A training method of an iterative reconstruction model, an NMR signal iterative reconstruction method and related products

Abstract

The application is suitable for the technical field of signal processing, and provides a training method of an iterative reconstruction model, an NMR signal iterative reconstruction method and related products. The training method of the iterative reconstruction model comprises the following steps: obtaining NMR training data; performing iterative reconstruction on the NMR training data based on an iterative soft threshold algorithm; in each iteration process, performing iterative reconstruction on the NMR training data based on the iterative soft threshold algorithm; in each iteration process, adaptively determining a control parameter of the current iteration according to iteration state information of the current iteration, and calculating a soft threshold value of the current iteration based on the control parameter, so as to filter signals by using the soft threshold value and update a reconstructed spectrum; constructing a training data set based on input features extracted in each iteration process and corresponding output labels; and training a deep learning network by using the training data set to obtain the iterative reconstruction model. The embodiments of the application can improve the quality of a spectrum.

Description

Technical Field

[0001] This application belongs to the field of signal processing technology, and in particular relates to a training method for an iterative reconstruction model, an iterative reconstruction method for NMR signals, and related products. Background Technology

[0002] Sampling techniques for Nuclear Magnetic Resonance (NMR) spectra significantly shorten experimental time by reducing the number of sampling points, but reconstruction algorithms are needed to recover complete frequency domain information. Existing reconstruction algorithms based on Iterative Soft Thresholding (IST) often use non-adaptive fixed thresholds, which cannot adapt to the dynamic changes in signal sparsity and residuals during iteration, leading to artifacts easily appearing in the reconstructed spectra. Summary of the Invention

[0003] This application provides a training method for an iterative reconstruction model, an iterative reconstruction method for NMR signals, and related products, which can improve the quality of spectra.

[0004] The first aspect of this application provides a training method for an iterative reconstruction model, comprising: acquiring NMR training data; iteratively reconstructing the NMR training data based on an iterative soft thresholding algorithm, wherein in each iteration, the control parameters of the current iteration are adaptively determined according to the iteration state information of the current iteration, and the soft threshold of the current iteration is calculated based on the control parameters, so as to use the soft threshold to filter signals and update the reconstructed spectrum; constructing a training dataset based on the input features extracted in each iteration and the corresponding output labels, wherein the output labels are used to control the iteration process; and training a deep learning network using the training dataset to obtain an iterative reconstruction model.

[0005] In some implementations of the first aspect, the control parameters of the current iteration are adaptively determined based on the iteration state information of the current iteration, including: calculating the residual change rate and peak change rate of the current iteration based on a sliding window; and determining the decay coefficient of the current iteration based on the residual change rate and peak change rate.

[0006] In some implementations of the first aspect, determining the attenuation coefficient for the current iteration based on the residual change rate and the peak change rate includes: decreasing the attenuation coefficient when the residual change rate is less than a first preset threshold; increasing the attenuation coefficient when the peak change rate is less than a second preset threshold; and maintaining the original attenuation coefficient if the residual change rate is greater than the first preset threshold or the peak change rate is greater than the second preset threshold.

[0007] In some embodiments of the first aspect, the training method for the iterative reconstruction model further includes: if the residual change rate is less than a first preset threshold and the peak change rate is less than a second preset threshold, then the attenuation coefficient is increased preferentially according to the peak change rate.

[0008] In some embodiments of the first aspect, the attenuation coefficient has a preset upper limit and a lower limit, and in each iteration, the updated attenuation coefficient is limited to between the upper limit and the lower limit.

[0009] In some implementations of the first aspect, the input features include at least one of the following: iteration progress, residual energy percentage, maximum peak value of frequency domain residual, non-uniform sampling NUS sampling rate, local signal-to-noise ratio, and residual descent rate.

[0010] In some implementations of the first aspect, the output label includes a threshold ratio for calculating the soft threshold of the current iteration, a decay coefficient, and a stop confidence level for determining whether the current iteration meets the iteration stop condition.

[0011] In some implementations of the first aspect, the stopping confidence is calculated as follows: the residual recovery term, the spectral peak recovery rate term, and the convergence rate term are calculated separately; the residual recovery term, the spectral peak recovery rate term, and the convergence rate term are weighted and summed to obtain the stopping confidence.

[0012] In some implementations of the first aspect, a deep learning network is trained using a training dataset to obtain an iterative reconstruction model, including: dividing the training dataset into a training set and a validation set according to a preset ratio; sampling samples from the training set in batches and inputting them into the deep learning network; calculating the loss value between the output and the corresponding output label; updating the network weights based on the loss value; and performing validation operations on the validation set at preset validation step intervals until the network convergence condition is met, thereby obtaining the iterative reconstruction model.

[0013] The second aspect of this application provides an iterative reconstruction method for NMR signals, comprising: acquiring an NMR signal to be reconstructed; performing iterative reconstruction on the NMR signal to be reconstructed, wherein in each iteration, input features are extracted from the current iteration state, the input features are input into an iterative reconstruction model pre-trained as in any of the first aspects, an output label is obtained for controlling the current iteration process, a soft threshold for the current iteration is calculated based on the output label, and the soft threshold is used to filter and update the reconstructed spectrum; until the iteration stopping condition is met, and the reconstructed frequency domain spectrum is output.

[0014] In some implementations of the second aspect, the iteration stopping condition includes at least one of the following: the current iteration number is greater than the minimum iteration number, and the stopping confidence in the output label reaches a preset confidence threshold; the L2 norm of the current time domain residual is lower than a preset residual threshold; or the current iteration number reaches a preset maximum iteration number.

[0015] The third aspect of this application provides a nuclear magnetic resonance spectrometer, including a signal acquisition unit for acquiring an NMR signal to be reconstructed; a storage unit for storing an iterative reconstruction model trained using any of the iterative reconstruction model training methods of the first aspect; and a processing unit coupled to the signal acquisition unit and the storage unit for executing any of the NMR signal iterative reconstruction methods of the second aspect and outputting the reconstructed frequency domain spectrum.

