A signal reconstruction method, system, apparatus and storage medium

Abstract

The application provides a signal reconstruction method, system, device and storage medium, which is used for reconstructing an original signal from a measurement signal containing only amplitude information, and comprises the following steps: obtaining the measurement signal containing only amplitude information by using a measurement device, and recording a measurement matrix corresponding to the measurement device; establishing a denoiser, and taking a function feature of the denoiser as denoising prior information; under the regular constraint based on the denoiser prior information, establishing a non-convex optimization inverse problem of signal reconstruction, and iteratively solving the problem by using a projection gradient method; and introducing the denoiser in the solving step, so that the convergence speed of the algorithm is improved. The application combines a solving algorithm of a traditional non-convex optimization problem with denoising prior, improves the reconstruction performance of a signal in a complex Gaussian random measurement matrix and coded diffraction imaging, guarantees convergence, reduces the necessary number of measurement signals, and meets the current demand for signal phase retrieval and reconstruction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of signal processing, in particular, to a signal reconstruction method, system, device and storage medium. BACKGROUND

[0002] In optical imaging, media signal processing, phase contains very important signal information, and phase information is usually difficult to record directly. Taking optical imaging as an example, the existing optical imaging equipment converts photons into electrons to record information, but the optical recording equipment generally cannot reach the oscillation frequency (about 10 15 Hz) of electromagnetic waves, so only the photon flux can be recorded to record the amplitude information. Phase retrieval and reconstruction of signals can solve the problem of reconstructing the original signal from the measured signal containing only amplitude information, so as to reconstruct the signal required by the application.

[0003] In view of the above technical needs, researchers have proposed solutions. One class of non-convex methods directly solves the non-convex optimization inverse problem of signal phase retrieval and reconstruction. Alternating projection, as a pioneer of phase retrieval, has a simple implementation procedure. By alternately applying known constraint information such as amplitude, support set, non-negativity, etc. in the original signal space and the imaging space for multiple times, signal reconstruction is achieved. One class of convex methods solves the problem by converting the non-convex optimization problem into a convex optimization problem. PhaseLift needs to perform signal reconstruction in a higher-dimensional space by dimension lifting, which increases the consumption of software and hardware resources in the signal reconstruction process. In recent years, some researchers have explored convex methods that avoid dimension lifting, but there are still problems such as the need for accurate reference signals, no theoretical convergence guarantee, etc. At present, another class of non-convex methods is still mostly used in practical applications. It uses gradient descent method to solve the non-convex optimization inverse problem of signal reconstruction, and establishes the theoretical convergence analysis.

[0004] Prior information plays a great role in signal reconstruction problem, which can effectively improve the signal reconstruction quality. Researchers introduce the sparsity, low-rankness and other prior information into the optimization problem of signal phase retrieval and reconstruction, and establish an optimization problem with regular constraint, so as to not only realize signal reconstruction, but also effectively reduce the sampling rate required for accurate reconstruction and improve the reconstruction quality. The traditional prior information can reduce the sampling rate of signal reconstruction and improve the reconstruction accuracy, but the robustness to noise needs to be further improved. In recent years, researchers have begun to explore more effective prior information. As an effective prior information, denoising prior is widely used in linear inverse problems such as compressed sensing, magnetic resonance imaging, image super-resolution, etc., which not only effectively improves the reconstruction performance of the inverse problem, but also has complete theoretical guarantee, so some scholars try to introduce denoising prior into the non-convex signal phase retrieval and reconstruction problem. However, the method based on denoising prior information cannot balance the signal phase retrieval and reconstruction performance and the theoretical convergence guarantee, the method based on traditional prior information has theoretical convergence but limited reconstruction performance, and the method based on denoising prior brings the improvement of signal phase retrieval and reconstruction performance but cannot demonstrate the convergence of the method from the optimization point of view. Therefore, it is difficult to meet the current demand of reconstructing the original signal from the measurement signal containing only amplitude information. SUMMARY

[0005] The present application provides a signal reconstruction method, system, terminal and storage medium to solve the problems in the prior art.

[0006] According to a first aspect of the present application, a signal reconstruction method is provided for recovering a signal from a measurement signal containing only amplitude information, the method comprising:

[0007] obtaining a measurement signal containing only amplitude information using a measurement device, and recording a measurement matrix corresponding to the measurement device that obtains the measurement signal;

[0008] establishing a denoiser, and taking the functional characteristics of the denoiser as denoising prior information;

[0009] under the regular constraint based on the denoising prior information, introducing a regular term function related to the denoiser, taking the measurement signal and the measurement matrix as inputs, and establishing a non-convex optimization inverse problem of signal reconstruction;

[0010] taking the measurement signal and the measurement matrix as inputs, initializing the measurement signal containing only amplitude information to obtain an initial solution of the non-convex optimization inverse problem, starting from the initial solution, adopting a gradient descent step and a proximal projection step related to the denoiser to form a projection gradient method, and combining the projection gradient method with a monitor with a monotone decreasing property to iteratively solve the final reconstructed signal.

[0011] Optionally, the measurement signal containing only amplitude information is obtained by using the measurement device, and a measurement matrix corresponding to the measurement device for obtaining the measurement signal is recorded, including any one of the following:

[0012] the measurement matrix corresponding to the measurement device is a random measurement matrix A, each element of the measurement matrix is a randomly generated real number or complex number: the measurement signal containing only amplitude information is obtained by using the measurement device, and the measurement matrix A corresponding to the measurement device for obtaining the measurement signal is recorded;

[0013] the measurement matrix corresponding to the measurement device corresponds to a measurement matrix FΛ of coded diffraction imaging, where Λ is a diagonal matrix with complex values, the diagonal elements of Λ are uniformly sampled from the unit circle of the complex plane, and F is a two-dimensional Fourier transform matrix: the measurement signal containing only amplitude information is obtained by using the measurement device, and the measurement matrix FΛ corresponding to the measurement device for obtaining the measurement signal is recorded.

[0014] Optionally, the denoiser is a traditional denoiser or a denoiser based on a neural network.

