Signal reconstruction method, system, medium and terminal based on mixed denoising prior

Abstract

The application provides a signal reconstruction method and system based on a hybrid denoising prior, comprising: processing an original signal which cannot be directly obtained to obtain a measurement signal; establishing a convex combination of a traditional denoiser and a neural network denoiser to form a new denoiser, and taking the functional characteristics of the new denoiser as denoising prior information; under the regular constraint based on the denoising prior information, introducing a regular term function related to the denoiser to establish an optimization inverse problem of signal reconstruction; obtaining an initial solution of the 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 proximal gradient method; establishing a reinforcement learning framework to adaptively obtain hyperparameters of the proximal gradient method; and obtaining a final reconstruction signal through iterative solution of the proximal gradient method, wherein the final reconstruction signal approximates the original signal. The application adaptively combines a traditional denoising prior and a deep denoising prior to improve the flexibility and reliability of signal reconstruction and meet the current demand for signal reconstruction.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to a signal reconstruction method, system, medium and terminal based on hybrid denoising prior. Background Art

[0002] Recovering indirect signals from limited measurements is crucial for quantum information, quantum communications, media signal processing, optical imaging, and other fields. For example, in the field of quantum information, quantum signal processing involves directly measuring quantum states, which disrupt the quantum system and thus destroy the original quantum state signal. Quantum state tomography, which reconstructs the original quantum state signal from the measured values ​​through repeated preparation and measurement of the original quantum state, has become a crucial tool for obtaining quantum state information. However, this technique suffers from the exponential growth of the number of measured signals.

[0003] In response to the above technical requirements, researchers have proposed solutions. One type of solution uses the prior information contained in the quantum state to reduce the number of required measurements, such as compressed sensing quantum state tomography, matrix product state tomography, and permutation invariant tomography. These traditional methods usually have a solid theoretical basis, but the tomography quality needs to be improved when the assumed prior information cannot be strictly met. In recent years, neural networks have been applied to quantum state tomography tasks and have great potential in improving the quality of quantum state tomography. The usual solution is to train a generative model to represent the distribution of quantum states, such as Restricted Boltzmann Machine (RBM) and Generative Adversarial Networks (GAN).

[0004] However, the current quantum state tomography method based on neural networks requires retraining different models for different experimental settings, which is inflexible and results in a waste of time and resources.

[0005] Furthermore, existing neural network-based quantum state tomography methods are completely data-driven and fail to consider the physical information of the quantum system. Therefore, they struggle to ensure stable reconstruction of different quantum states and lack the theoretical reliability of traditional methods. Consequently, they struggle to meet current demands for signal reconstruction. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the present invention provides a signal reconstruction method, system, terminal and storage medium based on hybrid denoising prior, combining the traditional optimization problem-solving algorithm with the denoising prior, and introducing a convex combination of a traditional denoiser and a deep denoiser in the solution step. Hyperparameters are adaptively obtained through reinforcement learning methods, thereby improving the flexibility and reliability of signal reconstruction and meeting current signal reconstruction needs.

[0007] According to a first aspect of the present invention, a signal reconstruction method based on hybrid denoising prior is provided, comprising:

[0008] Process the original signal that cannot be directly obtained to obtain the measurement signal;

[0009] A convex combination of the traditional denoiser and the neural network denoiser is established to form a new denoiser, and the functional characteristics of the new denoiser are used as denoising prior information;

[0010] Under the regularization constraint based on the denoising prior information, a regularization term function related to the new denoiser is introduced, and an inverse optimization problem of signal reconstruction is established based on the measurement signal;

[0011] Obtaining an initial solution to the inverse optimization problem, and starting from the initial solution, employing a proximal gradient method using a gradient descent step and a proximal projection step associated with a denoiser;

[0012] Establishing a reinforcement learning framework to adaptively obtain hyperparameters of the proximal gradient method;

[0013] Based on the hyperparameters, a final reconstructed signal is obtained by iteratively solving the proximal gradient method, and the final reconstructed signal is close to the original signal.

[0014] Preferably, the processing of the original signal that cannot be directly obtained to obtain the measurement signal includes:

[0015] The measured signal y is transformed from the original signal ρ through a linear perceptual mapping Obtain, specifically:

[0016] The original signal ρ is a vector signal, and the linear perceptual mapping Through m measurement vectors P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement vector P i Multiply to get the i-th measurement value y i =P i ρ, the measured value y i Composition measurement signal y=(y1,y2,…,y m ) T ;

[0017] or,

[0018] The original signal ρ is a matrix signal, and the linear perceptual mapping Through m measurement matrices P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement matrix P i Multiply to get the matrix Pi ρ, for the matrix P i ρ trace (trace) to obtain the i-th measurement value y i =Tr(P i ρ), the measured value y i Composition measurement signal y=(y1,y2,…,y m ) T .

[0019] Preferably, the traditional denoiser is a traditional denoiser containing prior information of the original signal structure, such as any one of a weighted nuclear norm minimization denoiser containing low-rank prior information, an arithmetic mean filter containing smooth prior information, a non-local mean filter or a 3-D collaborative filter based on block matching;

[0020] The neural network layers used by the neural network denoiser include: convolutional layers, nonlinear activation layers and batch normalization layers;

[0021] The neural network denoiser is obtained, comprising: collecting a reference signal to construct a training data set, using the training data set and a reverse gradient propagation method to train the neural network layer; and using the trained neural network layer as the neural network denoiser.

[0022] Preferably, under the regularization constraint based on the denoising prior information, a regularization term function related to the new denoiser is introduced, and based on the measurement signal, an optimization inverse problem of signal reconstruction is established, specifically:

[0023] Under the regularization constraint of the denoising prior information, an inverse optimization problem is established for signal reconstruction:

[0024]

[0025] in, g(ρ)=h(D), ρ is the reconstructed signal, y is the measured signal, is a linear perceptual mapping, λ is the parameter of the constrained regularization term, h(D) is the implicit regularization function related to the denoiser D, and the output of the proximal projection that satisfies h(D) is D.