[0016] The fourth aspect of this application provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the NMR signal iterative reconstruction method of the second aspect.

[0017] The fifth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the NMR signal iterative reconstruction method of the second aspect.

[0018] The sixth aspect of this application provides a computer program product that, when run on a nuclear magnetic resonance spectrometer, causes a processor to execute the steps of the NMR signal iterative reconstruction method of the second aspect.

[0019] In this application, by adaptively determining the control parameters and calculating the soft threshold based on the iterative state information, the problem that traditional fixed thresholds cannot adapt to the dynamic changes in signal sparsity and residuals during the iteration process is solved. This achieves the goal of reducing the risk of weak peak loss and noise artifacts while ensuring the fidelity of the spectrum. Specifically, by acquiring NMR training data, iterative reconstruction of the NMR training data is performed based on the iterative soft thresholding algorithm. In each iteration, the residual change rate and peak change rate of the current iteration are calculated based on a sliding window. Since the residual change rate reflects the convergence trend of the overall signal energy and the peak change rate reflects the recovery process of the key spectral peak height, the attenuation coefficient is updated based on the residual change rate and peak change rate. The soft threshold of the current iteration is calculated by combining the attenuation coefficient, the peak value of the current iteration residual spectrum, and the threshold ratio. The soft threshold is used to filter the signal and update the reconstructed spectrum. The signal filtering intensity can be dynamically adjusted according to the actual state of the iteration process, reducing the risk of weak peak loss and noise artifacts while ensuring the fidelity of the spectrum. Then, a training dataset is constructed based on the input features extracted in each iteration and the output labels controlling the iteration process. The trained iterative reconstruction model can improve the quality of the spectrum during iterative reconstruction. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram illustrating the implementation flow of the training method for the iterative reconstruction model provided in the embodiments of this application; Figure 2 This is a schematic diagram illustrating the specific implementation process of the output soft threshold and attenuation coefficient provided in the embodiments of this application; Figure 3 This is a schematic diagram of the structure of the MLP network provided in the embodiments of this application; Figure 4 This is a schematic diagram illustrating the implementation process of the NMR signal iterative reconstruction method provided in the embodiments of this application; Figure 5 This is a schematic diagram of the reconstructed spectrum comparison provided in the embodiments of this application; Figure 6 This is a schematic diagram of the specific structure of the nuclear magnetic resonance spectrometer provided in the embodiments of this application; Figure 7 This is a schematic diagram of the specific structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are protected by this application.

[0023] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0024] In the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0026] Currently, NMR spectrum sampling techniques significantly shorten experimental time by reducing the number of sampling points, but reconstruction algorithms are needed to recover complete frequency domain information. Existing reconstruction algorithms based on iterative soft thresholding often use non-adaptive fixed thresholds, leading to artifacts in the reconstructed spectra. Therefore, this application proposes a training method for an iterative reconstruction model, an iterative reconstruction method for NMR signals, and an NMR spectrometer. This method dynamically adjusts the signal filtering intensity according to the actual state of the iteration process, reducing the risk of weak peak loss and noise artifact introduction while ensuring spectrum fidelity. This allows the trained iterative reconstruction model to improve spectrum quality during iterative reconstruction.

[0027] To illustrate the technical solution of this application, specific embodiments are described below.

[0028] Please refer to Figure 1 , Figure 1 The diagram illustrates the implementation flow of the training method for the iterative reconstruction model provided in this application embodiment, which can be applied to nuclear magnetic resonance spectrometers.

[0029] Specifically, the training method for the above iterative reconstruction model may include the following steps S101 to S104.

[0030] Step S101: Obtain NMR training data.

[0031] The NMR training data refers to nuclear magnetic resonance signal data used to train the deep learning model, obtained by sampling the free induction decay (FID) in the time domain. The FID signal is the original acquired signal of the NMR spectrum in the time domain, containing the oscillation decay components corresponding to each spectral peak. The NMR training data can be uniformly sampled or non-uniformly sampled (NUS) data; this application does not impose any restrictions on this.

[0032] Step S102: The NMR training data is reconstructed iteratively based on the iterative soft thresholding algorithm. In each iteration, the control parameters of the current iteration are adaptively determined according to the iteration state information of the current iteration, and the soft threshold of the current iteration is calculated based on the control parameters, so as to use the soft threshold to filter the signal and update the reconstructed spectrum.

[0033] The iterative soft thresholding algorithm transforms the current residual signal to the frequency domain in each iteration, applies a soft threshold to the frequency spectrum to remove noise and weak signal components while retaining strong signal components, and then transforms it back to the time domain to update the residual. This process is repeated iteratively until convergence. In the embodiments of this application, iterative state information is introduced in each iteration. The iterative state information is a set of comprehensive descriptive indicators of the changing situation, convergence process, and solution quality at each iteration, and may specifically include the residual change rate and peak change rate.

[0034] The control parameters for the current iteration are adaptively determined based on the iteration state information. These parameters can be used to adjust the soft threshold for this iteration, adaptively determining its value according to the actual state of the iteration process. Then, using the adaptively determined soft threshold, frequency components with amplitudes higher than the soft threshold are identified as valid signals, retained, shrunk, and accumulated in the reconstructed spectrum. Frequency components with amplitudes lower than the soft threshold are considered noise or numerical residues and are discarded. The reconstructed spectrum, i.e., the frequency domain spectrum, can be refined in each iteration, gradually approximating the true spectrum.

[0035] Step S103: Based on the input features and corresponding output labels extracted during each iteration, construct a training dataset. The output labels are used to control the iteration process.