[0015] Optionally, under the regular constraint based on the denoising prior information, a regular term function related to the denoiser is introduced, and a non-convex optimization inverse problem of signal reconstruction is established, including any one of the following:

[0016] when the measurement matrix corresponding to the measurement device is a random measurement matrix, and the denoising prior information is in the form of PnP (English: plug-and-play priors): under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, wherein, g(z)=h(D(z)), z is the reconstructed signal, y is the measurement signal, A is the random measurement matrix, λ is the parameter of the constraint regular term, h(D) is an implicit regular term function related to the denoiser D, and the output of the proximal projection of h(D) is D.

[0017] when the measurement matrix corresponding to the measurement device is a random measurement matrix, and the denoising prior information is in the form of RED (English: Regularization by Denoising): under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, wherein, z is the reconstructed signal, y is the measurement signal, A is the random measurement matrix, λ is the parameter of the constraint regular term, and the regular term function wherein is the regular term function of the z τ-1 According to f(z) by step μ τ Gradient descent obtains:

[0018] - when the measurement matrix corresponding to the measurement device is a measurement matrix corresponding to coded diffraction imaging, the denoising prior information is in the form of PnP, and under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, where z is a reconstructed signal, y is a measurement signal, F is a Fourier transform matrix, Λ is a complex-valued diagonal matrix, elements of which are uniformly sampled from a unit circle in a complex plane, λ is a parameter of a regular term, and h(D) is an implicit regular term function related to the denoiser D, and an output of a proximal projection of h(D) is D.

[0019] - when the measurement matrix corresponding to the measurement device is a measurement matrix corresponding to coded diffraction imaging, the denoising prior information is in the form of RED, and under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, where z is a reconstructed signal, y is a measurement signal, F is a Fourier transform matrix, Λ is a complex-valued diagonal matrix, elements of which are uniformly sampled from a unit circle in a complex plane, λ is a parameter of a regular term, and h(D) is an implicit regular term function related to the denoiser D, and an output of a proximal projection of h(D) is D. where is a reconstructed signal z τ-1 According to f(z) by step size μ τ Gradient descent is obtained:

[0020] Optionally, the initial solution of the non-convex optimization inverse problem is obtained, including any one of the following:

[0021] - the initial solution z0 of the non-convex optimization inverse problem is obtained by using a spectral method, specifically: the initial solution z0 is the maximum eigenvector of the matrix Y=A * diag{y}A and normalizing its norm to Where y is a measurement signal, and A is a random measurement matrix.

[0022] - a constant value is used as the initial solution of the non-convex optimization inverse problem, where the constant value can be any value.

[0023] Optionally, the gradient descent step and the proximal projection step related to the denoiser constitute a projection gradient method, where:

[0024] At the τth iteration, the output of the gradient descent step is specifically: Where z τ-1 is a reconstructed signal obtained by solving the non-convex optimization inverse problem at the (τ-1)th iteration, μ τ is the step size of the gradient descent step at the τth iteration, and A *is the conjugate transpose of the measurement matrix, y is the measurement value, and ⊙ is the element-wise product of vectors;

[0025] The output of the proximal projection step includes any of the following:

[0026] - When the final reconstructed signal does not contain prior information with real pixel values and the denoising prior information is PnP, the output of the proximal projection step is specifically: where D is the denoiser.

[0027] - When the final reconstructed signal does not contain prior information with real pixel values and the denoising prior information is RED, the output of the proximal projection step is specifically: where D is the denoiser and α is a hyperparameter between 0 and 1.

[0028] - When the final reconstructed signal contains prior information with real pixel values and the denoising prior information is PnP, the output of the proximal projection step is specifically: <00001​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Otherwise, is a hyper-parameter between 0 and 1, D is a denoiser, s is a sampling rate, s h is a hyper-parameter for avoiding local minima, and s h > 0. The obtained z τ is the output z τ of the τ-th iteration.

[0033] - When the final reconstructed signal contains prior information that the pixel value is a real number, the denoising prior information is PnP, the final reconstructed signal is solved by combining the projection gradient method with the monitor iteration with the monotone decreasing property, specifically: when and rand(0, 1) < p, then Otherwise, wherein D is a denoiser, Re(·) is a real part taking operator, and p is a hyper-parameter for avoiding local minima, and the value range is between 0 and 1. The obtained z is the output z τ of the τ-th iteration.

[0034] - When the final reconstructed signal contains prior information that the pixel value is a real number, the denoising prior information is RED, the final reconstructed signal is solved by combining the projection gradient method with the monitor iteration with the monotone decreasing property, specifically: when and s ≥ s h , Otherwise, wherein α is a hyper-parameter between 0 and 1, D is a denoiser, Re(·) is a real part taking operator, s is a sampling rate, s h is a hyper-parameter for avoiding local minima, and s h > 0. The obtained z τ r is the output z τ of the τ-th iteration.

[0035] According to the second aspect of the present application, a signal reconstruction system is provided, comprising:

[0036] A measurement signal acquisition module: acquiring a measurement signal containing only amplitude information by using a measurement device, and recording a measurement matrix corresponding to the measurement device acquiring the measurement signal;

[0037] A denoiser construction module: constructing a denoiser, and taking the functional characteristics of the denoiser as denoising prior information;

[0038] The inverse problem establishing module: under the regular constraint of the de-noising prior information, a regular term function related to the de-noiser is introduced, and the measured signal and the measurement matrix are taken as inputs to establish a non-convex optimization inverse problem of signal reconstruction;

[0039] The signal reconstruction module: the measured signal and the measurement matrix are taken as inputs to obtain an initial solution of the non-convex optimization inverse problem; starting from the initial solution, a projection gradient method is constructed by using a gradient descent step and a proximal projection step related to the de-noiser, and the final reconstructed signal is obtained by iteratively solving the projection gradient method and the monitor with the monotone decreasing property.

[0040] According to a third aspect of the present application, a signal reconstruction device is provided, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor is configured to execute the signal reconstruction method described above.

[0041] According to a fourth aspect of the present application, a computer readable storage medium is provided, which stores a computer program executable by a processor to execute the signal reconstruction method described above.

[0042] Compared with the prior art, the present application has at least one of the following beneficial effects:

[0043] The signal reconstruction method, device and storage medium provided by the present application combine the solving algorithm of traditional non-convex optimization problem with de-noising prior, improve the reconstruction performance of signals in complex Gaussian random measurement matrix and coded diffraction imaging, guarantee convergence, reduce the number of necessary measurement signals, meet the current signal phase retrieval and reconstruction requirements, have higher reconstruction accuracy compared with the method based on traditional prior, and guarantee convergence while ensuring reconstruction accuracy compared with the existing method based on de-noising prior.