[0026] Preferably, the method of obtaining the initial solution to the inverse optimization problem includes:

[0027] Specifying an initial solution ρ0 of the inverse optimization problem according to the type of the signal to be reconstructed;

[0028] or,

[0029] The random signal is used as the initial solution ρ0 of the inverse optimization problem.

[0030] Preferably, the proximal gradient method is formed by using the gradient descent step and the proximal projection step associated with the denoiser, specifically:

[0031] At the τth iteration, the output of the gradient descent step is specifically: in, is the linear perceptual mapping The adjoint operator, ρ τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal;

[0032] At the τth iteration, the output of the proximal projection step associated with the denoiser is where α τ ∈[0,1] is the convex combination coefficient, or in is the output of the gradient descent step, D N It is a denoiser based on neural network training and contains smooth denoising prior information, σ n is the denoising strength, yes The conjugate transpose of Among them D W is a weighted nuclear norm minimization denoiser that incorporates low-rank prior information, σ w is the denoising strength; S(·) includes any of the following: S(·) is the identity matrix or S(·) is the simplex projection operator, specifically: As the input matrix, the input matrix ρ' τ Singular value decomposition is performed to obtain eigenvalues ​​and eigenvectors, the eigenvalues ​​are projected onto a unit simplex, and then multiplied by the eigenvectors.

[0033] Preferably, the reinforcement learning framework is established to adaptively obtain the hyperparameters of the proximal gradient method, specifically:

[0034] Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process. τ ,τ=1,…,T, the action space A is the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,…,T, where T is the total number of iterations of the proximal gradient method; the state transfer function P is composed of M iteration blocks in the proximal gradient method, 1≤M≤T, s t+1 =P(s t ,at ); the reward function R is

[0035]

[0036] in is the loss function, which is KL divergence or mean square error, y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space S, a t Belongs to the action space A, γ∈[0,1] is the discount coefficient;

[0037] The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as Establishing a state buffer B, storing the state in the state space in the state buffer;

[0038] Define the policy network π including convolutional layer, batch normalization layer, residual connection, fully connected layer and activation function, the input of the policy network is the state s sampled in the state buffer t , measurement signal y, the total number of iterations of the proximal gradient method T; the output of the policy network is action a t , comprising the convex combination coefficients in the state transfer function P and the step size of the gradient descent step;

[0039] Optimizing the policy network by a policy gradient method to maximize the expected value of the discounted reward in all possible trajectories;

[0040] The optimized policy network automatically gives the hyperparameters of the proximal gradient method: the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,…,T. According to a second aspect of the present invention, a signal reconstruction system based on hybrid denoising prior is provided, comprising:

[0041] Measurement signal acquisition module: processes the original signal that cannot be directly obtained to obtain the measurement signal;

[0042] Denoiser construction module: A convex combination of the traditional denoiser and the neural network denoiser is constructed to form a new denoiser, and the functional characteristics of the new denoiser are used as denoising prior information;

[0043] An inverse problem establishment module: under the regularization constraint based on the denoising prior information, introducing a regularization term function related to the new denoiser, and establishing an optimized inverse problem of signal reconstruction based on the measurement signal;

[0044] Signal solution module: obtains an initial solution to the inverse optimization problem, and based on the initial solution, adopts a gradient descent step and a denoiser-related proximal projection step to form a proximal gradient method; establishes a reinforcement learning framework to adaptively obtain the hyperparameters of the proximal gradient method; based on the hyperparameters, obtains a final reconstructed signal through iterative solution using the proximal gradient method, and the final reconstructed signal approximates the original signal.

[0045] According to a third aspect of the present invention, there is provided a terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor can be used to execute any one of the methods described, or to run the system described, when executing the program.

[0046] According to a fourth aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can be used to execute any one of the methods described above, or to operate the system described above.

[0047] Compared with the prior art, the embodiments of the present invention have at least one of the following beneficial effects:

[0048] Compared with traditional signal reconstruction methods, the hybrid denoising prior-based signal reconstruction method and system of the embodiment of the present invention can adaptively introduce prior information and have higher reconstruction accuracy.

[0049] The signal reconstruction method and system based on hybrid denoising priors in the embodiments of the present invention demonstrate greater flexibility than currently popular neural network-based quantum state tomography techniques. Specifically, the constructed denoiser does not require retraining when the measurement settings change, thereby reducing the resource consumption required for repeated network training. Furthermore, this technique demonstrates high reliability and achieves high reconstruction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0051] Figure 1 A flow chart of a signal reconstruction method based on hybrid denoising prior provided in a preferred embodiment of the present invention;

[0052] Figure 2 A flowchart of solving an optimization inverse problem based on a denoising prior by a proximal gradient method in a preferred embodiment of the present invention;

[0053] Figure 3 Flowchart of the proximal projection step in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that those skilled in the art may make various modifications and improvements without departing from the scope of the present invention. These modifications and improvements fall within the scope of protection of the present invention. Parts not described in detail below may be implemented using existing technologies.

[0055] like Figure 1 As shown, in one embodiment of the present invention, a signal reconstruction method based on hybrid denoising prior is provided, such as Figure 1 As shown, the main steps include:

[0056] S1, processes the original signal that cannot be directly obtained to obtain the measurement signal;

[0057] S2, a convex combination of the traditional denoiser and the neural network denoiser is established to form a new denoiser, and the functional features of the new denoiser are used as denoising prior information;

[0058] S3, under the regularization constraint based on the denoising prior information, introduce a regularization function related to the new denoiser in S2, and establish an inverse optimization problem for signal reconstruction based on the measurement signal of S1;

[0059] S4, obtains the initial solution of the inverse optimization problem of S3, and starting from the initial solution, adopts the gradient descent step and the proximal projection step related to the denoiser to form a proximal gradient method; establishes a reinforcement learning framework to adaptively obtain the hyperparameters of the proximal gradient method; based on the hyperparameters, obtains the final reconstructed signal by iteratively solving the proximal gradient method, and the final reconstructed signal is close to the original signal of S1.

