Error-resistant signal reconstruction method and system based on diffusion model

Abstract

The invention provides an error-resistant signal reconstruction method and system based on a diffusion model, and the method comprises the steps: multiplying an original signal by a measurement matrix, and obtaining a modulus, and obtaining a measurement signal; establishing a diffusion model, wherein the functional characteristic of the diffusion model is diffusion priori of an original signal; the method comprises the following steps of: carrying out inverse diffusion based on a diffusion model, and carrying out data consistency and decoupling sampling based on a measurement signal, starting from an initial value, and iteratively obtaining a signal to be detected, an initial reconstruction signal and an estimation measurement signal; establishing a signal reconstruction error detector, judging whether the initial reconstruction signal is the successful reconstruction of the original signal, repeating iteration and judgment to obtain the successfully reconstructed original signal or the initial reconstruction signal most matched with the measurement signal, and taking the initial reconstruction signal as an intermediate reconstruction signal; and iteratively solving the reconstruction signal based on the intermediate reconstruction signal through the steps of back diffusion of the diffusion model, data consistency of the measurement signal and combined decoupling sampling. According to the invention, the signal reconstruction performance during Fourier measurement is improved, and the number of repeated experiments required for successful reconstruction is reduced.

Description

Technical Field

[0001] This application relates to the field of signal processing, and more particularly, to an anti-error signal reconstruction method and system based on a diffusion model. Background Art

[0002] In the fields of optical imaging, medical imaging, computational holography, etc., the phase contains very important signal information, and the phase information is usually difficult to directly record. Signal phase retrieval and reconstruction can solve the problem of reconstructing the original signal from a measurement signal containing only amplitude information, so as to reconstruct the signal required by the application. Signal phase retrieval is mathematically modeled as a non-convex inverse problem, which contains many local minima and ambiguities such as global phase shifts, resulting in signal reconstruction failure. Since Fourier phase retrieval cannot theoretically guarantee the stability of reconstruction without additional constraints, the phenomenon of signal reconstruction failure is particularly obvious in Fourier phase retrieval.

[0003] In response to the above technical requirements, some researchers have proposed solutions. A class of traditional methods represented by the Wirtinger flow method proposed by Candes et al. in the paper "Phase Retrieval via Wirtinger Flow: Theory and Algorithms" in the IEEE Transactions on Information Theory journal in 2015 is simple to implement, but its performance degrades significantly in high-noise and low-sampling-rate scenarios. Prior information plays a great role in the signal reconstruction problem and can effectively improve the signal reconstruction quality. Researchers have introduced prior information such as sparsity, low rank, and denoising prior into the optimization problem of signal phase retrieval and reconstruction, and established an optimization problem with regular constraints, thereby not only realizing signal reconstruction, but also effectively reducing the sampling rate required for accurate reconstruction and improving the reconstruction quality. For example, Metlzer et al. disclosed a signal reconstruction method based on denoising prior in the paper "prDeep: Robust Phase Retrieval with a Flexible Deep Network" at the International Conference on Machine Learning in 2018. The above prior information can reduce the sampling rate of signal reconstruction and improve the reconstruction accuracy, but the robustness to noise still needs to be further improved. In recent years, with the rapid development and excellent performance of generative models, researchers have begun to explore applying more effective generative prior information to signal reconstruction. Chung et al. in the paper at the International Conference on Learning Representations in 2023

[0004] "Diffusion Posterior Sampling for General Noisy Inverse Problems" discloses a phase retrieval method based on the generative diffusion model. Further, some scholars alleviate the phenomenon of signal reconstruction failure based on the trial-and-error method, that is, conduct multiple repeated experiments, and then select the result that best matches the measured value or the known true signal information. Zhang et al. disclosed a signal reconstruction method based on the trial-and-error method and decoupled sampling in the paper "Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing" at the 2025 IEEE / CVF Conference on Computer Vision and Pattern Recognition. However, the trial-and-error method causes a large waste of time resources, especially in the growing high-resolution and large-scale imaging scenarios, and it is difficult to meet the current demand for reconstructing the original signal from the measured signal containing only amplitude information.

[0005] After retrieval, a Chinese patent with the application number 202211031139.3 discloses a signal reconstruction method. This method combines the solution algorithm of the traditional non-convex optimization problem with the denoising prior, improves the reconstruction performance of the signal in the complex Gaussian random measurement matrix and coded diffraction imaging, can ensure convergence, reduces the necessary number of measured signals, and meets the current requirements for signal phase retrieval and reconstruction. However, it still requires a large amount of time resources. Summary of the Invention

[0006] Aiming at one of the defects in the prior art, the purpose of this application is to provide an anti-error signal reconstruction method and system based on the diffusion model.

[0007] In the first aspect of this application, an anti-error signal reconstruction method based on the diffusion model is provided, including:

[0008] Obtain the original signal and the measurement matrix, multiply them and take the modulus to obtain the measured signal containing only amplitude information;

[0009] Establish a diffusion model, and its functional feature is the diffusion prior of the original signal;

[0010] Based on the reverse diffusion of the diffusion model, the data consistency of the measured signal, and the decoupled sampling step, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstructed signal, and the estimated measured signal;

[0011] A signal reconstruction error detector is established to determine whether the initial reconstructed signal is successfully reconstructed based on the signal to be detected. Iterations and judgments are repeated a preset number of times to obtain an initial reconstructed signal that successfully reconstructs the original signal or the estimated measurement signal that best matches it, which serves as the intermediate reconstructed signal;

[0012] Based on the intermediate reconstructed signal, through the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step, the reconstructed signal is iteratively solved.

[0013] Optionally, the obtaining of the original signal and the measurement matrix, multiplying them and taking the modulus to obtain the measurement signal containing only amplitude information includes:

[0014] Obtain the original signal;

[0015] Determine that the measurement matrix is a random matrix, and each element of it is a randomly generated real number or complex number;

[0016] Multiply the original signal by the measurement matrix to obtain a measurement value;

[0017] Take the modulus of each element of the measurement value to obtain the measurement signal;

[0018] Or,

[0019] Obtain the original signal;

[0020] Determine that the measurement matrix is the product of a Fourier transform matrix and an oversampling matrix;

[0021] Multiply the oversampling matrix by the original signal and pad zeros around the original signal to obtain a padded signal;

[0022] Multiply the Fourier transform matrix by the padded signal to obtain a measurement value;

[0023] Take the modulus of each element of the measurement value to obtain the measurement signal.

