Under-sampling nuclear magnetic resonance spectrum reconstruction method and system based on conditional diffusion probability model

Abstract

The invention discloses an under-sampling nuclear magnetic resonance spectrum reconstruction method and system based on a conditional diffusion probability model, and the method comprises the steps: employing a mathematical model to simulate a nuclear magnetic resonance FID signal according to the characteristics of a nuclear magnetic resonance spectrum signal, adding random Gaussian noise, and constructing a simulation data set for training; building a nuclear magnetic resonance spectrum reconstruction network based on the conditional diffusion probability model, and setting related training parameters; performing network model training and testing by using the simulation data set to obtain a trained nuclear magnetic resonance spectrum reconstruction network; the trained nuclear magnetic resonance spectrum reconstruction network is used to realize rapid reconstruction of the nuclear magnetic resonance spectrum; wherein in the reverse denoising process of the nuclear magnetic resonance frequency spectrum reconstruction network, an under-sampling frequency spectrum is introduced as a condition, so that a generation result is guided to approach a target full-sampling frequency spectrum. On the basis of a generative deep learning technology of a conditional diffusion probability denoising model, a high-resolution full-sampling spectrogram is generated by taking nuclear magnetic resonance spectrum data of Poisson sampling as a control condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear magnetic resonance, and particularly relates to a method and system for reconstructing under-sampling nuclear magnetic resonance spectrum based on a conditional diffusion probability model. BACKGROUND

[0002] Nuclear magnetic resonance (NMR) spectrum as a non-invasive analysis technology has important significance in many fields such as biology, chemistry and life science. Especially multi-dimensional NMR spectrum can provide rich information about molecular structure, dynamic behavior and interaction, and is widely used in molecular identification, drug development, protein structure analysis and metabolomics research, and has irreplaceable scientific value and application potential.

[0003] However, in the experimental acquisition process of multi-dimensional NMR spectrum, the particles need to be excited between each pulse transition, and enough spin relaxation time needs to be waited, resulting in a long experimental acquisition time. Especially for three-dimensional and above NMR spectrum, usually several tens of hours or even several days of acquisition time is needed, which greatly limits its application and promotion in high-throughput analysis. In order to solve this problem, non-uniform sampling (NUS) technology is widely used to accelerate the acquisition of multi-dimensional nuclear magnetic resonance data, and by pre-setting a sampling template (such as Poisson sampling and exponential sampling template), part of the sampling points in the indirect dimension is selected, thereby effectively shortening the experimental time. However, the partial loss of free induction decay (FID) signal inevitably leads to artifacts in the frequency domain spectrum after Fourier transform, and then leads to distortion of the spectrum resolution and loss of effective feature information. Therefore, the multi-dimensional NMR spectrum technology based on fast sampling often needs corresponding spectrum reconstruction technology to recover the complete spectrum information.