[0060] Compared with the traditional signal reconstruction method, the signal reconstruction method based on hybrid denoising prior in the above embodiment can adaptively introduce prior information and has higher reconstruction accuracy.

[0061] In a preferred embodiment of the present invention, step S1 is implemented to process the original signal that cannot be directly obtained to obtain the measurement signal. Specifically, the measurement signal y is obtained by processing the original signal ρ through a linear perceptual mapping. Obtain, including the following two situations:

[0062] The original signal ρ is a vector signal, and the linear perceptual mapping Through m measurement vectors P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement vector P i Multiply to get the i-th measurement value y i =P i ρ, the measured value yi Composition measurement signal y=(y1,y2,…,y m ) T ;

[0063] The original signal ρ is a matrix signal, and the linear perceptual mapping Through m measurement matrices P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement matrix P i Multiply to get the matrix P i ρ, for the matrix P i ρ trace (trace) to obtain the i-th measurement value y i =Tr(P i ρ), the measured value y i Composition measurement signal y=(y1,y2,…,y m ) T .

[0064] In a preferred embodiment of the present invention, step S2 is implemented to establish a denoiser, which is a convex combination of a traditional denoiser and a neural network-based denoiser, and the functional characteristics of the denoiser are used as denoising prior information.

[0065] Among them, traditional denoisers include any of the following: selecting a traditional denoiser architecture that contains prior information on the original signal structure, such as the weighted nuclear norm minimization denoiser (WNNM) containing low-rank prior information, the arithmetic mean filter (arithmetic mean filter) containing smooth prior information, the non-local mean filter (NLM), and the block matching and 3D collaborative filtering (BM3D).

[0066] Among them, the specific process of obtaining the neural network-based denoiser is as follows: collecting reference signals to construct a training data set, using convolutional layers, nonlinear activation layers, and batch normalization layers to construct a neural network layer, and using the training data set and the back gradient propagation algorithm to train the neural network layer as a neural network-based denoiser.

[0067] In a preferred embodiment of the present invention, step S3 is implemented to establish an inverse optimization problem for signal reconstruction under the regularization constraint of the denoising prior information:

[0068]

[0069] Where ρ is the reconstructed signal, y is the measured signal, is a linear perceptual mapping, λ is the parameter of the constrained regularization term, h(D) is the implicit regularization function related to the denoiser D, and the output of the proximal projection that satisfies h(D) is D.

[0070] In a preferred embodiment of the present invention, step S4 is performed as follows: Figure 2 As shown, it can be divided into the following steps:

[0071] S41, solve the initial solution.

[0072] The initial solution can be any of the following:

[0073] Specifying an initial solution ρ0 of the inverse optimization problem according to the type of the signal to be reconstructed;

[0074] The random signal is used as the initial solution ρ0 of the inverse optimization problem.

[0075] S42, gradient descent step.

[0076] At the τth iteration, the output of the gradient descent step is specifically: in, is the linear perceptual mapping The adjoint operator of ρ. τ -1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal.

[0077] S43, the proximal projection step related to the denoiser. Figure 3 As shown, the following steps are included:

[0078] S431, denoising step, the output at the τth iteration is specifically, or in is the output of the gradient descent step, D N It is a denoiser DnCNN based on neural network training with smooth prior information, σ n is the denoising strength, yes The conjugate transpose of . Among them D W is the weighted nuclear norm minimization denoiser (WNNM) with low-rank prior information, σ w is the denoising strength.

[0079] S432, convex combination step, the output of the proximal projection step associated with the denoiser at the τth iteration is where α τ ∈[0,1] is the convex combination coefficient.

[0080] S433, simplex projection step, performs proximal projection ρ in each iteration step τ =S(ρ′ τ ), where S(·) is a simplex projection operator, specifically: singular value decomposition is performed on the input matrix to obtain eigenvalues ​​and eigenvectors, the eigenvalues ​​are projected onto the unit simplex, and then multiplied by the eigenvectors.

[0081] S44, establishing a reinforcement learning framework to adaptively obtain hyperparameters of the proximal gradient method.

[0082] Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process τ ,τ=1,...,T, the action space A is the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,...,T, where T is the total number of iterations of the proximal gradient method. The state transfer function P is composed of M iteration blocks in the proximal gradient method, 1≤M≤T, s t+1 =P(s t , a t ). The reward function R is

[0083]

[0084] in is the loss function, you can choose KL divergence (Kullback-Leibler divergence) or mean squared error (Mean Squared Error), y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space S, a t Belongs to the action space A. γ∈[0,1] is the discount coefficient.

[0085] The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as A state buffer B is established and the state in the state space is stored in the state buffer. The policy network π consists of a convolutional layer, a batch normalization layer, a residual connection, a fully connected layer and an activation function. The input of the policy network is the state s sampled in the state buffer. t , measurement signal y, the total number of iterations of the proximal gradient method T, the output of the policy network is action a t, comprising the convex combination coefficients in the state transition function P (composed of M iteration blocks) and the step size of the gradient descent step. The policy network is optimized using a policy gradient method to maximize the expected value of the discounted reward across all possible trajectories. The optimized policy network automatically provides the hyperparameters of the proximal gradient method.

[0086] S45, combining the proximal gradient method composed of the gradient descent step and the proximal projection step, iteratively solving to obtain the final reconstructed signal.

[0087] In a preferred embodiment of the present invention, the above-mentioned signal reconstruction method based on hybrid denoising prior is used to reconstruct vector signals. The corresponding measurement signal acquisition process is: expand an image into a one-dimensional vector signal to obtain a vector signal ρ∈R n×1 As the original signal, R n×1 is an n-dimensional real vector. Sample m measurement vectors P from Gaussian distribution i ∈R 1 ×n , i=1,…,m is the row vector of matrix A, and matrix A is the linear perceptual mapping The linear perceptual mapping is used to obtain the corresponding measurement signal In the vector signal reconstruction process, the traditional denoiser uses 3D collaborative filtering based on block matching (BM3D). The remaining steps are the same as steps S3 and S4 provided in the above embodiment and are not described here.