[0024] Optionally, the establishing of the diffusion model includes:

[0025] Obtain a set of reference signals;

[0026] For any reference signal in the set of reference signals, add a set of increasing and time-differentiable noise intensities to obtain the noise signal corresponding to the reference signal;

[0027] Use the reference signal and the noise signal as a training sample pair to establish a training data set;

[0028] Build a U-Net deep neural network model;

[0029] For each pair of training sample pairs in the training dataset, use the noise signal and its noise intensity as the input of the U-Net deep neural network model, and the reference signal as the target output of the U-Net deep neural network model. Use the backpropagation algorithm to optimize the U-Net deep neural network model to obtain a predicted signal and make the predicted signal approximate the reference signal;

[0030] Train until convergence to obtain a trained neural network. Based on the trained U-Net deep neural network model, obtain the score function of the diffusion model.

[0031] Optionally, building the U-Net deep neural network model includes:

[0032] Construct an encoder, including an initial layer and multiple first intermediate layers connected in series. The initial layer includes a convolutional layer, and the first intermediate layer includes several residual blocks with time embedding blocks, attention blocks with time embedding blocks, and downsampling residual blocks with time embedding blocks;

[0033] Construct a decoder, including multiple second intermediate layers connected in series. The second intermediate layer includes several residual blocks with time embedding blocks, attention blocks with time embedding blocks, and upsampling residual blocks with time embedding blocks;

[0034] Construct an intermediate module to connect the encoder and the decoder. The intermediate module includes a first residual block with time embedding block, an attention block with time embedding block, and a second residual block with time embedding block connected in series. The first residual block with time embedding block is connected to the residual block with time embedding block or the attention block with time embedding block of the encoder, and the second attention block is connected to the residual block with time embedding block of the decoder.

[0035] Construct an output layer, which includes a convolutional layer, a non-linear activation layer, and a normalization layer. The attention block of the decoder is connected to the output layer.

[0036] Optionally, based on the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstruction signal, and the estimated measurement signal, including:

[0037] For any t = 0,..., T f -1, T f where T is the preset number of iterations. In the (t + 1)-th iteration:

[0038] The specific reverse diffusion step based on the diffusion model is: using the output x of the t-th iteration tis the initial value. Using the score function of the diffusion model, the output of the (t + 1)-th iteration of the reverse diffusion step is obtained based on the Euler method or the second-order Heun method;

[0039] The data consistency step based on the measurement signal is specifically as follows:

[0040] Establish a loss function for data consistency:

[0041] Taking the output of the (t + 1)-th iteration of the reverse diffusion step as the initial solution, perform T I steps of gradient descent to obtain the output of the data consistency step at the (t + 1)-th iteration;

[0042] The output of the decoupled sampling step is sampled from a normal distribution, the mean of the normal distribution is the output of the data consistency step, and the variance of the normal distribution is a constant related to time t multiplied by the identity matrix;

[0043] T f After T iterations, take the output of the reverse diffusion step of the diffusion model as the signal to be detected, take the output of the decoupled sampling step as the initial reconstruction signal, and take the output of the data consistency step of the measurement signal as the estimated measurement signal.

[0044] Optionally, the establishment of the signal reconstruction error detector includes:

[0045] Adopt a pre-trained network as a feature extractor;

[0046] Input the features extracted by the feature extractor into a linear classifier to form the signal reconstruction error detector;

[0047] Train the signal reconstruction error detector using any training dataset designed for the diffusion model, or construct a training dataset for the signal reconstruction task, distinguish positive samples and negative samples in the training dataset based on contrastive learning, and train to obtain a signal reconstruction error detector for the signal reconstruction task.

[0048] Optionally, judging whether the initial reconstruction signal is successfully reconstructed based on the signal to be detected, repeating the iteration and judgment for a preset number of times, and obtaining an initial reconstruction signal that successfully reconstructs the original signal or the most matching estimated measurement signal as the intermediate reconstruction signal, includes:

[0049] Input the signal to be detected into the signal reconstruction error detector to judge whether it is a real signal. If the signal to be detected is a real signal, the reconstruction is successful; otherwise, the reconstruction fails;

[0050] If the reconstruction is successful, output the initial reconstruction signal as the intermediate reconstruction signal;

[0051] If the maximum number of repetitions is not reached and the reconstruction fails, record the initial reconstruction signal and the estimated measurement signal, return to the iterative solution process, and repeat the judgment;

[0052] If the maximum number of repetitions is reached and the reconstruction fails, select the estimated measurement signal that best matches the measurement signal from the recorded estimated measurement signals, sample the corresponding initial reconstruction signal from the corresponding normal distribution, and output it as the intermediate reconstruction signal.

[0053] Optionally, based on the intermediate reconstruction signal, the reconstruction signal is obtained by iteratively solving the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling steps, including:

[0054] Using the intermediate reconstruction signal as the initial value, perform T - T f iterations, where T is the number of iterations during the training of the diffusion model. Each iteration is performed in sequence as follows:

[0055] For any t = 0,..., T - T f - 1, in the (t + 1)-th iteration:

[0056] The specific step of the reverse diffusion based on the diffusion model is: using the output of the t-th iteration as the initial value, and based on the score function of the diffusion model, obtaining the output of the reverse diffusion step of the (t + 1)-th iteration based on the Euler method or the second-order Heun method;

[0057] The specific step of the data consistency based on the measurement signal is:

[0058] Establish a loss function for data consistency:

[0059] Using the output of the reverse diffusion step of the (t + 1)-th iteration as the initial solution, perform T I gradient descent steps based on the loss function to obtain the output of the data consistency step at the (t + 1)-th iteration;

[0060] The output of the decoupled sampling step is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step;

[0061] After T - T f iterations, take the output of the combined decoupled sampling step as the reconstruction signal.