[0004] Currently, NMR spectrum undersampling reconstruction techniques can be divided into two categories: optimization iterative algorithms and deep learning methods. Optimization iterative algorithms introduce regularization constraints into a specific optimization model to constrain the properties and form of the solution, and then iteratively solve the model using different optimization algorithms. Typical methods include Iterative Soft Thresholding (IST), Sparse Dimension Iterative Linear Enhancement (SMILE), and Low-Rank Hankel Matrix Method (LRHM). However, these traditional algorithms heavily rely on manually adjusting regularization parameters, and only when the parameters are set appropriately can they achieve the desired results. Furthermore, traditional methods require lengthy iterative solution times, making them unsuitable for complex spectrum reconstruction tasks. In contrast, deep learning methods can automatically extract prior information from large amounts of training data, and high-quality spectra can be directly obtained based on the trained model, thus avoiding tedious parameter adjustments and lengthy iterative processes. This type of method heavily relies on the nonlinear modeling capabilities of neural networks, and different network structures have their own characteristics in spectrum reconstruction tasks. For example, the Deep Encoder-Decoder High Resolution Network (EDHRN) leverages its powerful frequency-domain nonlinear fitting capabilities to effectively suppress undersampling artifacts, but its training and reconstruction processes are time-consuming, and it suffers from insufficient accuracy in weak peak reconstruction. Deep Neural Networks (WNNs) based on the WaveNet architecture learn the temporal characteristics of signals, adapting to different sampling strategies and exhibiting strong detail preservation and artifact resistance. FID-Net, trained on temporal signals, adapts to different sampling densities and templates, demonstrating high flexibility. Deep Hankel Matrix Factorization Networks (DHMF) and Deep Thresholding Networks (MoDern) inspired by sparse models combine the ideas of classic iterative algorithms, enhancing the interpretability and reliability of the models. However, they still struggle to reconstruct weak peak signals in high dynamic range data and are sensitive to sampling patterns. Although deep learning methods have achieved significant improvements in reconstruction performance, reconstruction results remain limited in cases of extremely sparse sampling or varied sampling patterns, and problems such as difficulty in weak peak reconstruction and the creation of fictitious spectral details persist. Summary of the Invention

[0005] The purpose of this invention is to solve the problems in the prior art.

[0006] The technical solution adopted by this invention to solve its technical problem is: to provide an undersampled nuclear magnetic resonance spectrum reconstruction method based on a conditional diffusion probability model, comprising the following steps:

[0007] Based on the characteristics of nuclear magnetic resonance spectral signals, a mathematical model is used to simulate nuclear magnetic resonance FID signals and random Gaussian noise is added to construct a simulation dataset for training.

[0008] A nuclear magnetic resonance spectrum reconstruction network was built based on the conditional diffusion probability model, and relevant training parameters were set.

[0009] The network model is trained and tested using a simulation data set, and a trained nuclear magnetic resonance spectrum reconstruction network is obtained;

[0010] The trained nuclear magnetic resonance spectrum reconstruction network is used to realize rapid reconstruction of nuclear magnetic resonance spectrum;

[0011] The nuclear magnetic resonance spectrum reconstruction network is composed of a forward process and a reverse process, the forward process takes a high-resolution full-sampling simulation spectrum as input, the reverse process takes a noise picture as input, and the noise is gradually removed through a reverse Markov chain to restore the image to a distribution similar to the full-sampling spectrum data, and the required image is generated; In the reverse denoising process, an undersampled spectrum is introduced as a condition to guide the generated result to approximate the target full-sampling spectrum.

[0012] Preferably, according to the characteristics of the nuclear magnetic resonance spectrum signal, a mathematical model is used to simulate the nuclear magnetic resonance FID signal and add random Gaussian noise to construct a simulation data set for training, characterized by the following steps:

[0013] An ideal FID signal is generated using a mathematical model, and the mathematical model is represented as:

[0014]

[0015] wherein, represents an ideal FID signal, J represents the number of harmonics of the signal, and is a random integer between 1 and 200; and is a random amplitude, ranging from [0.05, 1.0], and is a random phase, ranging from [0, 2 ], is a random frequency, ranging from [0.01, 0.99], and is a random relaxation time, ranging from [10, 179.2], and is a time axis, both of which are 256, represents an outer product, represents noise, which is a normally distributed signal; i is the imaginary part of the index;

[0016] The generated ideal FID signal is Poisson sampled in the indirect dimension, and then Fourier transformed and normalized to obtain a frequency domain signal as a simulation data set for training.

[0017] Preferably, the nuclear magnetic resonance spectrum reconstruction network is composed of a forward process and a reverse process;

[0018] The forward process takes the high-resolution full-sampling simulation spectrum as input, and gradually adds Gaussian noise through a forward Markov chain until the image approaches a Gaussian noise distribution; the high-resolution full-sampling simulation spectrum At any time t, the Gaussian noise is added to the representation as:

[0019] ;

[0020] wherein N represents a normal distribution, ; intermediate parameters , intermediate parameters ;

[0021] The reverse process takes a noisy picture as input, and gradually removes noise through a reverse Markov chain to restore the image to a distribution similar to the full-sampling spectrum data, achieving the purpose of image generation; an undersampled spectrum is introduced as a condition in the reverse denoising process to guide the generated result to approximate the target full-sampling spectrum, and the mathematical expression of the reverse denoising process is:

[0022] ;

[0023] wherein, represents the noise added from to in the forward process.