[0088] In another embodiment of the present invention, the aforementioned signal reconstruction method based on hybrid denoising prior is applied to obtain the characteristics of the quantum state prepared by the current quantum computer to evaluate and optimize the performance of the quantum computer, which is of great significance for the further development of quantum computers. In this embodiment, the signal reconstruction method based on hybrid denoising prior is mainly used in quantum state tomography, that is, reconstructing the quantum state density matrix corresponding to the unknown quantum system through known measurement signals. Its specific operation steps are the same as the aforementioned S1-S4, wherein the S1 step involves the process of obtaining the measurement signal as follows: constructing a quantum circuit on a superconducting quantum computer provided by IBM (International Business Machines Corporation), preparing a quantum state as the original quantum state through the quantum circuit, and the density matrix of the original quantum state as the original signal. Construct a measurement circuit on the superconducting quantum computer as a measurement device, which corresponds to a linear perception mapping Use this measuring device to obtain the measurement signal in The linear perceptual mapping corresponding to the measuring device that obtains the measurement signal is recorded. In step S2, a weighted nuclear norm minimization denoiser is used when selecting a traditional denoiser. Subsequently, in step S3, an inverse optimization problem for signal reconstruction is established under the regularization constraint of the denoising prior; finally, a proximal gradient method consisting of gradient descent and proximal projection steps is used to solve the inverse optimization problem, wherein the proximal projection step is implemented by a convex combination of a traditional denoiser and a neural network-based denoiser, and the hyperparameters of the proximal gradient method are adaptively determined through a reinforcement learning framework. In the above-mentioned quantum state tomography process, a mathematically analytical deep learning method is established for quantum state signal reconstruction. This method has both the flexibility and reliability of an analytical iterative optimization algorithm and the adaptability of a data-driven algorithm. At the same time, the above-mentioned quantum state tomography combines analytical optimization problem solving methods and takes into account the physical information of the measurement process. Compared with the existing quantum state tomography method based on neural networks, it has higher flexibility and reliability.

[0089] The quantum state tomography method for signal reconstruction based on a hybrid denoising prior, provided in the above-mentioned embodiments of the present invention, can be applied to quantum state tomography of general quantum systems and related practical application scenarios. For a better understanding, the technical solutions provided by the above-mentioned embodiments of the present invention are further described below with reference to specific application examples.

[0090] In this specific example, quantum state tomography of a 5-qubit GHZ state based on a denoising prior is implemented. Specifically, the quantum state tomography method based on a denoising prior includes the following four main steps:

[0091] S101: Build a quantum circuit on the QASM simulator (an efficient C++-based quantum circuit simulator) in qiskit-aer provided by IBM to obtain a 5-qubit GHZ state. Build a measurement quantum circuit on the QASM simulator in qiskit-aer to measure the GHZ state and obtain 100 Pauli correlation measurements as the measurement signal y. Specifically, the Pauli correlation measurements are: is measured by the Pauri Calculated as follows:

[0092]

[0093] in s j ={I = [1,0; 0,1], σ x =[0,1;1,0],σ y =[0,-i;i,0],σ z=[1,0;0,-1]}, Is composed of P i The characteristic basis of the kth Pauli matrix, each Pauli matrix has two characteristic bases, through l (k) ∈{0,1}. f(·) transforms the bit string l to obtain f(l), so that the l corresponding to the unit matrix I (k) =0,χ f(l) The paulistin value is the frequency of occurrence of different paulistin in 4096 repeated measurement experiments.

[0094] S102, establish a denoiser, which is a convex combination of a traditional denoiser and a denoiser based on a neural network. w is a weighted nuclear norm minimization denoiser with denoising strength σ w =40; The specific structure and training method of the neural network-based denoiser adopt the DnCNN structure proposed in "Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising" published in the IEEE Transactions on Image Processing journal in 2017. The loss function is 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 image signal after adding Gaussian noise, and the denoising intensity is σ n ∈[20,40].

[0095] S103, under the regularization constraint of the denoising prior information, establish the inverse optimization problem of signal reconstruction:

[0096]

[0097] Where ρ is the reconstructed signal, is the linear perceptual mapping corresponding to the measurement quantum circuit, λ is the parameter of the constraint regularization term, g(z)=h(D) is the implicit regularization function related to the denoiser, and the output of the proximal projection satisfying h(D) is D.

[0098] S104, starting from the initial solution ρ0, a proximal gradient method based on a gradient descent step and a proximal step related to a denoiser is used to obtain a final reconstructed signal ρ through the proximal gradient method, and the final reconstructed signal ρ is close to the original signal

[0099] In S1041, the initial solution in is the unit matrix, n=5.

[0100] In S1042, the gradient descent step is as follows: the output at the τth iteration is in, is the linear perceptual mapping The adjoint operator of ρ. τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal.

[0101] In S1043, the output of the gradient descent step As the input of the proximal projection step, the output of the proximal gradient method is obtained through the proximal projection step associated with the denoiser. The proximal projection step associated with the denoiser specifically includes the following steps:

[0102] S1043-1, denoising step: The output at the τth iteration is specifically, in is the output of the gradient descent step, D N It is a DnCNN denoiser based on neural network training with smooth prior information, σ n ∈[20,40], yes The conjugate transpose of . Among them D W is the weighted nuclear norm minimization denoiser (WNNM) with low-rank prior information, σ w =40.

[0103] S1043-2, convex combination step: At the τth iteration, the output of the proximal projection step associated with the denoiser is where α τ ∈[0,1] is the convex combination coefficient.

[0104] S1043-3, simplex projection step: perform proximal projection ρ in each iteration step τ =S(ρ' τ ), where S(·) is a simplex projection operator, specifically: singular value decomposition is performed on the input matrix to obtain eigenvalues ​​and eigenvectors, the eigenvalues ​​are projected onto the unit simplex, and then multiplied by the eigenvectors.

[0105] In S1044, the hyperparameters of the proximal gradient method are adaptively obtained, specifically:

[0106] Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process. τ ,τ=1,…,T, the action space A is the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,…,T, where T is the total number of iterations of the proximal gradient method. The state transfer function P is composed of M=5 iteration blocks in the proximal gradient method, s t+1 =P(s t ,a t ). The reward function R is

[0107]

[0108] in is the mean square error of the loss function, y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space s, a t Belongs to the action space A. γ = 0.1 is the discount coefficient.

