matrix. If a noise source has an amplitude distribution that follows a Gaussian distribution and a uniform power spectral density, it is called Gaussian white noise. The noise measurement data M is estimated using the autocorrelation matrix method to obtain a coarse noise estimate N0. The denoising network obtained in Implementation Method 1 is initially assigned values; in this stage, except for the noise measurement matrix M and the coarse noise level estimate N0, all other operators are assigned a matrix of all zeros. The denoising network is then trained using a loss function to obtain the optimal denoising network. The noise measurement data M and the coarse noise estimate N0 are then input into the optimal denoising network to obtain the denoising result Y. out and noise level estimate σ out The denoising result Y was analyzed using the ESPRIT (Estimating Signal Parameter via Rotational Invariance Techniques) method. out and noise level estimate σ out The signal frequency is obtained by estimation. Line spectrum estimation refers to estimating the frequency of multiple superimposed complex exponential signals from a small number of noise samples.

[0116] Line spectrum estimation refers to estimating the frequencies of multiple superimposed complex exponential signals from a small number of noisy samples. In existing multi-measurement vector scenarios, the accuracy of line spectrum estimation is severely affected by noise, and denoising using atomic norm soft thresholding methods requires a large number of iterations. This embodiment provides a deep atomic norm denoising method for line spectrum estimation. This denoising method employs an iterative expansion algorithm to obtain a denoising network, learns the optimal network parameters through backpropagation to obtain the optimal denoising network, and then denoises the noisy measurement data for use in line spectrum estimation, achieving better denoising results with fewer iterations.

[0117] Line spectrum estimation refers to estimating the frequency of multiple superimposed complex exponential signals from a small number of noise samples. Existing subspace methods can be used to estimate signal frequencies from measurement data M. However, their estimation accuracy is severely degraded by noise. This embodiment provides a deep atomic norm denoising method for line spectrum estimation, which uses multi-measurement vector data to estimate frequencies to improve the robustness of frequency estimation, thereby improving estimation accuracy.

[0118] Implementation Method Six. This implementation method illustrates the complex exponential signal in the deep atom norm denoising method for line spectrum estimation described in Implementation Method Five. The complex exponential signal is:

[0119]

[0120] Where P is the number of indices of the measurement vector, P = 1, 2, ..., f k For the signal with the kth frequency component, ap,k Let be the complex amplitude of the Kth frequency component of the Pth measurement vector.

[0121] In practical applications, the measurement vector in this embodiment refers to multiple sets of measurement data, which have the same frequency support but different amplitudes. Based on P measurement vectors, and each measurement vector consisting of K frequency components, a complex exponential signal x is obtained. p (t).

[0122] Implementation Method Seven. This implementation method illustrates the discrete sampled values ​​in the deep atom norm denoising method for line spectrum estimation described in Implementation Method Five. The discrete sampled values ​​are represented as follows:

[0123]

[0124] Where n is the index of the sampled value, and j is the imaginary unit.

[0125] In practical applications, this embodiment uses a sampling rate f for the complex exponential signal. s Sampling is performed to obtain discrete sampled values.

[0126] Implementation Method 8. This implementation method provides a deep atomic norm denoising network system, the system comprising:

[0127] To select T, W, and Λ as auxiliary variables, define the matrices of the auxiliary variables T, W, and Λ as Hermitian matrices, and let... Storage device;

[0128] A storage device for collecting noise measurement values ​​M, analyzing the noise measurement values ​​M using the auxiliary variable matrix, and obtaining learning variable values;

[0129] Storage device for establishing the reconstruction layer Y based on the auxiliary variable matrix, noise measurement value M, and learning variable value;

[0130] Storage device for denoising the noise measurement value M using the reconstruction layer Y to obtain the denoising result;

[0131] Storage device for establishing noise estimation layer N based on the denoising results and using a piecewise linear mapping function and mapping grid;

[0132] Storage device for establishing the auxiliary layer based on the piecewise linear mapping function and the auxiliary variable matrix;

[0133] Storage device for obtaining the execution phase layer based on the reconstruction layer, noise estimation layer, and auxiliary layer;

[0134] A storage device for obtaining a denoising network using S execution stage layers.