[0024] Preferably, the Gaussian noise is predicted by a noise network model, and the noise network model includes a contraction path and an expansion path; the input of the noise network model is a noisy image obtained by randomly adding noise to the full-sampling simulation nuclear magnetic resonance spectrum through the forward process of the diffusion process; the contraction path extracts features from the noisy image, and the expansion path reconstructs according to the extracted features and outputs the noise required by the reverse process; the connection between the feature channels of the contraction path and the expansion path prevents the loss of detailed information in the convolution process, and a large number of feature channels enable the network to propagate structural information to higher resolution layers.

[0025] Preferably, the contraction path and the expansion path each include a plurality of steps;

[0026] Each step of the contraction path includes a first group of normalization modules GroupNorm, a first nonlinear unit Swish, a first 3x3 convolution, a second group of normalization modules GroupNorm, a second nonlinear unit Swish, a second 3x3 convolution, and a down-sampling, which doubles the number of feature channels through a pooling layer with a step of 2 and a size of 3x3, and then inputs the next step; the output of the second 3x3 convolution is also connected to the corresponding step of the expansion path through feature mapping.

[0027] Each ladder of the expansion path comprises a first group of normalization modules GroupNorm, a first nonlinear unit Swish, a first 3x3 convolution, a second group of normalization modules GroupNorm, a second nonlinear unit Swish, a second 3x3 convolution, and an upsampling, which is realized by a convolution layer with a step of 1, a size of 1x1, and a halved number of channels, and a nearest neighbor interpolation sampling, so as to halve the number of feature channels and then input to the next ladder;

[0028] The downsampling of the last ladder of the contraction path is connected to the upsampling of the last layer of the expansion path through an intermediate layer with an attention mechanism; the operation of the intermediate layer is represented as:

[0029] ;

[0030] wherein Q, K, and V are all from the output of the downsampling of the last ladder, is the dimension of the vector; is the input of the upsampling.

[0031] Preferably, the network model is trained and tested using the simulation data set to obtain a trained nuclear magnetic resonance spectrum reconstruction network, comprising the following steps:

[0032] The simulation data set is input into the network, the loss value between the output result and the actual noise is calculated, the gradient is calculated using the back propagation algorithm, and the network parameters are updated using the Adam optimization algorithm; the process is stopped after the network parameters are updated through continuous iteration until the loss value converges or a preset training round is reached; the loss value is calculated using the following loss function, which is represented as:

[0033]

[0034] wherein n is the number of data points, and represent the i-th point of the label data and the i-th point of the predicted data, respectively, is used to select the peak value region, the peak value region is set to 1, and the others are set to 0.

[0035] Preferably, the trained nuclear magnetic resonance spectrum reconstruction network is used to realize rapid reconstruction of nuclear magnetic resonance spectrum, specifically: a preprocessed undersampled nuclear magnetic resonance spectrum test set of any size is input into the trained network model as a condition, and a recovery result similar to the full-sampling spectrum is gradually generated through a guided backward denoising process; at the same time, the undersampled spectrum also undergoes data consistency processing with each iteration result in the backward denoising process, thereby effectively constraining the backward reasoning process and ensuring that the denoising result gradually approaches the full-sampling spectrum.