[0109] The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as A state buffer B is established and the state in the state space is stored in the state buffer. The policy network π consists of a convolutional layer, a batch normalization layer, a residual connection, a fully connected layer and an activation function. The input of the policy network is the state s sampled in the state buffer. t , measurement signal y, the total number of iterations of the proximal gradient method T = 40, the output of the policy network is action a t , comprising the convex combination coefficients in the state transition function P (consisting of five iteration blocks) and the step size of the gradient descent step. The policy network is optimized using the policy gradient method published in the Journal of Machine Learning Research in 2022 to maximize the expected value of the discounted reward across all possible trajectories. The optimized policy network automatically provides the hyperparameters of the proximal gradient method.

[0110] In S1045 , the gradient descent step and the proximal projection step are combined to iteratively solve the final reconstructed signal.

[0111] In the simulation experiment, this example uses the density matrix of the 5-qubit GHZ state obtained on the QASM simulator in the qiskit-aer provided by IBM as the original signal 100 randomly selected measurement values ​​form the measurement signal y. Calculate the original signal of the test And the fidelity of the output signal ρ, where fidelity is defined as This was used as a performance evaluation criterion to assess the performance of this example's quantum state tomography based on a denoising prior. This example compared the QST-CGAN method proposed in "Quantum State Tomography with Conditional Generative Adversarial Networks," published in the 2021 journal Physical Review Letters. The evaluation criterion was fidelity, with higher values ​​being better. The quality of the reconstructed quantum state density matrix in this example was significantly higher than that of existing neural network-based quantum state tomography methods, with the proposed method achieving a 42.92% improvement in fidelity compared to the QST-CGAN method.

[0112] In another embodiment, the present invention provides a tomography method for random quantum states based on denoising priors, which may include the following steps:

[0113] S201, build a quantum circuit on the QASM simulator in qiskit-aer provided by IBM to obtain a 5-qubit random quantum state, build a measurement quantum circuit on the QASM simulator in qiskit-aer to measure the random state, and obtain 256 Pauli correlation measurements as the measurement signal y, specifically: the Pauli correlation measurement value is measured by the Pauri Calculated as follows:

[0114]

[0115] in s j ={I = [1,0; 0,1], σ x =[0,1;1,0],σ y =[0,-i;i,0],σ z =[1,0;0,-1]}, Is composed of P i The characteristic basis of the kth Pauli matrix, each Pauli matrix has two characteristic bases, through l (k) ∈{0,1}. f(·) transforms the bit string l to obtain f(l), so that the l corresponding to the unit matrix I (k) =0,χ f(l)The paulistin value is the frequency of occurrence of different paulistin in 4096 repeated measurement experiments.

[0116] S202, establish a denoiser, which is a convex combination of a traditional denoiser and a denoiser based on a neural network. The traditional denoiser D w is a weighted nuclear norm minimization denoiser with denoising strength σ w =60; The specific structure and training method of the neural network-based denoiser adopt the DnCNN structure proposed in "Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising" published in the IEEE Transactions on Image Processing journal in 2017. The loss function is 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 image signal after adding Gaussian noise, and the denoising intensity is σ n ∈[20,40].

[0117] S203, under the regularization constraint of the denoising prior information, establish the inverse optimization problem of signal reconstruction:

[0118]

[0119] Where ρ is the reconstructed signal, is the linear perceptual mapping corresponding to the measurement quantum circuit, λ is the parameter of the constraint regularization term, g(z)=h(D) is the implicit regularization function related to the denoiser, and the output of the proximal projection satisfying h(D) is D.

[0120] S204, starting from the initial solution ρ0, a proximal gradient method based on a gradient descent step and a proximal step related to a denoiser is used to obtain a final reconstructed signal ρ through the proximal gradient method, and the final reconstructed signal ρ is close to the original signal

[0121] In S2041, the initial solution in is the unit matrix, n=5.

[0122] In S2042, the gradient descent step is as follows: the output at the τth iteration is in, is the linear perceptual mapping The adjoint operator of ρ. τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal.

[0123] In S2043, the output of the gradient descent step As the input of the proximal projection step, the output of the proximal gradient method is obtained through the proximal projection step associated with the denoiser. As an embodiment, the proximal projection step associated with the denoiser specifically includes the following steps:

[0124] S2043-1, denoising step, the output at the τth iteration is specifically, in is the output of the gradient descent step, D N It is a DnCNN denoiser based on neural network training with smooth prior information, σ n ∈[20,40], yes The conjugate transpose of . Among them D W is the weighted nuclear norm minimization denoiser (WNNM) with low-rank prior information, σ w =60.

[0125] S2043-2, convex combination step, the output of the proximal projection step associated with the denoiser at the τth iteration is ρ' τ = where α τ ∈[0,1] is the convex combination coefficient.

[0126] S2043-3, simplex projection step, implements proximal projection ρ in each iteration step τ =S(ρ' τ ), where S(·) is a simplex projection operator, specifically: singular value decomposition is performed on the input matrix to obtain eigenvalues ​​and eigenvectors, the eigenvalues ​​are projected onto the unit simplex, and then multiplied by the eigenvectors.

[0127] In S2044, the hyperparameters of the proximal gradient method are adaptively obtained, specifically:

[0128] Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process. τ ,τ=1,…,T, the action space A is the convex combination coefficient α τ and the step size η of the gradient descent step τ,τ=1,…,T, where T is the total number of iterations of the proximal gradient method. The state transfer function P is composed of M=1 iteration blocks in the proximal gradient method, s t+1 =P(s t ,a t ). The reward function R is

[0129]

[0130] in is the mean square error of the loss function, y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space s, a t Belongs to the action space A. γ = 0.99 is the discount coefficient.