[0036] The input features are a set of quantifiable parameters extracted from the current iteration state in each iteration, used to characterize the current state of the iteration process and enable the model to make decisions based on the iteration state. The output labels are parameter values ​​that are recorded synchronously after each iteration and used to control the current iteration process, and may include threshold ratio, decay coefficient, and stopping confidence.

[0037] Specifically, in the iterative reconstruction process based on the iterative soft thresholding algorithm, the current state of each iteration is described by information from multiple dimensions. This information is quantified as input features, serving as the basis for model decisions. Simultaneously, each iteration contains a set of control parameters that optimize the signal selection for that round. These parameters are determined through backtracking calculations across all iterations, serving as the true value labels for that state. By aggregating these samples into a training dataset, the deep learning model can learn the mapping relationships within these samples and master how to predict the optimal control parameters based on any given iteration state, thereby replacing manual experience-based control with data-driven intelligent control.

[0038] Step S104: Train a deep learning network using the training dataset to obtain an iterative reconstruction model.

[0039] Specifically, samples are drawn in batches from the training dataset, and the input features are fed into the network for forward propagation. The network outputs predicted control parameters, and the deviation between the predicted value and the output label is calculated as the loss value. This loss value is then backpropagated to each layer of the network. An optimization algorithm (such as Adam) is used to update the network weight parameters along the gradient direction, making the predicted value closer to the true label in the next forward propagation. As the number of training epochs increases, the network's prediction accuracy for the training samples gradually improves, and the network weight parameters gradually converge from a random initial state to an optimal state that accurately describes the mapping relationship. After training, an iterative reconstruction model is obtained. The iterative reconstruction model has learned how to predict the optimal control parameters in this state based on the input features.

[0040] In the embodiments of this application, NMR training data is acquired, and iterative reconstruction of the NMR training data is performed based on an iterative soft thresholding algorithm. In each iteration, the control parameters of the current iteration are adaptively determined according to the iteration state information of the current iteration, and the soft threshold of the current iteration is calculated based on the control parameters. The soft threshold is used to filter signals and update the reconstructed spectrum. The signal filtering intensity can be dynamically adjusted according to the actual state of the iteration process, which reduces the risk of weak peak loss and noise artifact introduction while ensuring the fidelity of the spectrum. Then, a training dataset is constructed based on the input features extracted in each iteration and the output labels controlling the iteration process. The trained iterative reconstruction model can improve the quality of the spectrum during iterative reconstruction.

[0041] In some embodiments of this application, obtaining NMR training data may include: generating an FID signal through signal simulation, and performing non-uniform sampling on the FID signal through a random sampling mask to obtain NMR training data.

[0042] Specifically, FID signals can be generated through signal simulation. Specifically, multiple Lorentz-type spectral peaks (e.g., 2-5) can be randomly generated based on simulation parameters. Simulation parameters can include: peak frequency range, peak intensity, transverse relaxation time T2, and Gaussian noise amplitude. For example, the peak frequency range can be randomly generated within the range of -900 to 900 Hz, the peak intensity can be randomly ordered between 0 and 100, the transverse relaxation time T2 can be randomly generated within the range of 0.05 to 0.20 s, and the Gaussian noise amplitude can be randomly generated within the range of 2 to 8. The random sampling mask is a binary sequence of the same length as the FID signal, used to identify whether each sampling point in the time domain has been actually acquired (e.g., 1 indicates acquisition, 0 indicates no acquisition). The NUS sampling rate of the random sampling mask can be randomly generated within the range of 15% to 50%. Preferably, to ensure the phase correctness of the NMR signal, the first sampling point in the time domain can be forcibly retained during sampling.

[0043] Next, an iterative soft thresholding algorithm can be used to iteratively reconstruct the NMR training data.

[0044] In some embodiments of this application, adaptively determining the control parameters of the current iteration based on the iteration state information of the current iteration may include: calculating the residual change rate and peak change rate of the current iteration based on a sliding window; and determining the decay coefficient of the current iteration based on the residual change rate and peak change rate.

[0045] Specifically, a sliding window is a window that extracts data from a series of iterations (e.g., the last 5 iterations) to calculate local trends. The residual change rate is the rate at which the L2 norm of the time-domain residual decreases within the sliding window, characterizing the speed of iterative convergence from the perspective of overall signal energy; the peak change rate characterizes the rate of change of the maximum peak value of the frequency-domain residual within the sliding window, characterizing the degree of recovery of the strongest signal component from the perspective of key spectral peak height. The attenuation coefficient is a control parameter used for iterative dynamic attenuation of the threshold.

[0046] Specifically, such as Figure 2 As shown, determining the attenuation coefficient for the current iteration based on the residual change rate and the peak change rate can include: decreasing the attenuation coefficient when the residual change rate is less than a first preset threshold; increasing the attenuation coefficient when the peak change rate is less than a second preset threshold; and maintaining the original attenuation coefficient if the residual change rate is greater than the first preset threshold or the peak change rate is greater than the second preset threshold.

[0047] In particular, if the residual change rate is less than the first preset threshold and the peak change rate is less than the second preset threshold, the attenuation coefficient can be increased according to the peak change rate to ensure the fidelity of the spectrum. The residual change rate is only used as an auxiliary reference.

[0048] Thus, when the signal recovers rapidly, the screening intensity can be maintained or moderately tightened; when convergence slows down, the screening intensity can be relaxed to fully extract the residual signal components; and when the spectral peaks have stabilized, the intensity can be moderately tightened to eliminate residual noise.

[0049] In one specific implementation, it can be first determined whether the residual change rate is less than a first preset threshold. If the residual change rate is less than the first preset threshold, the attenuation coefficient is reduced by a preset decrease n; otherwise, the original attenuation coefficient is maintained. Next, it is determined whether the peak change rate is less than a second preset threshold. If the peak change rate is less than the second preset threshold, the attenuation coefficient is increased by a preset increment m; otherwise, the original attenuation coefficient is maintained.