[0135] Implementation Method Nine. This implementation method provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs an implementation of a deep atomic norm denoising network as described in any one of Implementation Methods One to Four, or a deep atomic norm denoising method for line spectrum estimation as described in any one of Implementation Methods Five to Seven.

[0136] Implementation Method 10. This implementation method provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a deep atomic norm denoising network implementation as described in any one of Implementation Methods 1 to 4, or a deep atomic norm denoising method for line spectrum estimation as described in any one of Implementation Methods 5 to 7.

[0137] Implementation Method 11. See also Figure 2 This embodiment describes a method for denoising depth atomic norms for line spectrum estimation as described in any one of embodiments four through seven. The denoising performance is compared with existing techniques such as the Cazo denoising method, nuclear norm denoising method, atomic norm soft thresholding method, and multi-measurement vector atomic norm soft thresholding method. The evaluation metric is the normalized mean square error (NMSE), which is expressed as follows: Where R is the number of experiments. The number of frequency components of the signal to be tested is set to K = 4, the maximum frequency of the signal is set to 100kHz, and the sampling rate is f. s =100kHz, a total of P=50 measurement vectors, each sampling 50 data points. The number of stages in the deep atomic norm network is set to s=10. The noise level σ of the training data increases from 1 to 6 in increments of 0.1, generating 1000 sets of training data for each noise level, and a new network is trained for each increment of 1. For the test data, the noise level increases from 1 to 6 in increments of 0.5, generating 1000 sets of data for each noise level for experimental verification. The denoising results are compared to... Figure 2 As shown, the horizontal axis "noiseLevel" represents the noise level, and the vertical axis represents the normalized mean square error (NMSE). Figure 2 To date, the deep atomic norm denoising method has achieved lower NMSE values ​​at various noise levels, demonstrating that the deep atomic norm denoising method is significantly more effective and accurate than the Cazor denoising method, nuclear norm denoising method, atomic norm soft thresholding method, and multi-measurement vector atomic norm soft thresholding method.

[0138] Implementation Method Twelve. This implementation method involves conducting a frequency parameter estimation experiment using a deep atom norm denoising method for line spectrum estimation described in any one of Implementation Methods Four to Seven; the number of frequency components of the signal to be measured is set to K = 4, the maximum frequency of the signal is set to 100kHz, and the sampling rate f is... s =100kHz, with a total of P=50 measurement vectors, and 50 data points sampled from each measurement vector. When the noise level σ is 5, the sampled data are first denoised using a deep atomic norm denoising network, where the network parameters are the same as in Implementation Method 10. Subsequently, the ESPRIT method is used to extract data from the denoised result Y. out The signal frequency is estimated from the original, undisturbed data M, and the estimation results are as follows: Figure 3 As shown in the figure, the data denoised by the deep atomic norm denoising network can accurately estimate the signal frequency, while the estimation results of the undenoised data have a large error. This further proves the effectiveness of the deep atomic norm denoising method.

[0139] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for constructing a deep atomic norm denoising network, the method being suitable for a line spectrum estimation problem in radar detection, characterized in that, The construction method is: S1, select is an auxiliary variable, define an auxiliary variable is a Hermitian matrix, and let ； S2, collecting noise measurement value M, using the auxiliary variable matrix to analyze the noise measurement value M, and obtaining learning variable value; S3, establishing a reconstruction layer Y according to the auxiliary variable matrix, noise measurement value M and learning variable value; S4, using the reconstruction layer Y to denoise the noise measurement value M to obtain a denoising result; The expression of the reconstruction layer Y is: ； wherein, and are learnable variables; S5, establishing a noise estimation layer N according to the denoising result and using a piecewise linear mapping function and a mapping grid; The expression of the noise estimation layer N is: ； wherein, is a noise level, P is the number of measurement vectors, is a mapping grid, is a learning parameter; S6, establishing an auxiliary layer according to the piecewise linear mapping function and the auxiliary variable matrix; S7, obtaining an execution stage layer according to the reconstruction layer, the noise estimation layer and the auxiliary layer; S8, using S execution stage layers to obtain a denoising network; S9, using a gradient-based back propagation method to train the built deep atomic norm denoising network to complete the optimal selection of learnable parameters; S10, using ESPRIT to estimate the signal frequency from the denoising result.