[0044] The signal reconstruction method, device and storage medium provided by the present application, when the de-noiser used is a neural network-based de-noiser, compared with the method based on end-to-end neural network: first, the reconstruction accuracy is guaranteed, and the network architecture can be explained from the optimization point of view to guarantee convergence; second, for different measurement settings, the network only needs to be trained once, reducing the resource consumption of multiple network training.

[0045] The signal reconstruction method, device and storage medium provided by the application solve the problem of reconstructing phase information from a measurement signal containing only amplitude information, and have wide industrial application prospects, for example, can be applied to optical imaging scenarios such as coded diffraction imaging and coherent diffraction imaging that can only obtain amplitude information. In addition, the measurement values obtained in the scenarios of biomedical imaging, quantum information and astronomical imaging usually also contain only amplitude information, so the signal reconstruction method provided by the application also has very important application value in the scenarios of biomedical imaging, quantum information and astronomical imaging. BRIEF DESCRIPTION OF DRAWINGS

[0046] Other features, objects and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments with reference to the attached drawings:

[0047] Figure 1 A flowchart of the signal reconstruction method provided by a preferred embodiment of the application;

[0048] Figure 2 A flowchart of solving a non-convex optimization inverse problem based on a denoising prior in a preferred embodiment of the application by combining a projection gradient method and a monitor with a monotone decreasing property. DETAILED DESCRIPTION

[0049] The application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be noted that, for those skilled in the art, without departing from the concept of the application, a number of modifications and improvements can be made. These all belong to the protection scope of the application. The parts not described in detail below can be implemented by using the prior art.

[0050] The signal reconstruction method provided by the embodiments of the application can be used to reconstruct an original signal from a measurement signal containing only amplitude information, wherein a non-convex optimization inverse problem of signal reconstruction is established under the regular constraint of a denoising prior; a projection gradient method is formed by using a gradient descent step based on Wirtinger differentiation and a proximal projection step related to a denoiser, and the problem is iteratively solved by combining the projection gradient method and a monitor with a monotone decreasing property to obtain a final reconstructed signal; the proximal projection step related to the denoiser is introduced in the solving step, which can improve the reconstruction accuracy of the algorithm while ensuring the convergence of the algorithm compared with an algorithm containing only the gradient descent step. When each element of the random measurement matrix is randomly generated according to a Gaussian distribution, the signal reconstruction is called signal Gaussian phase retrieval, and at this time, the signal Gaussian phase retrieval is solved by combining the projection gradient method based on Wirtinger differentiation and the monitor with a monotone decreasing property, which allows the introduction of a denoiser containing signal prior information while ensuring theoretical convergence, thereby improving the reconstruction performance.

[0051] Figure 1 A flow chart of the signal reconstruction method provided by a preferred embodiment of the present application.

[0052] As shown in the figure, the signal reconstruction method provided by the preferred embodiment can include the following steps: Figure 1

[0053] S1, selecting a measurement device, so that the measurement matrix corresponding to the measurement device is a Gaussian random measurement matrix A. Using the measurement device to obtain a measurement signal y containing only amplitude information, and recording the measurement matrix A corresponding to the measurement device for obtaining the measurement signal.

[0054] S2, establishing a denoiser D, which can be a traditional denoiser or a denoiser based on a neural network; taking the functional characteristics of the denoiser D as denoising prior information.

[0055] The traditional denoiser can select a reasonable and good traditional denoiser architecture, such as an arithmetic mean filter, a non-local mean filter (NLM), and a block matching and 3D collaborative filtering (BM3D).

[0056] The denoiser based on the neural network can: use natural images to construct a training data set, construct a neural network, and train the neural network using the training data set as the denoiser D.

[0057] S3, under the regular constraint based on the denoising prior information, introducing a regular term function related to the denoiser, and establishing a non-convex optimization inverse problem for signal reconstruction:

[0058]

[0059] Wherein, z is the reconstructed signal, A is the Gaussian random measurement matrix, λ is the parameter of the constraint regular term, g(z) is the regular term function related to the denoiser D, specifically, when the denoising prior information is PnP, g(z)=h(D) is the implicit regular term function related to the denoiser, and the output of the proximal projection of h(D) is D; when the denoising prior information is RED, the regular term function at the τth iteration is Wherein is the z τ-1 According to f(z) by step μ τ Gradient descent is obtained:

[0060] ​S4, starting from the initial solution z0, a projection gradient method is formed by using a gradient descent step based on Wirtinger differential and a proximal step related to the denoiser, and a monitor with a monotone decreasing property is combined with the projection gradient method to obtain the final reconstructed signal z.

[0061] Compared with the existing signal reconstruction method based on the denoising prior, the above embodiments of the present application can ensure the reconstruction accuracy and theoretically ensure the convergence of the method.

[0062] As shown in Figure 2 , as a preferred embodiment, S4 can include the following steps:

[0063] S41, an initial solution z0 of the non-convex optimization inverse problem is obtained by using a spectral method, specifically: the initial solution z0 is the maximum eigenvector of the matrix Y=A * diag{y}A normalized to the norm , where y is the measurement signal, and A is a Gaussian random measurement matrix.

[0064] S42, a gradient descent step based on Wirtinger differential, specifically: , where z τ-1 represents the reconstructed image obtained by solving the non-convex optimization inverse problem at the (τ-1) th iteration, μ τ represents the step size of the gradient descent step at the τ th iteration, A * is the conjugate transpose of the Gaussian random measurement matrix A, y is the measurement signal, and is the element-wise product of vectors.

[0065] S43, a proximal projection step related to the denoiser, specifically:

[0066] When the final reconstructed signal does not contain the prior information of the pixel value being a real number, and the denoising prior information is PnP, the output of the proximal projection step is specifically: , where D is the denoiser.

[0067] When the final reconstructed signal does not contain the prior information of the pixel value being a real number, and the denoising prior information is RED, the output of the proximal projection step is specifically: , where D is the denoiser, and α is a hyperparameter between 0 and 1.

[0068] When the final reconstructed signal contains the prior information of the pixel value being a real number, and the denoising prior information is PnP, the output of the proximal projection step is specifically: , where D is the denoiser, and Re(·) is the real part operator.