[0050] The first and second preset threshold values ​​can be set according to actual conditions. For example, the first preset threshold value can be set to 5%, and the second preset threshold value can be set to 2%. The values ​​of n and m can be the same or different, and the range of values ​​can be 0.01 to 0.20.

[0051] In some embodiments of this application, the attenuation coefficient has a preset upper limit and a lower limit, and in each iteration, the updated attenuation coefficient is limited to between the upper limit and the lower limit. Specifically, as shown... Figure 2 As shown, after updating the decay coefficient, it can be determined whether the decay coefficient of the current iteration is greater than the lower limit. If not, the decay coefficient is set to the lower limit; otherwise, the updated decay coefficient is retained. It can also be determined whether the decay coefficient of the current iteration is greater than the upper limit. If not, the decay coefficient is set to the upper limit; otherwise, the updated decay coefficient is retained.

[0052] Accordingly, by combining the attenuation coefficient, the peak value of the current iteration residual spectrum, and the threshold ratio, the soft threshold of the current iteration can be calculated, so as to adaptively determine the soft threshold value according to the actual state of the iteration process.

[0053] The peak value of the residual spectrum in the current iteration is the amplitude value at the point where the amplitude reaches its highest value across the entire spectrum obtained after the Fourier transform of the residual signal calculated in the current iteration. The threshold ratio is a preset or adaptively calculated scalar coefficient used to calculate the soft threshold for the current iteration.

[0054] like Figure 2 As shown, the preset attenuation coefficient, maximum peak value, threshold ratio, and sliding window size N can be obtained. The soft threshold can be expressed as: maximum peak value × threshold ratio × (attenuation coefficient)^(current iteration number - 1). In the first N iterations, the attenuation coefficient is a preset value. Starting from the Nth iteration, the residual change rate and peak change rate within the sliding window can be calculated to update the preset attenuation coefficient.

[0055] Thus, after obtaining the attenuation coefficient, replacing the soft threshold of the previous iteration with the newly calculated soft threshold allows the soft threshold to evolve smoothly round by round along the iteration process, achieving the dynamic control objective of responding to real-time state changes while maintaining historical continuity. Similarly, it can be determined whether the soft threshold is greater than the preset lower threshold. If so, the soft threshold is set to the lower threshold; otherwise, the calculated soft threshold is maintained and the final soft threshold and attenuation coefficient are output.

[0056] After completing the iterative reconstruction, a training dataset can be constructed based on the input features and corresponding output labels extracted during each iteration.

[0057] The input features may include one or more of the following: 1. Iteration progress, which is the ratio of the current iteration number to the maximum iteration number, is used to characterize the relative position of the iteration process; 2. Residual energy ratio, which is the ratio of the L2 norm of the current time-domain residual to the L2 norm of the initial time-domain FID signal, is used to characterize the overall degree of signal recovery. 3. The maximum peak value of the frequency domain residual is the maximum amplitude of the frequency domain residual spectrum obtained after the Fourier transform of the current time domain residual. It is used to characterize the strongest unrecovered signal component in the current iteration. 4. NUS sampling rate, which is the ratio of the actual number of sampling points to the total number of signal points, is used to characterize the degree of underdeterminacy of non-uniform sampling, so that the model can adapt to the reconstruction requirements under different sampling rates. 5. Local signal-to-noise ratio, which is the ratio of the maximum amplitude of the frequency domain residual spectrum to its amplitude standard deviation, is used to characterize the distinguishability between signal and noise in the current iteration; 6. Residual descent rate, which is the difference between the L2 norm of the previous time-domain residual and the current time-domain residual divided by the L2 norm of the previous time-domain residual, is used to characterize the iteration convergence speed.

[0058] Output labels may include one or more of the following: 1. Threshold ratio, used to calculate the soft threshold of the current iteration, to achieve sparse filtering of signal components; 2. Attenuation coefficient, used for iterative dynamic attenuation of the threshold, balancing signal preservation and noise suppression; 3. Stop confidence score, used to determine whether the current iteration meets the iteration stopping condition, with a value range of 0.6 to 0.95, preferably 0.85.

[0059] In some embodiments of this application, the stopping confidence is calculated as follows: the residual recovery rate, the spectral peak recovery rate, and the convergence rate are calculated separately; the residual recovery rate, the spectral peak recovery rate, and the convergence rate are weighted and summed to obtain the stopping confidence.

[0060] The residual recovery term is an indicator used to evaluate the overall signal recovery degree in the current iteration, and can be defined as 1 - res_norm, where res_norm is the ratio of the L2 norm of the current time-domain residual to the L2 norm of the initial time-domain FID signal. res_norm reflects the proportion of the current residual energy relative to the initial signal energy, and 1 - res_norm represents the proportion of signal energy that has been recovered. The closer the residual recovery term is to 1, the more fully the overall signal has been recovered and the higher the confidence level; conversely, it indicates that a large number of signal components still need to be recovered.

[0061] The peak recovery rate is an indicator used to evaluate the degree of recovery of key spectral peaks in the current iteration. It can be defined as `peak_recovery`, which is the ratio of the maximum peak value of the frequency domain reconstructed spectrum in the current iteration to the maximum peak value of the final frequency domain reconstructed spectrum after all iterations. The peak recovery rate directly reflects the proportion of the most important spectral peak information in the NMR spectrum that has been recovered in the current iteration. The closer the peak recovery rate is to 1, the more stable the key spectral peaks are, and the less improvement further iterations will provide, resulting in higher confidence.

[0062] The convergence rate term is a metric used to evaluate the convergence efficiency of the current iteration. It can be calculated based on the rate of decrease of the residuals over the most recent iterations (e.g., the last 5 iterations), and can be defined as 1 - res_change_rate / 0.1. When res_change_rate approaches 0, the convergence rate term approaches 1, indicating that the iteration has entered a plateau and the signal gain for continued iteration is extremely low; conversely, it indicates that the iteration is still in the rapid convergence phase.