[0036] The application also provides an undersampling nuclear magnetic resonance spectrum reconstruction system based on a conditional diffusion probability model, comprising:

[0037] An simulation data generation module adopts a mathematical model to simulate nuclear magnetic resonance FID signals and adds random Gaussian noise according to nuclear magnetic resonance spectrum signal characteristics, and constructs a simulation data set for training;

[0038] A model construction module builds a nuclear magnetic resonance spectrum reconstruction network based on a conditional diffusion probability model and sets relevant training parameters;

[0039] A model training module trains a network model using the simulation data set and tests the network model to obtain a trained nuclear magnetic resonance spectrum reconstruction network;

[0040] A model application module uses the trained nuclear magnetic resonance spectrum reconstruction network to realize rapid reconstruction of nuclear magnetic resonance spectrum;

[0041] The nuclear magnetic resonance spectrum reconstruction network is composed of a forward process and a reverse process, the forward process takes a high-resolution full-sampling simulation spectrum as input, the reverse process takes a noise picture as input, and the noise is gradually removed through a reverse Markov chain to restore the image to a distribution similar to that of the full-sampling spectrum data, thereby generating the required image; the undersampling spectrum is introduced as a condition in the reverse denoising process to guide the generated result to approximate the target full-sampling spectrum.

[0042] The application has the following beneficial effects: the generative deep learning technology based on the conditional diffusion probability denoising model generates a high-resolution full-sampling spectrum with Poisson-sampled nuclear magnetic resonance spectrum data as a control condition; the training is performed through simulation data, and a large amount of real data is not required; the data consistency constraint strategy is combined to avoid the problem of fictitious details, significantly improve the reconstruction accuracy and adaptability, and realize accurate and widely applicable spectrum denoising and signal restoration.

[0043] The application will be further described in detail below in combination with the drawings and embodiments, but the application is not limited to the embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 A method step diagram of the undersampling nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model is provided for the embodiment of the application.

[0045] Figure 2 A flowchart of the nuclear magnetic resonance spectrum reconstruction network is provided for the embodiment of the application.

[0046] Figure 3 A model framework diagram of the nuclear magnetic resonance spectrum reconstruction network is provided for the embodiment of the application.

[0047] Figure 4A two-dimensional spectrum obtained by processing test data by a method for reconstructing under-sampling nuclear magnetic resonance spectrum based on a conditional diffusion probability model;

[0048] Figure 5 A structure diagram of a system for reconstructing under-sampling nuclear magnetic resonance spectrum based on a conditional diffusion probability model. DETAILED DESCRIPTION

[0049] Referring to Figure 1 , a method step diagram of a method for reconstructing under-sampling nuclear magnetic resonance spectrum based on a conditional diffusion probability model, comprising the following steps:

[0050] S101, according to the characteristics of nuclear magnetic resonance spectrum signal, a mathematical model is used to simulate the nuclear magnetic resonance FID signal and add random Gaussian noise to construct a simulation data set for training;

[0051] S102, a nuclear magnetic resonance spectrum reconstruction network is built based on a conditional diffusion probability model, and relevant training parameters are set;

[0052] S103, the simulation data set is used for network model training and testing, and a trained nuclear magnetic resonance spectrum reconstruction network is obtained;

[0053] S104, the trained nuclear magnetic resonance spectrum reconstruction network is used to realize fast reconstruction of nuclear magnetic resonance spectrum;

[0054] The reconstruction process diagram of the nuclear magnetic resonance spectrum reconstruction network is shown in Figure 2 , which is composed of a forward process and a reverse process. The forward process takes a high-resolution full-sampling simulation spectrum as input, and the reverse process takes a noise picture as input. By using a reverse Markov chain, the noise is gradually removed, the image is restored to a distribution similar to the full-sampling spectrum data, and the required image is generated. In the reverse denoising process, an under-sampling spectrum is introduced as a condition to guide the generated result to approximate the target full-sampling spectrum.