[0062] Optionally, the output of the decoupled sampling step is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step, including:

[0063] Sample z from the normal distribution where I is the identity matrix;

[0064] Based on variance σ t+1 and σ t Combine z, the output of the reverse diffusion step and the output of the data consistency step to obtain the output x of the decoupled sampling step t+1 , and the specific formula is:

[0065]

[0066] where λ is a constant.

[0067] In the second aspect of the present application, a signal reconstruction system for anti-error based on a diffusion model is provided, including:

[0068] Measurement signal acquisition module: Acquire the original signal and the measurement matrix, multiply them and take the modulus to obtain a measurement signal containing only amplitude information;

[0069] Diffusion model construction module: Establish a diffusion model, and its functional feature is the diffusion prior of the original signal;

[0070] Signal preliminary reconstruction module: Based on the reverse diffusion of the diffusion model, the data consistency of the measurement signal and the decoupled sampling step, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstructed signal and the estimated measurement signal;

[0071] Signal reconstruction error detection module: Establish a signal reconstruction error detector, based on the signal to be detected, judge whether the initial reconstructed signal is successfully reconstructed, repeat the iteration and judgment for a preset number of times, and obtain the initial reconstructed signal that successfully reconstructs the original signal or the most matching estimated measurement signal as the intermediate reconstructed signal;

[0072] Signal enhancement reconstruction module: Based on the intermediate reconstructed signal, through the reverse diffusion of the diffusion model, the data consistency of the measurement signal and the decoupled sampling step, iteratively solve to obtain the reconstructed signal.

[0073] The signal reconstruction method and system for anti-error based on a diffusion model provided by the present application adopt the technical means of combining the data consistency step based on the measurement signal with the diffusion prior and the signal reconstruction error detector, bringing the technical effects of accurately identifying the failed reconstruction in Fourier phase retrieval, improving the reconstruction performance of the signal in Fourier phase retrieval, reducing the necessary number of repeated experiments, and meeting the current requirements for signal phase retrieval and reconstruction.

[0074] Other technical effects brought by the additional features will be further elaborated in the corresponding embodiments. Brief Description of the Drawings

[0075] Other features, objects, and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments read in conjunction with the accompanying drawings:

[0076] Figure 1 It is a flowchart of an anti-error signal reconstruction method based on a diffusion model shown according to an exemplary embodiment;

[0077] Figure 2 It is a framework diagram of an anti-error signal reconstruction system based on a diffusion model shown according to an exemplary embodiment. Detailed Embodiments

[0078] The present application will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can be made, and these all belong to the protection scope of the present application. The parts not described in detail in the following embodiments can be implemented using the prior art.

[0079] The phenomenon of signal reconstruction failure is alleviated by the trial-and-error method, and it takes multiple repeated experiments to select the result that best matches the measured value or known true signal information, which leads to a waste of a large amount of time resources. Especially in the growing high-resolution and large-scale imaging scenarios, it is difficult to meet the current demand for reconstructing the original signal from the measured signal containing only amplitude information. Based on the above problems, the embodiments of the present application provide an anti-error signal reconstruction method based on a diffusion model to solve the above existing problems.

[0080] Referring to Figure 1 As shown, in an embodiment of the present application, an anti-error signal reconstruction method based on a diffusion model includes the following steps:

[0081] S100. Obtain the original signal and the measurement matrix, multiply them and take the modulus to obtain a measured signal containing only amplitude information;

[0082] S200. Establish a diffusion model and use its functional characteristics as the diffusion prior information of the original signal;

[0083] S300. Based on the reverse diffusion step, data consistency step, and decoupled sampling step of the diffusion model, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstructed signal, and the estimated measured signal;

[0084] S400. Establish a signal reconstruction error detector, determine whether the initial reconstructed signal is successfully reconstructed based on the signal to be detected, and repeat S300 - S400 for a preset number of times to obtain the initial reconstructed signal that successfully reconstructs the original signal or the most matching estimated measured signal as the intermediate reconstructed signal;

[0085] The S500 iteratively solves and enhances the reconstruction signal based on the intermediate reconstruction signal through the reverse diffusion step of the diffusion model, the data consistency step of the measurement signal, and the combined decoupling sampling step.

[0086] Specifically, the functional feature of the diffusion model refers to the fact that the diffusion model can generate a signal that conforms to the distribution of the original signal data. This signal, as the diffusion prior information of the original signal, can achieve higher reconstruction accuracy.

[0087] A signal reconstruction error detector is introduced to determine whether the original signal is successfully reconstructed, thereby reducing the necessary number of repeated experiments while ensuring the reconstruction accuracy and greatly reducing resource consumption.

[0088] Specifically, generally, sampling from a Gaussian distribution with a mean of 0 and a variance of the identity matrix is used as the initial value in S300.

[0089] The above embodiments of the present application are used to reconstruct the original signal from a measurement signal containing only amplitude information. By introducing a diffusion model in the solution step, it can improve the reconstruction accuracy of the algorithm while ensuring the convergence of the algorithm compared to an algorithm containing only the gradient descent step; by introducing a signal reconstruction error detector in the solution step, it can accurately identify the reconstruction failure phenomenon in Fourier phase retrieval. Compared with the signal phase retrieval method based on the trial-and-error method, it ensures the reconstruction accuracy while reducing the necessary number of repeated experiments and greatly reducing resource consumption.

[0090] In order to obtain the measurement signal from the original signal, in some specific embodiments of the present application, for S100, the original signal and the measurement matrix are obtained, multiplied and then the modulus is taken to obtain a measurement signal containing only amplitude information. The following steps can be adopted:

[0091] S101, obtain the original signal;

[0092] S102, confirm that the measurement matrix is a random measurement matrix;

[0093] S103, obtain the original signal Multiply the original signal by the measurement matrix A to obtain a measurement value, where each element of the measurement matrix can be a randomly generated real number or complex number;

[0094] S104, take the modulus of each element of the measurement value to obtain the measurement signal

[0095] Similarly, in order to obtain the measurement signal from the original signal, in some other specific embodiments of the present application, for S100, the original signal and the measurement matrix are obtained, multiplied and then the modulus is taken to obtain a measurement signal containing only amplitude information. The following steps can be adopted:

[0096] S1001, Obtain the original signal;

[0097] S1002, Determine that the measurement matrix is the product of the Fourier transform matrix and the oversampling matrix;

[0098] S1003, Multiply the original signal by the oversampling matrix P mn The oversampling matrix is a zero-padding matrix, which is used to pad 0 around the original signal to obtain a padded signal Multiply the two-dimensional Fourier transform matrix F by the padded signal to obtain the measurement value;

[0099] S1004, Take the modulus of each element of the measurement value as the measurement signal where c is the number of channels of the original signal, n is the dimension of the original signal, and m is the dimension of the padded signal.