[0063] Accordingly, the stopping confidence level can be expressed as w 1 ×(1-res_norm) + w 2 ×peak_recovery+ w 3 × (1-res_change_rate / 0.1) .in, 、w 2 、w 3 represents the weighting coefficients for the residual recovery term, the spectral peak recovery rate term, and the convergence rate term, respectively. w 1 + w 2 + w 3 = 1 In a preferred embodiment, w 1 = 0.3，w 2 = 0.4，w 3 = 0.3 It can achieve the best balance between weak peak preservation, artifact suppression and convergence speed.

[0064] In some embodiments of this application, training a deep learning network using a training dataset to obtain an iterative reconstruction model may include: dividing the training dataset into a training set and a validation set according to a preset ratio; extracting samples from the training set in batches and inputting them into the deep learning network; calculating the loss value between the output and the corresponding output label; updating the network weights based on the loss value; and performing validation operations on the validation set at preset validation step intervals until the network convergence condition is met, thereby obtaining the iterative reconstruction model.

[0065] Specifically, the training dataset can be preprocessed, and the input features and output labels can be normalized separately to scale each dimension to a similar numerical range, so that the network treats each feature dimension equally, while ensuring that the prediction accuracy of each label is not affected by the difference in units at the output end.

[0066] After data preprocessing, the training dataset can be randomly divided into a training set and a validation set according to a preset ratio (e.g., 8:2). The training set is used to drive the update and optimization of network weights; the validation set does not participate in weight updates and serves only as an independent evaluation benchmark.

[0067] Then, a deep learning network is constructed. This deep learning network can be a lightweight multilayer perceptron (MLP) network. For example... Figure 3 As shown, the MLP network structure can be sequentially comprised of an input layer (6-dimensional), a first fully connected layer (64 neurons), a ReLU activation layer, a second fully connected layer (32 neurons), another ReLU activation layer, and an output layer (3-dimensional). The input layer receives normalized 6-dimensional iterative features, and the output layer outputs 3-dimensional control parameters (threshold ratio, decay coefficient, and stopping confidence). The regression layer uses Mean Squared Error (MSE) as the loss function and Root Mean Squared Error (RMSE) as the evaluation metric.

[0068] Wherein, MSE is represented as Where Loss is the loss value, N is the number of samples, prediction is the model's predicted output, and Label is the true label, i.e., the output label. Prediction - Label represents the prediction error. .

[0069] During training, a batch of samples (batch size can be 64) is randomly selected from the training set and input into the deep learning network. The deep learning network outputs a prediction value for each sample in this batch, and then calculates the deviation between the network's prediction and the true label using the MSE loss function. This loss value is then differentiated with respect to all the network's weight parameters using the backpropagation algorithm to obtain the gradient direction of each parameter. The Adam optimizer adaptively adjusts the learning rate of each parameter and updates the weights along the gradient descent direction, making the predictions on the next batch of samples closer to the true label. By repeatedly selecting different batches of samples from the training set, calculating the loss, and updating the weights, the network's prediction accuracy for the training samples gradually improves.

[0070] To prevent overfitting, the current network is periodically applied to the validation set at preset validation step intervals (e.g., every 50 steps), and its loss value on the validation set is calculated and recorded. When the loss value on the validation set continues to decrease, it indicates that the network is still learning effectively, and the next round of training continues. When the loss value on the validation set stops decreasing or begins to increase, it indicates that the network has fully fitted the patterns in the training data (or has begun to overfit), and the network is considered to have converged, so training stops. The maximum number of training rounds does not exceed the maximum training depth (e.g., 50 rounds). During training, a segmented learning rate decay strategy is also used (decaying to 0.5 times the original rate every 20 rounds), automatically reducing the update step size in the later stages of training to allow the weights to converge finely near their optimal values. Redundant plotting output is disabled during training to ensure training efficiency.

[0071] After training, the network weight parameters converge from a random initial state to an optimal state that accurately describes the mapping relationship between input features and output labels. At this point, the trained iterative reconstruction model (including network weight parameters, input feature normalization parameters, and output label normalization parameters) can be stored in the spectrometer to ensure consistency in data preprocessing between the training and inference phases.

[0072] Correspondingly, Figure 4 The illustration shows a schematic diagram of the implementation process of the NMR signal iterative reconstruction method provided in the embodiments of this application. This method can be applied to nuclear magnetic resonance spectrometers.

[0073] Specifically, the above-mentioned NMR signal iterative reconstruction method may include the following steps S401 to S402.

[0074] Step S401: Obtain the NMR signal to be reconstructed.

[0075] The NMR signal to be reconstructed refers to the unknown NMR time-domain signal data that needs to be reconstructed, which can be obtained by non-uniform sampling of the time-domain free induction decay signal.

[0076] Step S402: Iteratively reconstruct the NMR signal to be reconstructed. In each iteration, the input features are extracted from the current iteration state and input into the pre-trained iterative reconstruction model to obtain the output label used to control the current iteration process. The soft threshold of the current iteration is calculated based on the output label and the soft threshold is used to filter and update the reconstructed spectrum. Until the iteration stopping condition is met, the reconstructed frequency domain spectrum is output.

[0077] The training method for the iterative reconstruction model can be referenced from [reference needed]. Figures 1 to 3 The relevant explanations are not elaborated here.

[0078] Specifically, before entering the iteration, initialization settings can be performed first: set the reconstructed spectrum to zero; set the time-domain residual to the initial NUS signal (i.e., the original acquired signal, with missing positions filled with zeros); initialize the iteration history array to record data such as the residual norm, soft threshold, and stop confidence for each iteration; calculate the L2 norm and sampling rate of the initial NUS signal. After initialization, iterative reconstruction begins.