[0055] Specifically, in S101, according to the characteristics of nuclear magnetic resonance spectrum signal, a simulation data is generated by using a relevant mathematical model and adding simulated noise, and an ideal frequency domain signal is generated as a network label. The mathematical model of the two-dimensional signal is:

[0056] ;

[0057] wherein J is the number of harmonics of the signal, and is a random integer between 1 and 200, and is a random amplitude, ranging from [0.05, 1.0], is a random phase, ranging from [0, 2 ], is a random frequency, ranging in [0.01, 0.99], and is a random relaxation time, ranging in [10, 179.2], and is a time axis, all of which are 256, denotes an outer product, is a normal distribution (i.e. mean is 0, and standard deviation is ). After the generated two-dimensional FID signal pair is Poisson sampled in the indirect dimension, then Fourier transform and normalization processing are performed, serving as input data for network training. The input data dimension is : 4x2x256x256, wherein 4 is the batch size, 2 is the channel number, and 256x256 is the size of the direct dimension and the indirect dimension, respectively, and the output data dimension is consistent with the input. The established network model has good generalization ability and can be used for fast reconstruction of spectrum graphs of any size.

[0058] Specifically, in S102, the nuclear magnetic resonance spectrum reconstruction network is composed of a forward process and a reverse process. In the forward process, Gaussian noise is gradually added to the high-resolution full-sampled simulation spectrum graph through a forward Markov chain, until the image approaches a Gaussian noise distribution. From the high-resolution full-sampled simulation spectrum graph at time t, the formula for adding Gaussian noise to any time t is:

[0059] ;

[0060] wherein N is a normal distribution, , , In the reverse process, the noise is gradually removed through a reverse Markov chain to restore the image to a distribution similar to the full-sampled spectrum graph data, achieving the purpose of image generation. Since the full-sampled spectrum graph obtained by directly removing noise from data close to a Gaussian noise distribution has countless possibilities, the present application introduces an undersampled spectrum as a condition in the reverse denoising process to guide the generation result to approximate the target full-sampled spectrum. The mathematical expression of the reverse denoising process is:

[0061] ;

[0062] wherein the mean and variance on the left side of the equation are to be solved, and the mean is obtained by substituting the equation on the right side through the formula of the forward process:

[0063] ;

[0064] The variance is:

[0065] ;

[0066] wherein is set in advance, and is independent of the input , so the network only needs to predict the unique uncertainty in the mean.

[0067] Specifically, the structure of the nuclear magnetic resonance spectrum reconstruction network is shown in Figure 3 . In the forward process, Gaussian noise is gradually added to the fully sampled simulation spectrum by Markov chain to make it close to pure Gaussian noise distribution. In the backward process, the model gradually denoises the spectrum according to the learned noise distribution combined with data consistency constraints to recover the true data. The main structure of the network model is shown in Figure 2 , the network is divided into two parts, the left part is the shrinkage path, and the right part is the expansion path, most of the two paths are left-right symmetric structure. Each step of the shrinkage path is composed of two layers of 3x3 convolution, and before each convolution layer, there is a group normalization module GroupNorm and a nonlinear unit Swish. After each step, a pooling layer with a step of 2 and a size of 3x3 is used for down-sampling. In each down-sampling step, the number of feature channels is doubled. In the middle of the last layer of down-sampling and the first layer of up-sampling, an intermediate layer with attention mechanism is connected. The output of the last layer of down-sampling is calculated by two self-attention calculations, and the obtained output is input to the first layer of up-sampling. The attention formula is:

[0068] ;

[0069] where Q, K, V are all from the output of the last layer of down-sampling, is the dimension of the vector. Each step of the expansion path includes 3x3 deconvolution for up-sampling, halving the number of feature channels, and connecting the corresponding feature mapping of the shrinkage path, as well as two 3x3 convolution layers, each of which is followed by a group normalization module GroupNorm and a nonlinear unit Swish. The shrinkage path extracts features, and the expansion path reconstructs according to the extracted features. The connection between the two parts of the feature channels prevents the loss of detailed information in the convolution process, and the large number of feature channels enables the network to propagate structural information to higher resolution layers.