[0069] - When the final reconstruction signal contains the prior information that the pixel values are real numbers, and the denoising prior information is RED, the output of the proximal projection step is specifically: wherein a is a hyperparameter between 0 and 1, D is a denoiser, and Re(·) is an operator for taking real parts.

[0070] S44, in combination with the gradient descent step and the proximal projection step, a monitor with a monotone decreasing property is iteratively solved to obtain the final reconstruction signal, specifically:

[0071] - When the final reconstruction signal does not contain the prior information that the pixel values are real numbers, and the denoising prior information is PnP: when and rand(0, 1)<p, otherwise, wherein p is a hyperparameter for avoiding local minimum, and the value range is between 0 and 1. The obtained z′ τ is the output z τ of the τth iteration.

[0072] - When the final reconstruction signal does not contain the prior information that the pixel values are real numbers, and the denoising prior information is RED: when and s≥s h , otherwise, a is a hyperparameter between 0 and 1, D is a denoiser, s is a sampling rate, and s h is a hyperparameter for avoiding local minimum, and the value range is s h >0. The obtained z″ τ is the output z τ of the τth iteration.

[0073] - When the final reconstruction signal contains the prior information that the pixel values are real numbers, and the denoising prior information is PnP: when and rand(0, 1)<p, otherwise, wherein D is a denoiser, Re(·) is an operator for taking real parts, and p is a hyperparameter for avoiding local minimum, and the value range is between 0 and 1. The obtained is the output z τ of the τth iteration.

[0074] - When the final reconstruction signal contains the prior information that the pixel values are real numbers, and the denoising prior information is RED: when and s≥s h , otherwise, wherein a is a hyperparameter between 0 and 1, D is a denoiser, Re(·) is an operator for taking real parts, s is a sampling rate, and sh is a hyperparameter for avoiding local minima, taking values in the range s h > 0. Obtain z" τ r as the output of the t-th iteration z τ .

[0075] In the above embodiments, the combination of the gradient descent step based on Wirtinger differentiation in S42 and the monitor with the monotone decreasing property in S44 has theoretical convergence for a wider range of problem settings compared to existing denoising prior-based signal reconstruction methods. The introduction of the proximal projection step of the denoising prior in S43 can improve the reconstruction accuracy compared to traditional signal reconstruction methods and has theoretical convergence and interpretability based on optimization theory compared to standard end-to-end neural network training methods.

[0076] The signal reconstruction method provided in the above embodiments of the application can be applied to general non-convex phase retrieval solving and related actual application scenarios. In order to better understand, the technical solutions provided in the above embodiments of the application are further described in detail below in combination with specific application examples.

[0077] In this specific example, signal reconstruction based on a traditional denoiser is implemented. Specifically, the denoising prior-based signal reconstruction method includes the following four main steps:

[0078] Step 1, select a measurement device, so that the measurement matrix corresponding to the measurement device is a Gaussian random measurement matrix A with a dimension of (576, 128). Use the measurement device to obtain a measurement signal y with a dimension of 576 containing only amplitude information, and record the measurement matrix A corresponding to the measurement device that obtains the measurement signal;

[0079] Step 2, select the structure of the denoiser D as a traditional arithmetic mean filter, and take the functional characteristics of the denoiser D as denoising prior information.

[0080] The prior information refers to the prior information contained in the denoising operation. In the inverse problem, it is embodied by a regular function g(z) = h(D) related to the denoising operation, and is realized by the denoising operation when solving the inverse problem.

[0081] Step 3, under the regular constraint of the prior information contained in the denoising operation D(·), take the Gaussian random measurement matrix A and the measurement signal y in step 1 as inputs to establish a non-convex optimization inverse problem:

[0082]

[0083] where z is the reconstructed signal, y is the measured signal, A is a Gaussian random measurement matrix, λ is a parameter of the non-negative constraint regularizer, g(z) = h(D) is an implicit regularizer function related to the denoiser D, and the output of the proximal projection of h(D) is D.

[0084] Step 4, taking the Gaussian random measurement matrix A and the measured signal y as inputs, the initial solution z0 of the non-convex optimization inverse problem in step 3 is obtained by using the spectral method, and the projection gradient method is composed of the gradient descent step based on Wirtinger differential and the proximal projection step related to the denoiser, and the final reconstructed signal z is obtained by combining the projection gradient method with the monitor with the monotone decreasing property.

[0085] In this step, the initial solution z0 of the non-convex optimization inverse problem in step 3 is obtained by using the spectral method, which is specifically: calculating the maximum eigenvector of the matrix Y = A * diag{y}A and normalizing the two-norm of the maximum eigenvector to The normalized maximum eigenvector is taken as the initial solution z0, where y is the measured signal and A is the Gaussian random measurement matrix.

[0086] In this step, the gradient descent step based on Wirtinger differential is specifically: where z τ-1 is the reconstructed signal obtained by solving the non-convex optimization inverse problem at the (τ-1)th iteration, μ τ is the step size of the gradient descent step at the τth iteration, A * is the conjugate transpose of the measurement matrix, y is the measurement value, and is the element-wise product of vectors.

[0087] The output of the denoiser-related proximal projection step in this step is: where D is the denoiser.

[0088] In this step, the monitor with the monotone decreasing property is combined with the outputs of the gradient descent step and the proximal projection step to iteratively solve the final reconstructed signal, which is specifically: the output of the gradient descent step The output of the proximal projection step is z ′ τ The input of the monitor is and z′ τ When the decision condition and rand(0,1) < p are satisfied, the output of the monitor is Otherwise, the output of the monitor is where p is a hyperparameter for avoiding local minimum, and the value is 0.9. The obtained z′ τ is taken as the output z τIn this embodiment, the specific role of the monitor with the monotone decreasing property is to ensure that the value of function f is monotonically decreasing as much as possible. When the hyperparameter p = 1, it can be strictly guaranteed that the value of function f is monotonically decreasing. When and rand(0, 1) < p is the decision condition of the monitor. The decision condition of the conventional monitor usually only contains one condition: "when ". In this embodiment, the hyperparameter p is introduced to avoid local minimum.