[0079] In each iteration, a Fast Fourier Transform is first performed on the current time-domain residual signal to obtain the frequency-domain residual spectrum, and input features are extracted from the current iteration state. Input features may include iteration progress, residual energy percentage, maximum peak value of the frequency-domain residual, NUS sampling rate, local signal-to-noise ratio, and residual descent rate.

[0080] The extracted input features are normalized according to the normalization parameters saved during the training phase to ensure that the input data distribution is consistent with that of the training phase. The normalized features are then input into the iterative reconstruction model for forward propagation. The model outputs three control parameters (threshold ratio, decay coefficient, and stopping confidence). Reasonable range limiting is applied to the three output parameters (e.g., limiting the threshold ratio and stopping confidence to 0-1) to prevent extreme prediction values ​​from causing iterative runaway.

[0081] Next, the soft threshold for the current iteration is calculated based on the output threshold ratio and attenuation coefficient. This initial soft threshold is obtained by multiplying the maximum peak value of the current frequency domain residual by the threshold ratio, and then multiplying it by the attenuation coefficient raised to the power of (current iteration number - 1) to obtain the final soft threshold for the current iteration. After obtaining the soft threshold, a soft thresholding operation is performed on the frequency domain residual spectrum: components with amplitudes higher than the threshold are retained and contracted (amplitude minus the threshold) as valid signals, while components with amplitudes lower than the threshold are set to zero. The selected valid signal components are accumulated into the reconstructed spectrum, while these extracted components are removed from the frequency domain residual spectrum. The updated residual is returned to the time domain via inverse Fourier transform to obtain a new time-domain residual signal. Its L2 norm is recorded in the iteration history array for use in subsequent rounds to calculate iterative features. Non-sampling points (i.e., positions marked as 0 in the sampling mask) in the time-domain residual signal and the reconstructed signal are forcibly set to zero to comply with the physical constraints of NUS sampling. That is, the actual acquired data points are based on the measured values, and the algorithm only reconstructs missing positions, ensuring that the iteration process does not deviate from the authenticity of the measured data.

[0082] After each iteration, it can be evaluated whether the stopping condition is met. If any stopping condition is met, the loop is exited and the current reconstructed spectrum is output as the final reconstructed frequency domain spectrum; otherwise, the next iteration continues.

[0083] In some embodiments of this application, the iteration stopping condition includes at least one of the following: 1. The current iteration count is greater than the minimum iteration count, and the stopping confidence in the output labels reaches the preset confidence threshold; 2. The L2 norm of the current time-domain residual is lower than the preset residual threshold; 3. The current iteration count has reached the preset maximum iteration count.

[0084] Specifically, stopping when the confidence level reaches a preset confidence threshold (e.g., 0.85) indicates that the iteration has fully converged. When the current time-domain residual L2 norm is below a preset residual threshold, it indicates that the residual energy is extremely small, and further iteration will yield limited benefits. Reaching the preset maximum number of iterations serves as a safety mechanism to prevent unexpected non-convergence from leading to an infinite loop.

[0085] To make it easier to understand, the following specific examples will illustrate the point: First, 500 independent two-dimensional NMR training samples can be generated. The direct dimension uses full sampling, while the indirect dimension uses non-uniform sampling. Each sample set randomly generates 2-5 Lorentz spectral peaks. The peak frequency of each peak is randomly selected between -900 and 900 Hz, the peak intensity is randomly selected between 0 and 100 and arranged in descending order, the Gaussian noise amplitude is randomly selected between 2 and 8, the transverse relaxation time T2 is randomly selected between 0.05 and 0.20 seconds, and the NUS sampling rate is randomly selected between 15% and 50%. The sampling method is simple random sampling, and the first sampling point in the time domain is forcibly retained to ensure the phase correctness of the NMR signal. All samples are iterated approximately 200,000 times. In each iteration, standardized 6-dimensional input features and 3-dimensional output labels are extracted and saved as the training dataset. The residual sliding window size is set to 10, the peak sliding window size is set to 10, the residual rate of change threshold is set to 5%, the peak rate of change threshold is set to 2%, the minimum number of iterations is set to 10, the maximum number of iterations is set to 500, and the minimum residual L2 norm is set to 0.01.

[0086] Load the saved training dataset to verify that the input features are 6-dimensional and the output labels are 3-dimensional. Perform mean-variance normalization on both the input features and output labels, setting the scaling factor to 1 for dimensions with a standard deviation of 0 to avoid division by zero. Randomly shuffle the normalized training data, selecting 80% as the training set and the remaining 20% ​​as the validation set. Construct a lightweight MLP network with the following structure: a 6-dimensional input layer, a 64-neuron fully connected layer, a ReLU activation layer, a 32-neuron fully connected layer, a ReLU activation layer, and a 3-dimensional output layer, using MSE as the loss function. The Adam optimizer is used during training, with a batch size of 64, a maximum training epoch of 50, and a learning rate that decays to 0.5 times the original rate every 20 epochs. Validation is performed on the validation set every 50 steps to monitor for overfitting. After training, simultaneously save the network weight model, input feature normalization parameters, and output label normalization parameters.