[0131] The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as A state buffer B is established and the state in the state space is stored in the state buffer. The policy network π consists of a convolutional layer, a batch normalization layer, a residual connection, a fully connected layer and an activation function. The input of the policy network is the state s sampled in the state buffer. t , measurement signal y, the total number of iterations of the proximal gradient method T = 30, the output of the policy network is action a t , comprising the convex combination coefficients in the state transition function P (consisting of M = 1 iteration blocks) and the step size of the gradient descent step. The policy network is optimized using the policy gradient method published in the Journal of Machine Learning Research in 2022 to maximize the expected value of the discounted reward across all possible trajectories. The optimized policy network automatically provides the hyperparameters of the proximal gradient method.

[0132] In S2045, the gradient descent step and the proximal projection step are combined to iteratively solve the final reconstructed signal.

[0133] In this specific application example, the 5-qubit random quantum state obtained on the QASM simulator in the qiskit-aer provided by IBM is taken as the test signal to implement the quantum state tomography method based on denoising prior. The example compares the QST-CGAN method proposed in "Quantum State Tomography with ConditionalGenerative Adversarial Networks" published in the journal Physical Review Letters in 2021. The evaluation standard is fidelity, and the higher the value, the better. Compared with QST-CGAN, the quantum state density matrix reconstructed in this example has increased the fidelity from 94.9% to 97.73%.

[0134] In another embodiment of the present invention, a quantum state tomography method for preparing a GHZ state in a real quantum computer is provided, which may include the following steps:

[0135] S301, build a quantum circuit on the quantum processing unit ibm_oslo provided by IBM to prepare a 4-qubit GHZ quantum state, build a measurement quantum circuit on the quantum processing unit ibm_oslo provided by IBM to measure the 4-qubit GHZ state, and obtain 100 Pauli correlation measurements as the measurement signal y, specifically: the Pauli correlation measurement value is measured by the Pauri Calculated as follows:

[0136]

[0137] in s j ={I = [1,0; 0,1], σ x =[0,1;1,0],σ y =[0,-i;i,0],σ z =[1,0;0,-1]}, Is composed of P i The characteristic basis of the kth Pauli matrix, each Pauli matrix has two characteristic bases, through l (k) ∈{0,1}. f(·) transforms the bit string l to obtain f(l), so that the l corresponding to the unit matrix I (k) =0,χ f(l) The paulistin value is the frequency of occurrence of different paulistin in 8192 repeated measurement experiments.

[0138] S302, establish a denoiser, which is a convex combination of a traditional denoiser and a denoiser based on a neural network. w is a weighted nuclear norm minimization denoiser with denoising strength σ w =10; The specific structure and training method of the neural network-based denoiser adopts the DnCNN structure, and the denoising intensity is σ n ∈[10,20].

[0139] S303, under the regularization constraint of the denoising prior information, establish the inverse optimization problem of signal reconstruction:

[0140]

[0141] Where ρ is the reconstructed signal, is the linear perceptual mapping corresponding to the measurement quantum circuit, λ is the parameter of the constraint regularization term, g(z)=h(D) is the implicit regularization function related to the denoiser, and the output of the proximal projection satisfying h(D) is D.

[0142] S304, starting from the initial solution ρ0, a proximal gradient method based on a gradient descent step and a proximal step related to a denoiser is used to obtain a final reconstructed signal ρ through the proximal gradient method, and the final reconstructed signal ρ is close to the original signal

[0143] In S3041, the initial solution in is the unit matrix, n=4.

[0144] In S3042, the output of the gradient descent step at the τth iteration is in, is the linear perceptual mapping The adjoint operator of ρ. τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal.

[0145] In S3043, the output of the gradient descent step As the input of the proximal projection step, the output of the proximal gradient method is obtained through the proximal projection step associated with the denoiser. As an embodiment, the proximal projection step associated with the denoiser specifically includes the following steps:

[0146] S3043-1, denoising step, the output at the τth iteration is specifically, in is the output of the gradient descent step, D NIt is a DnCNN denoiser based on neural network training with smooth prior information, σ n ∈[0,10]. yes The conjugate transpose of . Among them D W is the weighted nuclear norm minimization denoiser (WNNM) with low-rank prior information, σ w =5.

[0147] S3043-2, convex combination step, the output of the proximal projection step associated with the denoiser at the τth iteration is where α τ ∈[0,1] is the convex combination coefficient.

[0148] S3043-3, simplex projection step, specifically, performing proximal projection ρ in each iteration step τ =S(ρ' τ ), where S(·) is the simplex projection operator: the input matrix is ​​subjected to singular value decomposition to obtain eigenvalues ​​and eigenvectors, the eigenvalues ​​are projected onto the unit simplex, and then multiplied by the eigenvectors.

[0149] In S3044, the hyperparameters of the proximal gradient method are adaptively given by the policy network trained with the simulation data in the first embodiment of the present invention.

[0150] In S3045, the gradient descent step and the proximal projection step are combined to iteratively solve the final reconstructed signal.

[0151] In this specific application example, a 4-qubit GHz state obtained on the IBM quantum processing unit ibm_oslo was used as a test signal to implement a quantum state tomography method based on denoising priors. The example was compared with the ProjFGD method proposed in "Provable compressed sensing quantum statetomography via non-convex methods," published in the journal npjquantuminformation in 2018. The evaluation criterion was fidelity, with higher values ​​being better. The reconstructed quantum state density matrix in this example improved its fidelity from 75.64% to 93.45% compared to ProjFGD.

[0152] It can be seen from the above embodiments that the signal reconstruction method based on hybrid denoising prior provided in the embodiments of the present invention has broad industrial application prospects. The signal reconstruction method based on hybrid denoising prior solves the difficult problem of flexibly and reliably reconstructing the original signal from the measurement signal, and can realize precise quantum measurement technology. As an important means of obtaining information about quantum systems, quantum measurement is of great significance to the description, application and further development of quantum systems, and has important application value in the fields of quantum information, quantum communication, etc. In addition, it can also be used in compressed sensing image reconstruction scenarios such as nuclear magnetic resonance imaging, or optical imaging scenarios such as coded diffraction imaging and coherent diffraction imaging that can only obtain amplitude information. Therefore, the signal reconstruction method based on hybrid denoising prior provided by the present invention has very important application value in scenarios such as quantum information, quantum communication, optical imaging, and medical imaging.