[0070] Specifically, the loss function used by the network is:

[0071] ;

[0072] where n is the number of data points, and represent the i-th point of the label data and the i-th point of the predicted data, is used to select the peak region, and the peak region is set to 1 and the others are set to 0.

[0073] Specifically, in S103, the training method of the network is: inputting the generated simulation data into the network, calculating the loss value between the output result and the actual noise through the loss function, calculating the gradient using the back propagation algorithm, and updating the network parameters using the Adam optimization algorithm. The process updates the network parameters through continuous iteration until the loss value converges or the preset training round is reached.

[0074] Specifically, the trained network model is tested, and the preprocessed undersampled nuclear magnetic resonance spectrum test set of any size is input into the trained network model as a condition, and a guided reverse denoising process is used to gradually generate a recovery result similar to the full sampling spectrum. In this process, the undersampled spectrum is not only input as a condition, but also data consistency processing is performed with each iteration result in the reverse denoising process, thereby effectively constraining the reverse reasoning process and ensuring that the denoising result gradually approaches the full sampling spectrum. In this way, the reverse denoising process can more accurately recover the full sampling nuclear magnetic resonance spectrum. Finally, the peak position and relative peak amplitude obtained from the output result can be used as a basis for further analysis to provide high-quality spectrum recovery information. The present embodiment uses 15% Poisson sampling of 2D protein GB1 1 H- 15 N heteronuclear single quantum coherence data for testing, and the test results are as shown in Figure 4 Figure 4 (a) is an undersampled spectrum after preprocessing as network input data, Figure 4 (b) is a spectrum output by the proposed diffusion probability model reconstruction, Figure 4 (c) is the corresponding full sampling spectrum. As can be seen from Figure 4 , the network model can accurately reconstruct the peak position and relative peak amplitude of the actual nuclear magnetic resonance spectrum data, verifying the effectiveness and practical value of the present application.

[0075] Referring to Figure 5 , it is a structure schematic diagram of an undersampled nuclear magnetic resonance spectrum reconstruction system based on a conditional diffusion probability model according to an embodiment of the present application, which comprises:

[0076] The simulation data generation module 501 uses a mathematical model to simulate the nuclear magnetic resonance FID signal according to the characteristics of the nuclear magnetic resonance spectrum signal and adds random Gaussian noise to construct a simulation data set for training;

[0077] The model construction module 502 builds a nuclear magnetic resonance spectrum reconstruction network based on a conditional diffusion probability model and sets relevant training parameters;

[0078] The model training module 503 trains and tests the network model using the simulation data set to obtain a trained nuclear magnetic resonance spectrum reconstruction network;

[0079] ​The model application module 504 implements the fast reconstruction of the nuclear magnetic resonance spectrum by using the trained nuclear magnetic resonance spectrum reconstruction network.

[0080] The function implementation process of each module is the same as the steps of the undersampling nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model, and will not be described here.

[0081] The application is based on the generative deep learning technology of the conditional diffusion probability denoising model, generates a high-resolution full-sampling spectrum under the control condition of the Poisson-sampled nuclear magnetic resonance spectrum data. The training is performed through the simulation data, without a large amount of real data, and the data uniformization constraint strategy is combined to avoid the problem of fictitious details, significantly improve the reconstruction accuracy and adaptability, and realize the accurate and widely applicable spectrum denoising and signal recovery.

[0082] The above is only a preferred embodiment of the application, and is not used to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for undersampling nuclear magnetic resonance spectrum reconstruction based on a conditional diffusion probability model, characterized in that, Includes the following steps: Based on the characteristics of nuclear magnetic resonance spectral signals, a mathematical model is used to simulate nuclear magnetic resonance FID signals and random Gaussian noise is added to construct a simulation dataset for training. A nuclear magnetic resonance spectrum reconstruction network was built based on the conditional diffusion probability model, and relevant training parameters were set. The network model was trained and tested using a simulation dataset to obtain a trained nuclear magnetic resonance spectrum reconstruction network. A trained nuclear magnetic resonance spectrum reconstruction network is used to achieve rapid nuclear magnetic resonance spectrum reconstruction. The nuclear magnetic resonance spectrum reconstruction network consists of a forward process and a backward process. The forward process takes a high-resolution fully sampled simulated spectrum as input, while the backward process takes a noisy image as input. The noise is gradually removed through a reverse Markov chain to restore the image to a distribution similar to the fully sampled spectrum data, generating the desired image. In the backward denoising process, an undersampled spectrum is introduced as a condition to guide the generated result to approximate the target fully sampled spectrum.