[0087] Subsequently, a standard test signal was generated: an NMR signal containing three Lorentz peaks was constructed with a peak intensity ratio of 5:2:1, a transverse relaxation time T2 of 0.1 seconds, a data dimension of 128×128, a sampling frequency of 2000Hz, and Gaussian random noise with an amplitude of 5 added. Random non-uniform sampling was performed at a ratio of 25%. The parameters of the three core peaks were as follows: Peak 1 (strongest peak): indirect dimension frequency 500Hz, direct dimension frequency 200Hz, peak intensity 5; Peak 2: indirect dimension frequency 200Hz, direct dimension frequency 400Hz, peak intensity 2; Peak 3 (weakest peak): indirect dimension frequency 350Hz, direct dimension frequency 600Hz, peak intensity 1. A pre-trained iterative reconstruction model and normalization parameters were loaded, with a maximum number of iterations of 500 and a minimum residual threshold of 1×10⁻⁶. -4 The algorithm sets a minimum number of iterations of 10 and a stopping confidence threshold of 0.85 to perform iterative reconstruction. It automatically performs threshold prediction, attenuation coefficient adjustment, and stopping confidence determination for each iteration, automatically terminating the iteration and outputting the final reconstructed spectrum and all iteration data.

[0088] Reconstruction results as follows Figure 5 As shown, the traditional IST algorithm terminates after 96 iterations, while the NNR signal iterative reconstruction method of this application terminates after 78 iterations, reducing the number of iterations by 18.8%. The signal-to-noise ratio of the reconstructed spectrum of the NMR signal iterative reconstruction method of this application is improved by 4.3% compared with the traditional IST algorithm; the correlation coefficient with the full sampled spectrum increases by 3.50%; and the reconstruction error is significantly reduced. In particular, the traditional IST algorithm reconstructs a spurious peak at F1=500Hz and F2=273Hz, while the reconstructed spectrum of the NMR signal iterative reconstruction method of this application does not show this artifact at these positions. This indicates that this application performs outstandingly in terms of weak peak recovery capability and peak position reconstruction accuracy, effectively preserving subtle features in the spectrum and improving the fidelity and reliability of the reconstruction results.

[0089] It should be noted that, for the sake of simplicity, the aforementioned method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, because according to this application, some steps can be performed in other orders.

[0090] like Figure 6 The diagram shown is a schematic diagram of a nuclear magnetic resonance spectrometer 6 provided in an embodiment of this application.

[0091] Nuclear magnetic resonance spectrometer 6 may include: The signal acquisition unit 10 is used to acquire the NMR signal to be reconstructed; Storage unit 20 stores the iterative reconstruction model; The processing unit 30 is coupled to the signal acquisition unit 10 and the storage unit 20, and is used to execute the NMR signal iterative reconstruction method and output the reconstructed frequency domain spectrum.

[0092] Among them, the iterative reconstruction model can be based on Figures 1 to 3 The iterative reconstruction model shown was trained using the method described. For instructions on performing iterative reconstruction of NMR signals, please refer to [reference needed]. Figures 4 to 5 The relevant descriptions are not repeated in this application.

[0093] In some embodiments of this application, the signal acquisition unit 10 may include a magnet system, a probe, a radio frequency system, and a signal detection system.

[0094] Magnet systems can be used to generate uniform static magnetic fields that cause energy level splitting in atomic nuclei within a sample. These systems typically employ superconducting magnets (such as NbTi or Nb3Sn superconducting coils immersed in liquid helium) to produce a stable magnetic field with high intensity and extremely high uniformity, supplemented by a shimming coil system to correct for magnetic field inhomogeneities and ensure spectral resolution.

[0095] The probe is an assembly inserted into the central channel of a magnet, comprising a sample tube housing and an RF coil, used to hold the sample and transmit and receive RF signals. In transmit mode, the RF coil in the probe applies RF pulses generated by the RF system to the sample to excite atomic nuclei to resonate. In receive mode, it detects the free induction decay signal generated during atomic nucleus relaxation and outputs this weak signal to the subsequent system.

[0096] The radio frequency system includes a radio frequency transmitter and a radio frequency receiver. The radio frequency transmitter is used to generate radio frequency pulses at a specific frequency. The frequency, power, and timing of the radio frequency pulses are controlled by the processing unit 30 according to a preset pulse sequence. The radio frequency receiver is used to receive the NMR signal detected by the probe and perform primary amplification and detection processing.

[0097] The signal detection system includes a preamplifier and an analog-to-digital converter (ADC). The preamplifier is positioned adjacent to the probe and is used to amplify the received analog NMR signal with low noise. The ADC is used to convert the amplified analog signal into a digitized time-domain FID signal. The digitized time-domain FID signal is then sent as raw data to the processing unit 30.

[0098] The processing unit 30 is used to control the pulse sequence transmission timing of the radio frequency system and receive the digitized time-domain FID signal output by the signal detection system. If the time-domain FID signal is a uniformly sampled complete signal, the processing unit 30 directly performs a Fourier transform on it to obtain the frequency domain spectrum. If the time-domain FID signal is a non-uniformly sampled signal, the processing unit 30 loads the iterative reconstruction model in the storage unit 20, executes the aforementioned NMR signal iterative reconstruction method, obtains the reconstructed frequency domain spectrum, and outputs it to the user interface.

[0099] Understandable, Figure 6 This is merely an example of nuclear magnetic resonance spectrometer 6 and does not constitute a limitation on nuclear magnetic resonance spectrometer 6. It may include more or fewer components than shown, or combine certain components, or different components. For example, nuclear magnetic resonance spectrometer 6 may also include a power supply, bus, etc.

[0100] The processing unit 30 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0101] Storage unit 20 can be an internal storage unit of the NMR spectrometer 6, such as a hard drive or memory of the NMR spectrometer 6. Storage unit 20 can also be an external storage device of the NMR spectrometer 6, such as a plug-in hard drive, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the NMR spectrometer 6. Furthermore, storage unit 20 can include both internal and external storage devices of the NMR spectrometer 6. Storage unit 20 is used to store computer programs and other programs and data required by the NMR spectrometer 6. Storage unit 20 can also be used to temporarily store data that has been output or will be output.

[0102] It should be noted that, for the sake of convenience and brevity, the structure of the nuclear magnetic resonance spectrometer 6 described above can also be referred to the specific description of the structure in the method embodiment, and will not be repeated here.