[0089] In the numerical experiment, this example generates a 128-dimensional constant signal with an element value of (1 + 1i) as the original signal A (576, 128) Gaussian matrix A is randomly generated as the measurement matrix, and the measurement signal y is obtained The denoiser D is a conventional arithmetic mean filter with a sliding window size of 3*1; the step size of the gradient descent step at the τth iteration, the specific value is μ τ = min{1-exp(-τ / τ0), 0.2}, τ0 = 330; the measurement matrix A and the measurement signal y are input, and 200 iterations are performed according to the method of this embodiment to obtain 200 reconstructed signals z τ , τ = 1, 2, …, 200, the original signal and the output signal z τ , τ = 1, 2, …, 200 are calculated, and the relative error is calculated, where the relative error is defined as This is used as a performance evaluation criterion to evaluate the convergence speed and performance of the signal reconstruction method based on the denoising prior of this embodiment.

[0090] This example compares the Wirtinger flow method proposed in "Phase Retrieval via Wirtinger Flow: Theory and Algorithms" published in IEEE Transactions on Information Theory in 2015, and the evaluation standard is the relative error, the lower the better. The relative error of the signal reconstructed by this example is less than 0.1 after 50 iterations, while the relative error of the Wirtinger flow method is less than 0.1 after 127 iterations. The relative error of the signal reconstructed by this example is 0.004 at the 110th iteration, while the relative error of the Wirtinger flow method is 0.144.

[0091] In another example, the present application provides a signal reconstruction method based on a neural network denoiser, which can include the following steps:

[0092] S100, selecting a measurement device, so that the measurement matrix corresponding to the measurement device is a Gaussian random measurement matrix A with sampling rates of 2.0, 3.0, and 4.0, that is, the number of rows of the measurement matrix is 2.0, 3.0, and 4.0 times the number of columns. The measurement device is used to obtain a measurement signal y containing only amplitude information, and the measurement matrix A corresponding to the measurement device for obtaining the measurement signal is recorded;

[0093] S101, selecting a denoiser D with a structure based on a neural network, and taking the functional characteristics of the denoiser D as denoising prior information.

[0094] In this embodiment, the construction of the denoiser based on the neural network can adopt the following steps:

[0095] (1) obtaining a reference signal, adding Gaussian noise to the reference signal to obtain a noise signal, taking the reference signal and the noise signal as a training sample pair, and establishing a training data set;

[0096] (2) building a deep neural network model using a convolution layer, a nonlinear activation layer, and a batch normalization layer;

[0097] (3) for each pair of reference signal and noise signal in the training data set, taking the noise signal as the input of the deep neural network model and the reference signal as the target output of the deep neural network model, optimizing the deep neural network model using a backpropagation algorithm, obtaining a denoised signal, and making the denoised signal approximate to the reference signal;

[0098] (4) training until convergence, and taking the obtained deep neural network model as the denoiser.

[0099] The specific structure of the denoiser in this embodiment adopts a DnCNN structure, and the loss function used for training is l D (Θ)+l R (Θ), wherein N is the number of training samples, is the output of the neural network, Θ is the parameter of the neural network, is a training sample pair, is the original signal, is the signal after adding Gaussian noise, wherein ρ is a parameter of a constraint regular term, z f is a signal satisfying z f =D(z f ).

[0100] S102, under the regular constraint of the denoising prior information, establishing a non-convex optimization inverse problem:

[0101]

[0102] where z is the reconstructed signal, A is a Gaussian random measurement matrix, λ is a parameter of the regularization term, g(z) = h(D) is an implicit regularization function related to the denoiser D, and the output of the proximal projection of h(D) is D.

[0103] S103, obtaining an initial solution z0 of the non-convex optimization inverse problem by using a spectral method, and obtaining a final reconstructed signal z by using a projected gradient method composed of a gradient descent step based on Wirtinger differentiation and a proximal projection step related to the denoiser, in combination with a monitor having a monotone decreasing property, starting from the initial solution z0.

[0104] As an embodiment, S103 can include the following steps:

[0105] S1031, obtaining an initial solution z0 of the non-convex optimization inverse problem by using a spectral method, specifically, calculating the maximum eigenvector of the matrix Y = A * diag{y}A and normalizing the two-norm of the maximum eigenvector to and taking the normalized maximum eigenvector as the initial solution z0, where y is the measurement signal, and A is a Gaussian random measurement matrix.

[0106] S1032, a gradient descent step: where z τ-1 is a reconstructed signal obtained by solving the non-convex optimization inverse problem at the (τ-1)-th iteration, μ τ is a step size of the gradient descent step at the τ-th iteration, A * is a conjugate transpose of the Gaussian random measurement matrix A, and y is a measurement signal.

[0107] S1033, the output of the proximal projection step combined with the PnP (plug-and-play priors) denoising prior information is: where D is a denoiser, and Re(·) is an operator for taking a real part.

[0108] S1034, when and rand(0, 1) < p, otherwise, where D is a denoiser, Re(·) is an operator for taking a real part, p is a hyperparameter for avoiding local minimum, and the value of p is 0.99. The obtained is the output z τ of the τ-th iteration.

[0109] Based on the above technical scheme, in a specific application example, a natural image with a dimension of (32, 32) is taken as a test signal, a signal reconstruction method based on a neural network denoiser is implemented, and is compared with a Wirtinger flow method proposed in “Phase Retrieval via Wirtinger Flow: Theory and Algorithms” published in IEEE Transactionson Information Theory in 2015. The evaluation standard is relative error, and the lower the value is, the better.

[0110] The experimental results in Table 1 show that the signal Gaussian phase retrieval result obtained by the system of the embodiment is obviously higher than that of the traditional signal phase retrieval method Wirtinger flow. The traditional signal phase retrieval method Wirtinger flow does not contain prior information, and therefore the performance is limited.

[0111] Table 1: Comparison of relative errors of Wirtinger flow (WF) and the method proposed in the application in signal reconstruction

[0112]

[0113] In another embodiment of the application, an image signal reconstruction method for encoding diffraction imaging is also provided. In the measurement process of the embodiment, Poisson noise is introduced, the application is extended to a noisy application scenario, and the method can include the following steps:

[0114] S200, an original image signal with a dimension of (128, 128) is obtained is multiplied by a complex-valued diagonal matrix Λ and a two-dimensional Fourier transform matrix F to obtain a measurement value, the diagonal elements of Λ are uniformly sampled from the unit circle of the complex plane, and the square of the measurement value is taken element by element to obtain A certain Poisson noise is added to obtain a measurement signal y, and the Poisson noise is specifically: for the r-th component of The value after adding noise is , which represents a standard normal distribution with a mean of 0 and a variance of .