[0100] In the above embodiments of the present application, the process of obtaining the measurement signal can be applied to the actual coded diffraction imaging process, solve the problem of error reconstruction in actual imaging, and bring application value to actual imaging.

[0101] In order to ensure the algorithm convergence and improve the reconstruction accuracy of the algorithm, in some specific embodiments of the present application, a diffusion model is introduced. For S200, to establish a diffusion model, the following steps can be adopted:

[0102] S201, Obtain a set of reference signals. For any reference signal in the set of reference signals, add Gaussian noise with a noise intensity of σ t , t = T,..., 0, where σ t , t = T,..., 0 is an increasing and differentiable noise addition mechanism with respect to time t, obtain the noise signal corresponding to the reference signal, and use the reference signal and the noise signal as a training sample pair to establish a training data set. Signals belonging to the same distribution as the original signal belong to the reference signals.

[0103] S202, Build a U-Net deep neural network model using convolutional layers, non-linear activation layers, self-attention layers, cross-layer connection layers, etc.

[0104] Specifically, the U-Net deep neural network consists of an encoder, an intermediate module, a decoder, and an output layer. The encoder has a convolutional layer as the initial layer, followed by multiple first intermediate layers connected in series. Each first intermediate layer contains a residual block, an attention block, and a downsampling residual block that introduce a temporal embedding block. The decoder includes multiple second intermediate layers connected in series. Each second intermediate layer contains a residual block, an attention block, and an upsampling residual block that introduce a temporal embedding block. The encoder and the decoder are connected by an intermediate module containing a first residual block, an attention block, and a second residual block that introduce a temporal embedding block. The first residual block is connected to the attention block or the residual block of the encoder, and the second residual block is connected to the residual block of the decoder. The attention block of the decoder is connected to the output layer.

[0105] S203. For each pair of reference signal and noise signal in the training dataset, use the noise signal and the noise intensity as the input of the neural network, and the reference signal as the target output of the neural network. Optimize the neural network using the backpropagation algorithm to obtain a predicted signal and make the predicted signal approximate the reference signal. Note that the predicted signal is the output of the neural network.

[0106] S204. Train until convergence to obtain the trained neural network D(·,σ t ), and obtain the score function of the diffusion model based on the trained neural network σ t is a constant related to t.

[0107] In the above embodiments of the present application, the trained neural network as the score function of the diffusion model can learn the prior information in a large amount of data. Compared with traditional signal reconstruction methods and systems, the signal reconstruction quality is effectively improved. For different measurement settings, only need to train the neural network once, reducing the resource consumption of training the network multiple times.

[0108] To ensure the reconstruction accuracy, in some specific embodiments of the present application, for S300, based on the reverse diffusion step of the diffusion model, the data consistency step based on the measurement signal, and the decoupled sampling step, starting from the initial value, the signal to be detected, the initial reconstructed signal, and the estimated measurement signal can be obtained iteratively by the following steps:

[0109] S301. For any t = 0,..., T f -1, T f is the preset number of iterations. In the (t + 1)-th iteration, the reverse diffusion step based on the diffusion model is specifically: taking x t as the initial value, using the score function of the diffusion model, and obtaining the output of the reverse diffusion step of the (t + 1)-th iteration based on the Euler method or the second-order Heun method

[0110] In S302, the data consistency step based on the measurement signal is specifically as follows:

[0111] Establish a loss function for data consistency:

[0112]

[0113] where σ t is a constant related to t, β y is a constant, y is the measurement signal, F is a two-dimensional Fourier transform matrix, and P mn is an oversampling matrix;

[0114] Using the output of the (t + 1)-th iteration of the reverse diffusion step as the initial solution, perform T I steps of gradient descent to obtain the output of the data consistency step at the (t + 1)-th iteration where the output of the j-th gradient descent step is

[0115]

[0116] where η t is the step size of gradient descent;

[0117] In S303, the output x of the decoupled sampling step t+1 is sampled from a normal distribution where I is the identity matrix.

[0118] In S304, after T f iterations, the output of the reverse diffusion step of the diffusion model is used as the signal to be detected, the output of the decoupled sampling step is used as the initial reconstruction signal, and the output of the data consistency step of the measurement signal is used as the estimated measurement signal.

[0119] In the above embodiments of the present application, the data consistency loss function and the gradient descent step in the data consistency step of the measurement signal are established based on strict optimization theory. Compared with the end-to-end signal reconstruction method and system, it can explain the signal reconstruction method and system from the perspective of optimization, improving the interpretability of the method in practical applications.

[0120] In order to accurately identify the reconstruction failure phenomenon in Fourier phase retrieval, in some specific embodiments of the present application, a signal reconstruction error detector is introduced. In some specific embodiments of the present application, the following steps can be adopted to establish a signal reconstruction error detector:

[0121] Use a pre-trained network as a feature extractor, and input the features extracted by the feature extractor into a linear classifier to form a signal reconstruction error detector. Specifically, the pre-trained network can adopt the CLIP pre-trained network, where the visual end is based on the Vision Transformer (ViT). Exemplarily, the pre-trained network adopts CLIP:ViT-L / 14.

[0122] Train the signal reconstruction error detector using any training dataset designed for the diffusion model, or construct a training dataset for the signal reconstruction task, distinguish positive and negative samples in the training dataset based on contrastive learning, and train to obtain a signal reconstruction error detector for the signal reconstruction task.

[0123] In the above embodiments of the present application, the signal reconstruction error detector can effectively detect the failure phenomenon in the signal reconstruction process, and effectively improve the robustness of the signal reconstruction method and system in actual signal reconstruction applications.