[0103] like Figure 7As shown, this application also provides an electronic device 7, including a memory 70 and a processor 71. The memory 70 stores a computer program 72, and when the processor executes the computer program 72, it implements the steps of the NMR signal iterative reconstruction method provided in this application.

[0104] Specifically, the electronic device can be a computer, testing fixture, artificial intelligence equipment, or other device that requires NMR signal reconstruction. The functions and specific forms of the memory and processor can be found in the aforementioned memory unit 20 and processing unit 30, and this application does not impose any limitations on them. The structure of the aforementioned electronic device 7 can also be found in the detailed description of the structure in the method embodiments, and will not be repeated here.

[0105] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0106] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0107] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for various specific applications, but such implementations should not be considered beyond the scope of this application.

[0108] In the embodiments provided in this application, it should be understood that the disclosed spectrometer and method can be implemented in other ways. For example, the spectrometer device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0109] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0110] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0111] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0112] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A training method for an iterative reconstruction model, characterized in that, include: Obtain NMR training data; The NMR training data is reconstructed iteratively based on the iterative soft thresholding algorithm. In each iteration, the control parameters of the current iteration are adaptively determined according to the iteration state information of the current iteration, and the soft threshold of the current iteration is calculated based on the control parameters, so as to use the soft threshold to filter the signal and update the reconstructed spectrum. A training dataset is constructed based on the input features and corresponding output labels extracted during each iteration, wherein the output labels are used to control the iteration process. A deep learning network is trained using the training dataset to obtain an iterative reconstruction model.

2. The training method for the iterative reconstruction model according to claim 1, characterized in that, The step of adaptively determining the control parameters for the current iteration based on the iteration state information of the current iteration includes: The residual rate of change and peak rate of change for the current iteration are calculated based on a sliding window. The decay coefficient for the current iteration is determined based on the residual change rate and the peak change rate.

3. The training method for the iterative reconstruction model according to claim 2, characterized in that, The determination of the decay coefficient for the current iteration based on the residual rate of change and the peak rate of change includes: When the residual change rate is less than the first preset threshold, the attenuation coefficient is reduced; When the peak change rate is less than the second preset threshold, the attenuation coefficient is increased; If the residual change rate is greater than the first preset threshold, or the peak change rate is greater than the second preset threshold, the original attenuation coefficient is maintained.

4. The training method for the iterative reconstruction model according to claim 2, characterized in that, The training method for the iterative reconstruction model also includes: If the residual change rate is less than the first preset threshold and the peak change rate is less than the second preset threshold, then the attenuation coefficient is increased preferentially according to the peak change rate.

5. The training method for the iterative reconstruction model according to claim 1, characterized in that, The attenuation coefficient has a preset upper limit and a lower limit. In each iteration, the updated attenuation coefficient is limited to between the upper limit and the lower limit.

6. The training method for the iterative reconstruction model according to any one of claims 1-5, characterized in that, The input features include at least one of the following: iteration progress, residual energy ratio, maximum peak value of frequency domain residual, non-uniform sampling NUS sampling rate, local signal-to-noise ratio, and residual descent rate.

7. The training method for the iterative reconstruction model according to any one of claims 1-5, characterized in that, The output labels include a threshold ratio and a decay coefficient used to calculate the soft threshold of the current iteration, and a stop confidence level used to determine whether the current iteration meets the iteration stop condition.

8. The training method for the iterative reconstruction model according to claim 7, characterized in that, The stopping confidence level is calculated as follows: Calculate the residual recovery term, the spectral peak recovery rate term, and the convergence rate term respectively; The stopping confidence is obtained by weighted summation of the residual recovery term, the spectral peak recovery rate term, and the convergence rate term.

9. The training method for the iterative reconstruction model according to any one of claims 1-5, characterized in that, The step of training a deep learning network using the training dataset to obtain an iterative reconstruction model includes: The training dataset is divided into a training set and a validation set according to a preset ratio; Samples are extracted in batches from the training set and input into the deep learning network. The loss value between the output and the corresponding output label is calculated. The network weights are updated based on the loss value. The verification operation is performed on the verification set at preset verification step intervals until the network convergence condition is met, and the iterative reconstruction model is obtained.

10. An iterative reconstruction method for NMR signals, characterized in that, include: Acquire the NMR signal to be reconstructed; The NMR signal to be reconstructed is reconstructed iteratively. In each iteration, input features are extracted from the current iteration state. The input features are input into the iterative reconstruction model pre-trained in the manner described in any one of claims 1-9 to obtain the output label used to control the current iteration process. The soft threshold of the current iteration is calculated based on the output label. The soft threshold is used to filter and update the reconstructed spectrum. The iteration continues until the stopping condition is met, at which point the reconstructed frequency domain spectrum is output.

11. The NMR signal iterative reconstruction method according to claim 10, characterized in that, The iteration stopping condition includes at least one of the following: The current iteration count is greater than the minimum iteration count, and the stopping confidence in the output label reaches the preset confidence threshold; The L2 norm of the current time-domain residual is lower than the preset residual threshold; The current iteration count has reached the preset maximum iteration count.

12. A nuclear magnetic resonance spectrometer, characterized in that, include: The signal acquisition unit is used to acquire the NMR signal to be reconstructed; The storage unit stores an iterative reconstruction model trained using the training method of the iterative reconstruction model according to any one of claims 1-9; The processing unit, coupled to the signal acquisition unit and the storage unit, is used to execute the NMR signal iterative reconstruction method according to any one of claims 10 or 11 and output the reconstructed frequency domain spectrum.

13. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the NMR signal iterative reconstruction method according to claim 10 or 11.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the NMR signal iterative reconstruction method according to claim 10 or 11.

15. A computer program product, characterized in that, When the computer program product is run on a processor, the steps of the NMR signal iterative reconstruction method according to claim 10 or 11 are executed.

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