[0115] S201, the structure of the denoiser D is selected as a neural network-based denoiser, and the specific structure of the denoiser in the embodiment adopts DnCNN. The loss function used for training is l D (Θ) + l R (Θ), wherein wherein N is the number of training samples, ​is the output of the neural network, Θ is the parameter of the neural network, is a training sample pair, is the original image, is the image after adding Gaussian noise, where ρ is the parameter of the constraint regularization term, z f is the image satisfying z f = D(z f ).

[0116] S202, under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established:

[0117]

[0118] where z is the reconstructed signal, A is the measurement matrix corresponding to the coded diffraction imaging, λ is the parameter of the constraint regularization term, g(z) = h(D) is an implicit regularization term function related to the denoiser D, and the output of the proximal projection of h(D) is D.

[0119] S203, taking the initial solution z0 of the non-convex optimization inverse problem as a constant image with element values of 255, starting from the initial solution z0, the final reconstructed signal z is obtained by iterative solving combining the projection gradient method and the monitor with the monotone decreasing property.

[0120] As an embodiment, S203 can include the following steps:

[0121] S2031, taking the constant image with element values of 255 as the initial solution z0 of the non-convex optimization inverse problem in step 3.

[0122] S2032, gradient descent step based on Poisson log-likelihood and Wirtinger differential: where z τ-1 represents the reconstructed image obtained by solving the non-convex optimization inverse problem at the (τ-1) th iteration, μ τ represents the step size of the gradient descent step at the τ th iteration, A * represents the conjugate transpose of the measurement matrix A corresponding to the coded diffraction imaging, and y represents the measurement signal.

[0123] S2033, the output of the proximal projection step combining the PnP denoising prior information is: where D is the denoiser, and Re(·) is the real part operator.

[0124] S2034, when and rand(0,1) < p, otherwise, where D is a denoiser, Re(·) is an operator that takes the real part, and p is a hyperparameter for avoiding local minima, which is set to 1. The resulting The output z of the i-th iteration τ .

[0125] In this specific application example, 6 natural images and 6 non-natural images are taken as test signals to realize signal reconstruction of coded diffraction imaging, and are compared with two other signal reconstruction methods, namely the prDeep method in “prDeep: Robust Phase Retrieval with a Flexible Deep Network” published in the International Conference on Machine Learning (ICML) in 2018, and the Deep-ITA-F and Deep-ITA-S methods in “When deep denoising meets iterative phase retrieval” published in the International Conference on Machine Learning (ICML) in 2020. The evaluation standard is the peak signal-to-noise ratio (PSNR) in dB, and the higher the value is, the better. The experimental results show that when the coded diffraction image is reconstructed under Poisson noise, the PSNR of the image reconstructed by the system of the embodiment is 1.16 dB, 1.08 dB and 0.68 dB higher than that of the images obtained by the Deep-ITA-F method, the Deep-ITA-S method and the prDeep method, respectively.

[0126] Based on the same technical concept as above, in another embodiment of the present application, a signal reconstruction system is provided for implementing the signal reconstruction method in the above embodiment to achieve the purposes of signal Gaussian phase retrieval and coded diffraction imaging. Specifically, the signal reconstruction system comprises:

[0127] A measurement signal acquisition module: selecting a measurement device, using the measurement device to acquire a measurement signal containing only amplitude information, and recording a measurement matrix corresponding to the measurement device that acquires the measurement signal;

[0128] A denoiser construction module: constructing a denoiser, taking the functional characteristics of the denoiser as denoising prior information; when the denoiser structure is a traditional denoiser, a traditional denoiser architecture is selected. When the denoiser structure is a neural network, specifically: constructing a training data set, building a deep neural network, optimizing the deep neural network with the training data set and the backpropagation algorithm, and obtaining the optimized deep neural network as the denoiser.

[0129] Inverse problem establishing module: under the regular constraint of the de-noising prior information, a regular term function related to the de-noiser is introduced, and the measurement signal and the measurement matrix are taken as inputs to establish a non-convex optimization inverse problem of signal reconstruction;

[0130] Signal reconstruction module: taking the measurement signal and the measurement matrix as inputs, the measurement signal containing only amplitude information is initialized to obtain an initial solution of the non-convex optimization inverse problem, and starting from the initial solution, a projection gradient method is constructed by using a gradient descent step and a proximal projection step related to the de-noiser, and the final reconstructed signal is obtained by combining the projection gradient method with a monitor with a monotone decreasing property.

[0131] The technology implemented by each module in the system in the above embodiments of the application can refer to the technology in the corresponding steps of the signal reconstruction method embodiments, which will not be described here.

[0132] In the above embodiments of the application, under the regular constraint based on the de-noiser prior information, a non-convex optimization inverse problem of signal reconstruction is established, and the projection gradient method is used to iteratively solve the problem; the de-noiser is introduced in the solving step, which improves the convergence speed of the algorithm. Because the solving algorithm of the traditional non-convex optimization problem is combined with the de-noising prior, the embodiments of the application improve the reconstruction performance of the signal in the complex Gaussian random measurement matrix and the coded diffraction imaging, guarantee the convergence, reduce the necessary number of measurement signals, and meet the current demand for signal phase retrieval and reconstruction.

[0133] In another embodiment of the application, a signal reconstruction device is also provided, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor can be used to execute the signal reconstruction method of any one of the above embodiments when executing the program.

[0134] Optionally, the memory is configured to store a program; the memory can include volatile memory (e.g., random access memory (RAM), such as static random access memory (SRAM), Double Data Rate SDRAM (DDR SDRAM), etc.), and / or non-volatile memory (e.g., flash memory). The memory is configured to store computer programs (e.g., application programs, functional modules, etc. for implementing the above-described methods), computer instructions, etc. The computer programs, computer instructions, etc. described above can be stored in one or more memories in a distributed manner. The computer programs, computer instructions, data, etc. described above can be invoked by the processor.

[0135] The computer programs, computer instructions, etc. described above can be stored in one or more memories in a distributed manner. The computer programs, computer instructions, data, etc. described above can be invoked by the processor.

[0136] The processor is configured to execute the computer programs stored in the memory to implement each step in the methods described in the above embodiments. Details can be referred to the related descriptions in the method embodiments above.