[0124] In order to be able to further accurately identify the reconstruction failure phenomenon in Fourier phase retrieval, in some specific embodiments of the present application, for S400, for determining whether the initial reconstructed signal is a successful reconstruction of the original signal, repeat S300 - S400 a preset number of times to obtain an initial reconstructed signal that successfully reconstructs the original signal or best matches the measured signal, as the intermediate reconstructed signal, the following steps can be adopted:

[0125] S401, input the signal to be detected into the signal reconstruction error detector, and judge whether it is a real signal. If it is a real signal, the reconstruction is successful; otherwise, the reconstruction fails.

[0126] S402, if the reconstruction is successful, output the initial reconstructed signal as the intermediate reconstructed signal.

[0127] S403, if the maximum number of repetitions is not reached and the reconstruction fails, record the initial reconstructed signal and the estimated measured signal, execute step S300, and repeat the above S401 - S402.

[0128] S404, if the maximum number of repetitions is reached and the reconstruction fails, select the estimated measured signal that best matches the measured signal from the recorded estimated measured signals sample the initial reconstructed signal from the normal distribution and output it as the intermediate reconstructed signal.

[0129] ​Specifically, multiply the estimated measurement signal by the measurement matrix and take the modulus to obtain the estimated measurement value, and take the square of the two-norm of the difference between the estimated measurement value and the measurement signal. The one with the smallest result is the estimated measurement signal that best matches the measurement signal.

[0130] In the above embodiments of the present application, by introducing a signal reconstruction error detector, compared with the existing diffusion prior-based method, while ensuring the reconstruction accuracy, the necessary number of repeated experiments is reduced, and the resource consumption is greatly reduced.

[0131] In order to obtain a more accurate reconstructed signal, in some specific embodiments of the present application, for S500, based on the intermediate reconstructed signal, the reconstructed signal is iteratively solved and enhanced by the reverse diffusion step of the diffusion model, the data consistency step of the measurement signal, and the combined decoupled sampling step, which can be carried out by the following steps:

[0132] S501, using the intermediate reconstructed signal as the initial value, perform T - T f iterations. T is the number of iterations during the training of the diffusion model. Each iteration is sequentially performed as follows:

[0133] For any t = 0,..., T - T f - 1, in the (t + 1)-th iteration, based on the reverse diffusion step of the diffusion model, specifically: using x t as the initial value, and using the score function of the diffusion model, obtain the output of the reverse diffusion step of the (t + 1)-th iteration based on the Euler method or the second-order Heun method

[0134] Specifically, introducing the diffusion model in this step can improve the reconstruction accuracy compared with the traditional signal reconstruction method, and there is no need to repeatedly train the network for different experimental settings compared with the standard end-to-end neural network training method.

[0135] S502, the data consistency step based on the measurement signal is specifically as follows:

[0136] Establish a data consistency loss function:

[0137]

[0138] where σ t is a constant related to t, β y is a constant, y is the measurement signal, F is the two-dimensional Fourier transform matrix, and P mn is the oversampling matrix;

[0139] using the output of the reverse diffusion step of the (t + 1)-th iteration as the initial solution, perform T I gradient descent steps to obtain the output of the data consistency step at the (t + 1)-th iteration The output of the j-th gradient descent step is

[0140]

[0141] where η t is the step size of the gradient descent;

[0142] S503. The output x of the decoupled sampling step t+1 is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step ; Specifically, this step introduces a combined decoupled sampling step, which effectively improves the reconstruction accuracy compared with the existing signal Fourier phase retrieval method based on decoupled sampling in diffusion models.

[0143] Specifically, this step introduces a combined decoupled sampling step, which effectively improves the reconstruction accuracy compared with the existing signal Fourier phase retrieval method based on decoupled sampling in diffusion models.

[0144] S504. After T - T f iterations, the output x of the combined decoupled sampling step T is used as the reconstructed signal.

[0145] In the above embodiments of the present application, the data consistency loss function and the gradient descent step in the data consistency step of the measurement signal are established based on strict optimization theory. Compared with the end-to-end signal reconstruction method and system, the signal reconstruction method and system can be explained from the perspective of optimization. The decoupled sampling step effectively improves the reconstruction accuracy compared with the existing signal Fourier phase retrieval method based on decoupled sampling in diffusion models.

[0146] Furthermore, in some specific embodiments of the present application, for the above S503, the output x of the decoupled sampling step t+1 is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step , and the specific operation is as follows:

[0147] S5031. Sample z from the normal distribution , where I is the identity matrix;

[0148] S5032. Combine z, the output of the reverse diffusion step t+1 and σ t and the output of the data consistency step to obtain the output x of the combined decoupled sampling step t+1 , and the specific formula is:

[0149]

[0150]

[0151] where λ is a constant.

[0151] In the above embodiments of the present application, compared with the existing signal Fourier phase retrieval method based on decoupled sampling of the diffusion model, the combined decoupled sampling step effectively improves the reconstruction accuracy.

[0152] Based on the same technical concept, in some other embodiments of the present application, such as Figure 2 shown, a diffusion model-based anti-error signal reconstruction system is provided, including:

[0153] Measurement signal acquisition module: Acquire the original signal and the measurement matrix, multiply them and take the modulus to obtain a measurement signal containing only amplitude information;

[0154] Diffusion model construction module: Establish a diffusion model and use its functional characteristics as diffusion prior information;

[0155] Signal preliminary reconstruction module: Based on the reverse diffusion step of the diffusion model, the data consistency step based on the measurement signal, and the decoupled sampling step, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstructed signal, and the estimated measurement signal;

[0156] Signal reconstruction error detection module: Establish a signal reconstruction error detector to determine whether the initial reconstructed signal is a successful reconstruction of the original signal. Through multiple repeated iterations and judgments, obtain the initial reconstructed signal that successfully reconstructs the original signal or best matches the measurement signal as the intermediate reconstructed signal;

[0157] Signal enhancement reconstruction module: Based on the intermediate reconstructed signal, use the reverse diffusion step of the diffusion model, the data consistency step of the measurement signal, and the combined decoupled sampling step to iteratively solve and enhance to obtain the reconstructed signal.