[0153] Based on the same technical concept as above, another embodiment of the present invention provides a signal reconstruction system based on hybrid denoising prior, which is used to implement the signal reconstruction method based on hybrid denoising prior in the above embodiment. Specifically, the signal reconstruction system includes:

[0154] Measurement signal acquisition module: processes the original signal that cannot be directly obtained to obtain the measurement signal;

[0155] Denoiser construction module: For the traditional denoiser in the denoiser, a traditional denoiser architecture is selected. For the neural network-based denoiser in the denoiser, the following steps are performed: constructing a training dataset, building a deep neural network, and using the training dataset and the back gradient propagation algorithm to optimize the deep neural network, obtaining the optimized deep neural network as the neural network-based denoiser;

[0156] Inverse problem establishment module: establishing an optimized inverse problem of signal reconstruction under the regularization constraint of the denoising prior information;

[0157] The signal reconstruction module obtains an initial solution and, starting from this initial solution, implements a proximal gradient method consisting of a gradient descent step and a proximal projection step associated with a convex combination of denoisers. The hyperparameters of this proximal gradient method are adaptively derived using reinforcement learning. The measured signal is used as input and the final reconstructed signal is obtained through an iterative solution of the proximal gradient method.

[0158] The various modules / units in the above examples of the present invention may specifically refer to the implementation techniques of the corresponding steps of the signal reconstruction method based on hybrid denoising prior in the above embodiment, which will not be described in detail here.

[0159] Based on the same inventive concept, in other embodiments of the present invention, a terminal is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the terminal can be used to execute the above-mentioned method, or to run the above-mentioned system.

[0160] Optionally, the memory is used to store programs; the memory may include volatile memory (English: volatile memory), such as random-access memory (English: random-access memory, abbreviated: RAM), such as static random-access memory (English: static random-access memory, abbreviated: SRAM), double data rate synchronous dynamic random access memory (English: Double Data Rate Synchronous Dynamic Random Access Memory, abbreviated: DDRSDRAM), etc.; the memory may also include non-volatile memory (English: non-volatile memory), such as flash memory (English: flash memory). The memory is used to store computer programs (such as applications, functional modules, etc. that implement the above-mentioned methods), computer instructions, etc., and the above-mentioned computer programs, computer instructions, etc. can be partitioned and stored in one or more memories.

[0161] The processor is configured to execute the computer program stored in the memory to implement the various steps of the method involved in the above embodiment. For details, please refer to the relevant description in the above method embodiment.

[0162] The processor and memory can be independent structures or integrated structures. When the processor and memory are independent structures, the memory and processor can be coupled via a bus.

[0163] Based on the same inventive concept, in other embodiments of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, it can be used to execute the above method or run the above system.

[0164] Computer-readable media include computer storage media and communication media, wherein communication media include any medium that facilitates the transfer of computer programs from one location to another. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer. An exemplary storage medium is coupled to a processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC. Alternatively, the ASIC can be located in a user device. Of course, the processor and storage medium can also exist as discrete components in a communication device.

[0165] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0166] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0167] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0168] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0169] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A signal reconstruction method based on hybrid denoising prior, characterized in that: include: Process the original signal that cannot be directly obtained to obtain the measurement signal; A convex combination of the traditional denoiser and the neural network denoiser is established to form a new denoiser, and the functional characteristics of the new denoiser are used as denoising prior information; Under the regularization constraint based on the denoising prior information, a regularization term function related to the new denoiser is introduced, and an inverse optimization problem of signal reconstruction is established based on the measurement signal; Obtaining an initial solution to the inverse optimization problem, and starting from the initial solution, employing a proximal gradient method using a gradient descent step and a proximal projection step associated with a denoiser; Establishing a reinforcement learning framework to adaptively obtain hyperparameters of the proximal gradient method; Based on the hyperparameters, a final reconstructed signal is obtained by iteratively solving the proximal gradient method, where the final reconstructed signal approximates the original signal; The proximal gradient method is formed by using the gradient descent step and the proximal projection step associated with the denoiser, specifically: At the τth iteration, the output of the gradient descent step is: in, It is a linear perceptual mapping The adjoint operator, ρ τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal; At the τth iteration, the output of the proximal projection step associated with the denoiser is: where α τ ∈[0,1] is the convex combination coefficient, or in is the output of the gradient descent step, D N It is a denoiser based on neural network training and contains smooth denoising prior information, σ n is the denoising strength, yes The conjugate transpose of Among them D W is a denoiser containing low-rank prior information, σ w is the denoising strength; S(·) is the unit matrix or S(·) is the simplex projection operator, specifically: As the input matrix, the input matrix ρ' τ Performing singular value decomposition to obtain eigenvalues ​​and eigenvectors, projecting the eigenvalues ​​onto a unit simplex, and then multiplying the eigenvalues ​​by the eigenvectors; The reinforcement learning framework is established to adaptively obtain the hyperparameters of the proximal gradient method, specifically: Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process. τ ,τ=1,…,T, A is the action space, where T is the total number of iterations of the proximal gradient method; the state transfer function P is composed of M iteration blocks in the proximal gradient method, 1≤M≤T, s t+1 =P(s t ,a t ); the reward function R is in is the loss function, which is KL divergence or mean square error, y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space S, a t Belongs to the action space A, γ∈[0,1] is the discount coefficient; The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as Establishing a state buffer B, storing the state in the state space in the state buffer; The input of the policy network is the state s sampled in the state buffer t , measurement signal y, the total number of iterations of the proximal gradient method T; the output of the policy network is action a t , comprising the convex combination coefficients in the state transfer function P and the step size of the gradient descent step; Optimizing the policy network by a policy gradient method to maximize the expected value of the discounted reward in all possible trajectories; The optimized policy network automatically gives the hyperparameters of the proximal gradient method: the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,…,T.