[0137] The processor and the memory can be independent structures, or can be integrated into an integrated structure. When the processor and the memory are independent structures, the memory and the processor can be coupled by a bus.

[0138] In an embodiment of the present application, a computer readable storage medium is provided, which stores a computer program. The computer program is executable by a processor to perform the signal reconstruction method of any one of the above embodiments.

[0139] In an embodiment of the present application, a computer program product is also provided. The computer program product includes a non-transitory computer readable storage medium storing a computer program. The computer program is operable to cause a computer to perform the signal reconstruction method.

[0140] In an embodiment of the present application, a chip system is also provided. The chip system includes a processor and a memory. The memory stores program instructions. When the program instructions stored in the memory are executed by the processor, the signal reconstruction method is implemented.

[0141] In an embodiment of the present application, a computer device is also provided, comprising a communication interface, a memory and a processor, wherein the memory is configured to store a program for implementing the signal reconstruction method in any of the above embodiments; and the processor is configured to load and execute the program stored in the memory to implement each step of the signal reconstruction method in any of the above embodiments.

[0142] The number of the communication interface, the memory and the processor can be at least one, and the communication interface, the memory and the processor can communicate with each other through a communication bus. The communication interface can be used to receive data sent by other devices, and can include an interface for the computer device to communicate with other devices, or can include a communication interface used for communication between components in the computer device. The specific description of the processor and the memory can refer to the above embodiments, and will not be described here.

[0143] In actual application, the computer device can be a server, a computer, etc. Therefore, the structure of the computer device is not limited to the communication interface, the memory and the processor, and can also include other hardware devices, such as other storage devices, etc., which can be determined according to the functions of the computer device.

[0144] The signal reconstruction method, system, device and readable medium provided by the present application can maintain high reconstruction accuracy while ensuring theoretical convergence compared to the existing phase retrieval method based on denoising priori. Compared with the traditional phase retrieval algorithm, the operation speed and reconstruction accuracy are improved. Compared with the end-to-end deep neural network phase retrieval, the reconstruction accuracy is guaranteed, and the convergence can be theoretically proved from the optimization point of view. The reconstruction method can be applied to general non-convex linear inverse problem solving, and can also be applied to specific scenarios, such as signal Gaussian phase retrieval, coded diffraction imaging image reconstruction, and image Fourier phase retrieval, etc.

[0145] It should be noted that the steps in the method provided by the present application can be implemented by corresponding modules, devices, units, etc. in the system, and those skilled in the art can refer to the technical solution of the method to realize the composition of the system, that is, the embodiments in the method can be understood as preferred examples of constructing the system, which will not be described here.

[0146] Those skilled in the art should know that, besides implementing the system and each device thereof provided by the present application in the form of pure computer readable program code, the system and each device thereof provided by the present application can also be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers, etc. by logically programming the method steps to achieve the same functions. Therefore, the system and each device thereof provided by the present application can be considered as a hardware component, and the devices included therein for achieving various functions can also be considered as structures in the hardware component; the devices for achieving various functions can also be considered as both software modules for implementing methods and structures in the hardware component.

[0147] The various embodiments are described in a progressive manner in the specification, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be understood by referring to each other. For the devices and computer devices disclosed by the embodiments, since they correspond to the methods disclosed by the embodiments, the description is relatively simple, and the relevant parts can be understood by referring to the method part.

[0148] The specific embodiments of the present application are described above. It should be understood that the present application is not limited to the specific embodiments described above, and various modifications or changes can be made by those skilled in the art within the scope of the claims, which does not affect the essential content of the present application.

Claims

1. A signal reconstruction method for recovering a signal from a measured signal containing only amplitude information, characterized in that, The method comprises the following steps: obtaining a measurement signal containing only amplitude information by using a measurement device, and recording a measurement matrix corresponding to the measurement device used to obtain the measurement signal; establishing a denoiser, and taking the functional characteristics of the denoiser as denoising prior information; under the regular constraint based on the denoising prior information, introducing a regular term function related to the denoiser, taking the measurement signal and the measurement matrix as inputs, and establishing a non-convex optimization inverse problem of signal reconstruction; taking the measurement signal and the measurement matrix as inputs, initializing the measurement signal containing only amplitude information, obtaining an initial solution of the non-convex optimization inverse problem, and starting from the initial solution, adopting a gradient descent step and a proximal projection step related to the denoiser to form a projection gradient method, and iteratively solving the final reconstructed signal by combining the projection gradient method with a monitor having a monotone decreasing property.

2. The signal reconstruction method of claim 1, wherein, The method for obtaining the measurement signal containing only amplitude information by using the measurement device and recording the measurement matrix corresponding to the measurement device used to obtain the measurement signal adopts any one of the following methods: the measurement matrix corresponding to the measurement device is a random measurement matrix A, and each element of the measurement matrix is a randomly generated real number or complex number: a measurement signal containing only amplitude information is obtained by using the measurement device, and a measurement matrix A corresponding to the measurement device used to obtain the measurement signal is recorded; the measurement matrix corresponding to the measurement device is an encoding diffraction imaging measurement matrix FΛ, wherein Λ is a diagonal matrix with complex values, the diagonal elements of Λ are obtained by uniformly sampling from the unit circle of the complex plane, and F is a two-dimensional Fourier transform matrix: a measurement signal containing only amplitude information is obtained by using the measurement device, and a measurement matrix FΛ corresponding to the measurement device used to obtain the measurement signal is recorded.

3. The signal reconstruction method of claim 1, wherein, The denoiser is a traditional denoiser or a denoiser based on a neural network.