2. The method of claim 1, wherein, The auxiliary layers include an auxiliary layer W, an auxiliary layer U, an auxiliary layer and an auxiliary layer T. The expression of the auxiliary layer W is: ； The expression of the auxiliary layer U is: ； auxiliary layer The expression is: ； The expression of the auxiliary layer T is: ； ； wherein , , , , , and are learning parameters, is the inverse operator of the Toeplitz projection, is the eigenvalue decomposition, is a diagonal matrix with the eigenvalues larger than 0, is a matrix with the eigenvectors resulting from the eigenvalue decomposition.

3. A deep atomic norm denoising method for line spectrum estimation, the denoising method is suitable for line spectrum estimation problem in radar detection, characterized in that, The denoising method is implemented by using the deep atomic norm denoising network of any one of claims 1-2, and the denoising method is: A1, obtaining a measurement vector by using multiple groups of measurement data; A2. From P measurement vectors, each consisting of K frequency components, a complex exponential signal is obtained ; A3, sampling the complex exponential signal at a sampling rate to obtain discrete sample values; A4, obtaining noiseless measurement data X according to the discrete sampling value; A5, combining the noiseless measurement data X with a Gaussian white noise matrix to obtain noise measurement data; A6. The noise measurement data is estimated using the autocorrelation matrix method to obtain a rough estimate of the noise. ; A7, initializing the denoising network and training the denoising network using a loss function to obtain an optimal denoising network; A8、 respectively the noise measurement data and the noise rough estimate into the optimal denoising network to obtain a denoising result and a noise level estimate ; A9. Using the ESPRIT method on the denoised result and noise level estimates Estimates are made to obtain signal frequencies.

4. The deep atomic norm denoising method for line spectrum estimation according to claim 3, characterized in that, The complex exponential signal is: ； where p is the index number of the measurement vector, p = 1, 2,..., is the signal of the kth frequency component, is the complex amplitude of the kth frequency component of the pth measurement vector.

5. The deep atomic norm denoising method for line spectrum estimation according to claim 3, characterized in that, The discrete sampling value is expressed as: ； Wherein, n is the index of the sampling value, and j is the imaginary unit.

6. A deep atomic norm denoising network system, the system is suitable for line spectrum estimation problem in radar detection, characterized in that, The system comprises: for selecting For the auxiliary variable, define the auxiliary variable The matrix is a Hermitian matrix, and let a storage device; A storage device for collecting noise measurement value M, using the auxiliary variable matrix to analyze the noise measurement value M, and obtaining learning variable value; A storage device for establishing a reconstruction layer Y according to the auxiliary variable matrix, noise measurement value M and learning variable value; The expression of the reconstruction layer Y is: ； wherein, and are learnable variables; A storage device for using the reconstruction layer Y to denoise the noise measurement value M to obtain a denoising result; A storage device for establishing a noise estimation layer N according to the denoising result and using a piecewise linear mapping function and a mapping grid; The expression of the noise estimation layer N is: ； wherein, is a noise level, P is the number of measurement vectors, is a mapping grid, is a learning parameter; A storage device for establishing an auxiliary layer according to the piecewise linear mapping function and the auxiliary variable matrix; A storage device for obtaining an execution stage layer according to the reconstruction layer, the noise estimation layer and the auxiliary layer; A storage device for using S execution stage layers to obtain a denoising network; A storage device for using a gradient-based back propagation method to train the built deep atomic norm denoising network to complete the optimal selection of learnable parameters; A storage device for using ESPRIT to estimate the signal frequency from the denoising result.

7. A computer readable storage medium characterized in that, The computer readable storage medium stores a computer program, and the computer program is run by the processor to execute the deep atomic norm denoising network implementation of any one of claims 1-2 or the deep atomic norm denoising method for line spectrum estimation of any one of claims 3-5.

8. A computer device, comprising: The device comprises a memory and a processor, and the memory stores a computer program, and the processor executes the deep atomic norm denoising network implementation of any one of claims 1-2 or the deep atomic norm denoising method for line spectrum estimation of any one of claims 3-5 when the processor runs the computer program stored in the memory.

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