[0158] In the above embodiments of the present application, the specific implementation techniques of each module / unit can refer to the corresponding steps of the diffusion model-based anti-error signal reconstruction method in the above embodiments, which will not be elaborated here.

[0159] Each of the above-mentioned preferred features in the embodiments can be used alone in any one of the embodiments, and can also be used in any combination on the premise of not conflicting with each other. In addition, the parts not described in detail in the embodiments can be implemented using existing technologies.

[0160] The following will further illustrate the present application in combination with specific application examples / comparative examples to better understand the above technical solutions of the present application. It should be understood that the following are only partial examples and are not used to limit the present application.

[0161] In this specific embodiment, the diffusion model-based anti-error signal reconstruction method mainly adopts the following 6 main steps:

[0162] Step 1, a raw signal with a dimension of (3, 256, 256) Multiply with the oversampling matrix P mn The oversampling matrix P mn Pad zeros around the second and third dimensions of the original signal to obtain a signal with dimensions (3, 512, 512) Multiply the two-dimensional Fourier transform matrix F with to obtain the measurement values, and take the modulus of each element of the measurement values as the measurement signal

[0163] Step 2: Construct a training dataset, build a neural network, and use the training dataset to train the neural network as the score function of the diffusion model. In this embodiment, the diffusion model adopts the network structure U-net, training method, and training dataset Flickr-Faces-HQ (FFHQ) used in "Diffusion Posterior Sampling for General Noisy Inverse Problems" published at the International Conference on Learning Representations (ICLR) in 2023. The noise intensity where σ max = 100, σ min = 0.1, T = 200, p = 7.

[0164] Step 3: Starting from the initial solution perform T f = 150 iterations. Each iteration sequentially performs: the reverse diffusion step based on the diffusion model, the data consistency step based on the measurement signal, and the decoupled sampling step to obtain the initial reconstructed signal

[0165] Step 4: The signal reconstruction error detector in this embodiment adopts the signal reconstruction error detector proposed in "Towards Universal Fake Image Detectors that Generalize Across Generative Models" published at the Conference on Computer Vision and Pattern Recognition (CVPR) in 2023. Set the hyperparameter - fake image threshold in the signal reconstruction error detector to γ = 0.3.

[0166] Input the signal f to be detected after T iterations into the signal reconstruction error detector to determine whether it is a real signal. If If it is a real signal, the reconstruction is successful; otherwise, the reconstruction fails.

[0167] If the reconstruction is successful, output the initial reconstructed signal as the intermediate reconstructed signal;

[0168] If the maximum number of repetitions is not reached and the reconstruction fails, record the initial reconstructed signal and the estimated measurement signal, execute step 3, and repeat the above steps;

[0169] If the maximum number of repetitions is reached and the reconstruction fails, select the estimated measurement signal that best matches the measurement signal from the recorded estimated measurement signals from the normal distribution to sample the initial reconstructed signal as the intermediate reconstructed signal output.

[0170] Step 5, starting from the intermediate reconstructed signal perform T - T f = 50 iterations. In each iteration, sequentially execute the reverse diffusion step based on the diffusion model, the data consistency step based on the measurement signal, and the combined decoupling sampling step, and iteratively solve and enhance to obtain the reconstructed signal x T .

[0171] In step 3, the reverse diffusion step based on the diffusion model is specifically: with x t as the initial value, use the score function of the diffusion model, that is to solve the probability flow constant differential equation based on the Euler method to obtain the output of the (t + 1)-th iteration reverse diffusion step where is the reciprocal of the time of σ t , and the discrete sampling time step of the probability flow constant differential equation is set to where N ODE = 5, p = 7, t min = 0.02, t = σ t .

[0172] In step 3, the data consistency step based on the measurement signal is specifically: establish a data consistency loss function: where is the output of the (t + 1)-th iteration reverse diffusion step, σ t is a constant related to t, β y = 0.01, y is the measurement signal, F is the two-dimensional Fourier transform matrix, P mn is the oversampling matrix. With the output of the (t + 1)-th iteration reverse diffusion step as the initial solution, execute T I= The output of the data consistency step at the (t + 1)-th iteration obtained by 100-step gradient descent where the output of the j-th gradient descent step is η t = 5e-5×[1 + (0.01 - 1)t / T] is the step size of gradient descent.

[0173] In step 3, the output x of the decoupled sampling step at the (t + 1)-th iteration t+1 is sampled from the normal distribution where I is the identity matrix.

[0174] In step 5, the reverse diffusion step based on the diffusion model is specifically: with x t as the initial value, using the score function of the diffusion model, that is solving the probability flow constant differential equation based on the Euler method or the second-order Heun method to obtain the output of the reverse diffusion step at the (t + 1)-th iteration where is the reciprocal of time of σ t and the discrete sampling time step of the probability flow constant differential equation is set to where N ODE = 5, p = 7, t min = 0.02, t = σ t .

[0175] In step 5, the data consistency step based on the measurement signal is specifically: establishing the loss function of data consistency: where is the output of the reverse diffusion step at the (t + 1)-th iteration, σ t is a constant related to t, β y = 0.01, y is the measurement signal, F is the two-dimensional Fourier transform matrix, P mn is the oversampling matrix. With the output of the reverse diffusion step at the (t + 1)-th iteration as the initial solution, perform T I = 100-step gradient descent to obtain the output of the data consistency step at the (t + 1)-th iteration where the output of the j-th gradient descent step is η t = 5e-5×[1 + (0.01 - 1)t / T] is the step size of gradient descent.

[0176] In step 5, the output of the combined decoupled sampling step at the (t + 1)-th iteration is where z is sampled from the normal distribution and I is the identity matrix. If the output of the subsequent reverse diffusion step is a real image, λ = 0.25, otherwise, λ = 1, is the output of the reverse diffusion step at the (t + 1)-th iteration, is the output of the data consistency step at the (t + 1)-th iteration.