4. The signal reconstruction method of claim 1, wherein, The method for introducing the regular term function related to the denoiser under the regular constraint based on the denoising prior information, taking the measurement signal and the measurement matrix as inputs, and establishing the non-convex optimization inverse problem of signal reconstruction adopts any one of the following methods: - when the measurement matrix corresponding to the measurement device is a random measurement matrix, the form of the denoising prior information is PnP: under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, wherein, g(z)=h(D(z)), z is a reconstructed signal, y is a measurement signal, A is a random measurement matrix, λ is a parameter of a constraint regular term, h(D) is an implicit regular term function related to a denoiser D, and the output of the proximal projection of h(D) is D; - when the measurement matrix corresponding to the measurement device is a random measurement matrix, the form of the denoising prior information is RED: under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, wherein z is a reconstructed signal, y is a measurement signal, A is a random measurement matrix, λ is a parameter of a regular term, and the regular term function at the τth iteration is wherein is the z τ-1 According to f(z) by step size μ τ Gradient descent obtains: - when the measurement matrix corresponding to the measurement device is a measurement matrix corresponding to coded diffraction imaging, the form of the denoising prior information is PnP: under the regular constraint of the denoising prior information, a non-convex optimization inverse problem is established, wherein z is a reconstructed signal, y is a measurement signal, F is a Fourier transform matrix, Λ is a complex-valued diagonal matrix, elements of which are uniformly sampled from a unit circle of a complex plane, λ is a parameter of a constraint regular term, h(D) is an implicit regular term function related to the denoiser D, and an output of a proximal projection of h(D) is D. - when the measurement matrix corresponding to the measurement device is a measurement matrix corresponding to coded diffraction imaging, the de-noising prior information is in the form of RED: under the regular constraint of the de-noising prior information, a non-convex optimization inverse problem is established: where z is a reconstructed signal, y is a measurement signal, F is a Fourier transform matrix, A is a complex-valued diagonal matrix, elements of which are uniformly sampled from a unit circle in a complex plane, and λ is a parameter of a regular term, a regular term function at the τth iteration where is the z τ-1 According to f(z) by step size μ τ Gradient descent is obtained:

5. The signal reconstruction method of claim 1, wherein, The method for obtaining the initial solution of the non-convex optimization inverse problem comprises any one of the following methods: - obtaining an initial solution z0 of the non-convex optimization inverse problem by using a spectral method, specifically, the initial solution z0 is the maximum eigenvector of the matrix Y=A * diag{y}A normalized to have unit norm where y is a measurement signal, and A is a random measurement matrix. a constant value signal is taken as the initial solution of the non-convex optimization inverse problem.

6. The signal reconstruction method of claim 4, wherein, The method for adopting the gradient descent step and the proximal projection step related to the denoiser to form the projection gradient method comprises the following steps: At the τth iteration, the output of the gradient descent step is specifically: where z τ-1 is the reconstructed signal obtained by solving the non-convex optimization inverse problem at the (τ-1)th iteration, μ τ is the step size of the gradient descent step at the τth iteration, A * is the conjugate transpose of the measurement matrix, y is the measurement signal, and is the element-wise product of vectors. The output of the proximal projection step comprises any one of the following: - when said final reconstructed signal does not contain a-priori information on the pixel values being real numbers, said de-noising a-priori information being PnP, the output of said proximal projection step is in particular: where D is a de-noiser; - when the final reconstructed signal does not contain a priori information that the pixel values are real numbers, the output of the denoising step is specifically: where D is a denoiser, and a is a hyperparameter between 0 and 1. - when said final reconstructed signal contains a-priori information that the pixel values are real numbers, said de-noising a-priori information is PnP, the output of said proximal projection step is in particular: where D is a de-noiser and Re(·) is the real part operator. - when the final reconstructed signal contains a-priori information that the pixel values are real numbers, the denoising a-priori information is RED, the output of the proximal projection step is specifically: wherein a is a hyper-parameter between 0 and 1, D is a denoiser, and Re(·) is an operator taking the real part.

7. The signal reconstruction method of claim 6, wherein, The method for iteratively solving the final reconstructed signal by combining the projection gradient method with the monitor having the monotone decreasing property comprises the following steps: - when the final reconstructed signal does not contain prior information of pixel value being real number, the denoising prior information is PnP, the final reconstructed signal is iteratively solved by combining projection gradient method and monitor with monotone decreasing property, specifically: and rand(0,1) < p, z Otherwise, z ′ τ is unchanged; wherein p is a hyperparameter for avoiding local minimum, and the value range is between 0 and 1; the obtained z' τ is output z τ as the output of the τth iteration. - when the final reconstructed signal does not contain prior information of pixel values being real numbers, the de-noising prior information is RED, the final reconstructed signal is iteratively solved by combining the projection gradient method and a monitor with a monotone decreasing property, specifically: and s≥s h , otherwise, α is a hyperparameter between 0 and 1, D is a de-noiser, s is a sampling rate, s h is a hyperparameter for avoiding local minimum, and s h >0; the obtained z τ is the output z τ of the τth iteration. - when the final reconstructed signal contains prior information that the pixel value is a real number, the denoising prior information is PnP, the final reconstructed signal is iteratively solved by combining the projection gradient method and the monitor with the monotone decreasing property, specifically: and rand(0,1) < p, then Otherwise, Wherein, D is a denoiser, Re(·) is an operator for taking the real part, p is a hyperparameter for avoiding local minimum, the value range is between 0 and 1; the obtained As the output z τ of the τth iteration - when the final reconstructed signal contains prior information that the pixel value is a real number, the denoising prior information is RED, the final reconstructed signal is iteratively solved by combining the projection gradient method and the monitor with the monotone decreasing property, specifically: and s≥s h , otherwise, wherein α is a hyperparameter between 0 and 1, D is a denoiser, Re(·) is an operator taking the real part, s is a sampling rate, s h is a hyperparameter for avoiding local minimum, and the value range is s h >0; obtaining z τ as the output of the τth iteration.

8. A signal reconstruction system characterized by, The method comprises the following steps: a measurement signal obtaining module: obtaining a measurement signal containing only amplitude information by using a measurement device, and recording a measurement matrix corresponding to the measurement device used to obtain the measurement signal; a denoiser establishing module: establishing a denoiser, and taking the functional characteristics of the denoiser as denoising prior information; an inverse problem establishing module: under the regular constraint based on the denoising prior information, introducing a regular term function related to the denoiser, taking the measurement signal and the measurement matrix as inputs, and establishing a non-convex optimization inverse problem of signal reconstruction; A signal reconstruction module: taking the measurement signal and the measurement matrix as inputs, initializing the measurement signal containing only amplitude information, obtaining an initial solution of the non-convex optimization inverse problem, and using a gradient descent step and a proximal projection step related to a denoiser to form a projected gradient method, and iteratively solving the projected gradient method in combination with a monitor having a monotonic decreasing property to obtain a final reconstructed signal.

9. A signal reconstruction apparatus comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein, The processor executes the program, which can be used to execute the signal reconstruction method of any one of claims 1-7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor, which can be used to execute the signal reconstruction method of any one of claims 1-7.

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