2. The signal reconstruction method based on hybrid denoising prior according to claim 1, characterized in that: The processing of the original signal that cannot be directly obtained to obtain the measurement signal includes: The measured signal y is transformed from the original signal ρ through a linear perceptual mapping Obtain, specifically: The original signal ρ is a vector signal, and the linear perceptual mapping Through m measurement vectors P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement vector P i Multiply to get the i-th measurement value y i =P i ρ, the measured value y i Composition measurement signal y=(y1,y2,…,y m ) T ; or, The original signal ρ is a matrix signal, and the linear perceptual mapping Through m measurement matrices P i , i=1,…,m, for i=1,…,m, the original signal ρ is sequentially combined with the i-th measurement matrix P i Multiply to get the matrix P i ρ, for the matrix P i ρ finds the trace to obtain the i-th measurement value y i =Tr(P i ρ), the measured value y i Composition measurement signal y=(y1,y2,…,y m ) T .

3. The signal reconstruction method based on hybrid denoising prior according to claim 1, characterized in that: The traditional denoiser is a traditional denoiser based on prior information of the original signal structure, including any one of the following denoisers: A weighted nuclear norm minimization denoiser incorporating low-rank prior information; Arithmetic mean filter with smoothness prior information, non-local mean filter or 3-D collaborative filtering based on block matching; The neural network layers used by the neural network denoiser include: convolutional layers, nonlinear activation layers and batch normalization layers; The neural network denoiser is obtained, comprising: collecting a reference signal to construct a training data set, using the training data set and a reverse gradient propagation method to train the neural network layer; and using the trained neural network layer as the neural network denoiser.

4. The signal reconstruction method based on hybrid denoising prior according to claim 1, characterized in that: Under the regularization constraint based on the denoising prior information, a regularization function related to the new denoiser is introduced, and an optimization inverse problem of signal reconstruction is established based on the measurement signal, specifically: Under the regularization constraint of the denoising prior information, an inverse optimization problem is established for signal reconstruction: in, g(ρ)=h(D), ρ is the reconstructed signal, y is the measured signal, is a linear perceptual mapping, λ is the parameter of the constrained regularization term, h(D) is the implicit regularization function related to the denoiser D, and the output of the proximal projection that satisfies h(D) is D.

5. The signal reconstruction method based on hybrid denoising prior according to claim 1, characterized in that: The method of obtaining the initial solution to the inverse optimization problem includes: Specifying an initial solution ρ0 of the inverse optimization problem according to the type of the signal to be reconstructed; or, The random signal is used as the initial solution ρ0 of the inverse optimization problem.

6. A signal reconstruction system based on hybrid denoising prior, characterized in that include: Measurement signal acquisition module: processes the original signal that cannot be directly obtained to obtain the measurement signal; Denoiser construction module: A convex combination of the traditional denoiser and the neural network denoiser is constructed to form a new denoiser, and the functional characteristics of the new denoiser are used as denoising prior information; An inverse problem establishment module: under the regularization constraint based on the denoising prior information, introducing a regularization term function related to the new denoiser, and establishing an optimized inverse problem of signal reconstruction based on the measurement signal; A signal solving module is configured to obtain an initial solution to the inverse optimization problem, and based on the initial solution, a proximal gradient method is constructed using a gradient descent step and a proximal projection step associated with a denoiser. A reinforcement learning framework is established to adaptively obtain hyperparameters of the proximal gradient method. Based on the hyperparameters, a final reconstructed signal is obtained by iteratively solving the proximal gradient method to obtain a signal that approximates the original signal. The proximal gradient method is formed by using the gradient descent step and the proximal projection step associated with the denoiser, specifically: At the τth iteration, the output of the gradient descent step is: in, It is a linear perceptual mapping The adjoint operator, ρ τ-1 is the reconstructed signal obtained by solving the inverse optimization problem at the τ-1th iteration, η τ is the step size of the gradient descent step at the τth iteration, and y is the measurement signal; At the τth iteration, the output of the proximal projection step associated with the denoiser is: where α τ ∈[0,1] is the convex combination coefficient, or in is the output of the gradient descent step, D N It is a denoiser based on neural network training and contains smooth denoising prior information, σ n is the denoising strength, yes The conjugate transpose of Among them D W is a denoiser containing low-rank prior information, σ w is the denoising strength; S(·) is the unit matrix or S(·) is the simplex projection operator, specifically: As the input matrix, the input matrix ρ' τ Performing singular value decomposition to obtain eigenvalues ​​and eigenvectors, projecting the eigenvalues ​​onto a unit simplex, and then multiplying the eigenvalues ​​by the eigenvectors; The reinforcement learning framework is established to adaptively obtain the hyperparameters of the proximal gradient method, specifically: Define a Markov decision process (S, A, P, R, γ), where the state space S is the density matrix ρ in the proximal gradient method iteration process. τ ,τ=1,…,T, A is the action space, where T is the total number of iterations of the proximal gradient method; the state transfer function P is composed of M iteration blocks in the proximal gradient method, 1≤M≤T, s t+1 =P(s t ,a t ); the reward function R is in is the loss function, which is KL divergence or mean square error, y is the measurement signal, is the linear perceptual mapping, s t Belongs to the state space S, a t Belongs to the action space A, γ∈[0,1] is the discount coefficient; The trajectory T'={s0,a0,R0,…,s N ,a N ,R N The discount reward in} is defined as Establishing a state buffer B, storing the state in the state space in the state buffer; The input of the policy network is the state s sampled in the state buffer t , measurement signal y, the total number of iterations of the proximal gradient method T; the output of the policy network is action a t , comprising the convex combination coefficients in the state transfer function P and the step size of the gradient descent step; Optimizing the policy network by a policy gradient method to maximize the expected value of the discounted reward in all possible trajectories; The optimized policy network automatically gives the hyperparameters of the proximal gradient method: the convex combination coefficient α τ and the step size η of the gradient descent step τ ,τ=1,…,T.

7. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, it can be used to perform the method according to any one of claims 1 to 5, or to run the system according to claim 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, it can be used to perform the method described in any one of claims 1 to 5, or to run the system described in claim 6.

Images