[0177] In this specific application example, 100 natural images with dimensions of (3, 256, 256) are taken as test signals to implement the anti-error signal reconstruction method based on the diffusion model in the above implementation manner, and compared with the Wirtinger flow method proposed in "Phase Retrieval via Wirtinger Flow: Theory and Algorithms" published in the IEEE Transactions on Information Theory journal in 2015, and that in "DiffFPR: Diffusion prior for oversampled Fourier phase retrieval" published in the International Conference on Machine Learning (ICML) in 2024. The evaluation criteria include: peak signal-to-noise ratio (PSNR), in dB, the higher the value, the better; structural similarity (SSIM), the higher the value, the better; learned perceptual image patch similarity (LPIPS), the lower the value, the better; repeated experiment ratio (Re-Ratio), defined as the ratio of the average number of repeated experiments to the maximum average number of experiments, the lower the value, the better.

[0178] The experimental results in Table 1 show that the signal Fourier phase retrieval result obtained by the implementation manner of this application is significantly 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, so its performance is limited. The number of repeated experiments required for the signal Fourier phase retrieval method obtained by the system in this embodiment is significantly lower than that of the signal phase retrieval method DiffFPR based on the diffusion model. Since DiffFPR does not contain a signal reconstruction error detector and cannot accurately identify whether the signal reconstruction is successful, a higher number of repeated experiments is required.

[0179] Table 1: Comparison of peak signal-to-noise ratio, structural similarity, learned perceptual image patch similarity, and repeated experiment ratio of Wirtinger flow (WF), DiffFPR, and the method proposed in this application in signal Fourier phase retrieval

[0180] Metrics PSNR SSIM LPIPS Re-Ratio WF 12.64 0.2238 0.8054 100％ DiffFPR 30.56 0.7255 0.2625 100％ Proposed 33.32 0.9049 0.1021 39.06％

[0181] The signal reconstruction method and system provided by this application, compared with the existing phase retrieval method based on diffusion models, maintain a high reconstruction accuracy while greatly reducing the necessary number of repeated experiments; compared with traditional phase retrieval algorithms, improve the operation speed and reconstruction accuracy; compared with the phase retrieval of end-to-end deep neural networks, ensure the reconstruction accuracy while not requiring repeated training of the network for different experimental settings; this reconstruction method can be applied to the solution of general non-convex linear inverse problems and can also be applied to specific scenarios, such as Gaussian phase retrieval of signals, image reconstruction of coded diffraction imaging, and Fourier phase retrieval of images, etc.

[0182] The signal reconstruction method and system provided by this application have broad industrial application prospects. The signal reconstruction method provided by this application solves the problem of reconstructing phase information from measurement signals that only contain amplitude information and can be applied to optical imaging scenarios such as far-field imaging where only amplitude information can be obtained. In addition, the measured values obtained in scenarios such as biomedical imaging, quantum information, astronomical imaging, and computational holography usually only contain amplitude information. Therefore, the signal reconstruction method provided by this application also has very important application values in scenarios such as biomedical imaging, quantum information, astronomical imaging, and computational holography.

[0183] The specific embodiments of this application have been described above. It should be understood that this application is not limited to the above specific implementation manners, and those skilled in the art can make various deformations or modifications within the scope of the claims, which do not affect the essence of this application.

Claims

1. A method for reconstructing an error-resistant signal based on a diffusion model, characterized in that, Including: Obtain the original signal and the measurement matrix, multiply them and take the modulus to obtain a measurement signal containing only amplitude information; Establish a diffusion model, the functional characteristic of which is the diffusion prior of the original signal; Based on the reverse diffusion of the diffusion model, the data consistency of the measurement signal and the decoupled sampling step, starting from the initial value, iteratively obtain the signal to be detected, the initial reconstructed signal and the estimated measurement signal; Establish a signal reconstruction error detector, and based on the signal to be detected, judge whether the initial reconstructed signal is successfully reconstructed. Repeat the iteration and judgment for a preset number of times to obtain the initial reconstructed signal that successfully reconstructs the original signal or the estimated measurement signal that best matches it as the intermediate reconstructed signal; Based on the intermediate reconstructed signal, through the reverse diffusion of the diffusion model, the data consistency of the measurement signal and the decoupled sampling step, iteratively solve to obtain the reconstructed signal.

2. The anti-error signal reconstruction method based on a diffusion model according to claim 1, wherein The obtaining of the original signal and the measurement matrix, multiplying them and taking the modulus to obtain a measurement signal containing only amplitude information includes: Obtain the original signal; Determine that the measurement matrix is a random matrix, and each element of it is a randomly generated real number or complex number; Multiply the original signal and the measurement matrix to obtain a measurement value; Take the modulus of each element of the measurement value to obtain the measurement signal; Or, Obtain the original signal; Determine that the measurement matrix is the product of a Fourier transform matrix and an oversampling matrix; Multiply the oversampling matrix and the original signal, and pad zeros around the original signal to obtain a padded signal; Multiply the Fourier transform matrix and the padded signal to obtain a measurement value; Take the modulus of each element of the measurement value to obtain the measurement signal.

3. The anti-error signal reconstruction method based on a diffusion model according to claim 1, wherein The establishing of the diffusion model includes: Obtain a set of reference signals; For any reference signal in the set of reference signals, add a set of increasing and time-differentiable noise intensities to obtain the noise signal corresponding to the reference signal; Use the reference signal and the noise signal as a training sample pair to establish a training data set; Build a U-Net deep neural network model; For each pair of training sample pairs in the training data set, use the noise signal and its noise intensity as the input of the U-Net deep neural network model, and the reference signal as the target output of the U-Net deep neural network model. Use the backpropagation algorithm to optimize the U-Net deep neural network model to obtain a predicted signal and make the predicted signal approximate the reference signal; Train until convergence to obtain the trained neural network, and based on the trained U-Net deep neural network model, obtain the scoring function of the diffusion model.

4. The anti-error signal reconstruction method based on a diffusion model according to claim 3, wherein, The building of the U-Net deep neural network model includes: Construct an encoder, including an initial layer and multiple first intermediate layers connected in series in sequence. The initial layer includes a convolutional layer, and the first intermediate layer includes several residual blocks introducing time embeddings, attention blocks introducing time embeddings, and downsampling residual blocks introducing time embeddings; Construct a decoder, including multiple second intermediate layers connected in series in sequence. The second intermediate layer includes several residual blocks introducing time embeddings, attention blocks introducing time embeddings, and upsampling residual blocks introducing time embeddings; Construct an intermediate module to connect the encoder and the decoder. The intermediate module includes a first residual block introducing a time embedding block, an attention block introducing a time embedding block, and a second residual block introducing a time embedding block, which are connected in series in sequence. The first residual block of the introducing time embedding block is connected to the residual block or the attention block of the introducing time embedding block of the encoder, and the second attention block is connected to the residual block of the introducing time embedding block of the decoder. Construct an output layer. The output layer includes a convolutional layer, a non-linear activation layer, and a normalization layer. The attention block of the introducing time embedding block of the decoder is connected to the output layer.

5. The anti-error signal reconstruction method based on a diffusion model according to claim 1, wherein The reverse diffusion based on the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step, starting from an initial value, iteratively obtain the signal to be detected, the initial reconstructed signal, and the estimated measurement signal, including: For any t = 0,..., T f -1, T f is the preset number of iterations. In the (t + 1)-th iteration: The specific reverse diffusion step based on the diffusion model is as follows: using the output x of the t-th iteration t as the initial value, and based on the Euler method or the second-order Heun method using the score function of the diffusion model to obtain the output of the reverse diffusion step of the (t + 1)-th iteration; The data consistency step based on the measurement signal is specifically: Establish a loss function for data consistency: Using the output of the reverse diffusion step in the (t + 1)-th iteration as the initial solution, perform T I steps of gradient descent based on the loss function to obtain the output of the data consistency step in the (t + 1)-th iteration; The output of the decoupled sampling step is sampled from a normal distribution. The mean of the normal distribution is the output of the data consistency step, and the variance of the normal distribution is a constant related to time t multiplied by the identity matrix; T f After the T -th iteration, the output of the reverse diffusion step of the diffusion model is used as the signal to be detected, the output of the decoupled sampling step is used as the initial reconstruction signal, and the output of the data consistency step of the measurement signal is used as the estimated measurement signal.

6. The anti-error signal reconstruction method based on a diffusion model according to claim 1, wherein, The establishment of the signal reconstruction error detector includes: Use a pre-trained network as a feature extractor; Input the features extracted by the feature extractor into a linear classifier to form the signal reconstruction error detector; Train the signal reconstruction error detector using any training dataset designed for the diffusion model, or construct a training dataset for the signal reconstruction task, and distinguish positive and negative samples in the training dataset based on contrastive learning to train a signal reconstruction error detector for the signal reconstruction task.

7. The anti-error signal reconstruction method based on a diffusion model according to claim 1, characterized in that, Based on the signal to be detected, determine whether the initial reconstructed signal is successfully reconstructed. Repeat the iteration and judgment for a preset number of times to obtain an initial reconstructed signal that successfully reconstructs the original signal or the most matching estimated measurement signal as the intermediate reconstructed signal, including: Input the signal to be detected into the signal reconstruction error detector to determine whether it is a real signal. If the signal to be detected is a real signal, the reconstruction is successful; otherwise, the reconstruction fails; If the reconstruction is successful, output the initial reconstructed signal as the intermediate reconstructed signal; If the maximum number of repetitions is not reached and the reconstruction fails, record the initial reconstructed signal and the estimated measurement signal, return to the iterative solution process, and repeat the judgment; If the maximum number of repetitions is reached and the reconstruction fails, select the estimated measurement signal that most matches the measurement signal from the recorded estimated measurement signals, and sample the corresponding initial reconstructed signal from the corresponding normal distribution as the intermediate reconstructed signal for output.

8. The anti-error signal reconstruction method based on a diffusion model according to claim 1, characterized in that Based on the intermediate reconstructed signal, the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step are used to iteratively solve for the reconstructed signal, including: Using the intermediate reconstruction signal as the initial value, perform T-T f iterations, where T is the number of iterations during the training of the diffusion model. Each iteration is performed in sequence as follows: For any t = 0,..., T - T f - 1, in the (t + 1)-th iteration: The reverse diffusion step based on the diffusion model is specifically: taking the output of the t-th iteration as the initial value, using the score function of the diffusion model, and obtaining the output of the reverse diffusion step of the (t + 1)-th iteration based on the Euler method or the second-order Heun method; The data consistency step based on the measurement signal is specifically as follows: Establish a loss function for data consistency: Using the output of the reverse diffusion step in the (t + 1)-th iteration as the initial solution, perform T I steps of gradient descent based on the loss function to obtain the output of the data consistency step in the (t + 1)-th iteration; The output of the decoupled sampling step is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step; T-T f After the next iteration, the output of the combined decoupled sampling step is used as the reconstructed signal.

9. The anti-error signal reconstruction method based on a diffusion model according to claim 8, wherein The output of the decoupled sampling step is sampled from a normal distribution based on the output of the reverse diffusion step and the output of the data consistency step, including: Sampling z from a normal distribution where I is the identity matrix; Based on variance σ t+1 and σ t Combine z, the output of the reverse diffusion step and the output of the data consistency step to obtain the output x of the decoupled sampling step t+1 , and the specific formula is: where λ is a constant.

10. An anti-error signal reconstruction system based on a diffusion model, characterized in that, Including: Measurement signal acquisition module: Acquire the original signal and the measurement matrix, multiply them and take the modulus to obtain a measurement signal containing only amplitude information; Diffusion model construction module: Establish a diffusion model, whose functional feature is the diffusion prior of the original signal; Signal preliminary reconstruction module: Based on the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step, starting from an initial value, iteratively obtain the signal to be detected, the initial reconstructed signal, and the estimated measurement signal; Signal reconstruction error detection module: Establish a signal reconstruction error detector, and based on the signal to be detected, judge whether the initial reconstructed signal is successfully reconstructed. Repeat the iteration and judgment for a preset number of times to obtain the initial reconstructed signal that successfully reconstructs the original signal or the initial reconstructed signal that best matches the estimated measurement signal as the intermediate reconstructed signal; Signal enhancement and reconstruction module: Based on the intermediate reconstructed signal, iteratively solve to obtain the reconstructed signal by the reverse diffusion of the diffusion model, the data consistency of the measurement signal, and the decoupled sampling step.

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