2. The undersampled nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 1, characterized in that, The method involves constructing a simulation dataset for training by simulating nuclear magnetic resonance (NMR) FID signals using a mathematical model based on the characteristics of NMR spectral signals and adding random Gaussian noise. The method is characterized by the following steps: An ideal FID signal is generated using a mathematical model, which is expressed as follows: ； in, This represents the ideal FID signal, where J represents the number of harmonics in the signal, and its value is a random integer between 1 and 200. and The amplitude is random, ranging from [0.05, 1.0]. and It is a random phase, ranging from [0, 2]. ], and The frequency is random, ranging from [0.01, 0.99]. and The random relaxation time ranges from [10, 179.2]. and The timeline is 256 in total. Indicates the outer product. Let represent noise, which is a normally distributed signal; i is the imaginary part of the exponent. The generated ideal FID signal is Poisson sampled on the indirect dimension, and then subjected to Fourier transform and normalization to obtain the frequency domain signal as a simulation dataset for training.

3. The undersampled nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 1, characterized in that, The nuclear magnetic resonance spectrum reconstruction network consists of a forward process and a reverse process; The forward process takes a high-resolution, fully sampled simulated spectrum as input and progressively adds Gaussian noise through a forward Markov chain until the image approximates a Gaussian noise distribution; from the high-resolution, fully sampled simulated spectrum... Adding Gaussian noise to any time t is represented as: ； Where N represents a normal distribution, Intermediate parameters intermediate parameters ; The reverse process takes a noisy image as input and gradually removes noise through a reverse Markov chain, restoring the image to a distribution similar to the fully sampled spectral data, thus achieving the goal of image generation. The reverse denoising process introduces an undersampled spectrum as a condition to guide the generated result to approximate the target fully sampled spectrum. The mathematical expression for the reverse denoising process is: ； in, Indicates the forward process from arrive The added noise.

4. The undersampled nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 3, characterized in that, The Gaussian noise is predicted by a noise network model, which includes a contraction path and an expansion path. The input to the noise network model is a noisy image obtained by randomly adding noise to a fully sampled simulated nuclear magnetic resonance spectrum through a forward diffusion process. The contraction path extracts features from the noisy image, and the expansion path reconstructs the image based on the extracted features and outputs the noise required for the reverse process. The connection of feature channels between the contraction path and the expansion path prevents the loss of detailed information during convolution, while the large number of feature channels enables the network to propagate structural information to higher resolution layers.

5. The undersampling nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 4, characterized in that, Both the contraction path and the expansion path consist of the same number of steps. Each step of the contraction path includes a first group of normalization modules (GroupNorm), a first nonlinear unit (Swish), a first 3×3 convolution, a second group of normalization modules (GroupNorm), a second nonlinear unit (Swish), a second 3×3 convolution, and downsampling, connected in sequence. The downsampling doubles the number of feature channels through a pooling layer with a stride of 2 and a size of 3×3 before inputting it into the next step. The output of the second 3×3 convolution is also connected to the steps of the corresponding level of the expansion path through feature mapping. Each step of the extended path includes a first group of normalization modules (GroupNorm), a first nonlinear unit (Swish), a first 3×3 convolution, a second group of normalization modules (GroupNorm), a second nonlinear unit (Swish), a second 3×3 convolution, and upsampling, which are connected in sequence. The upsampling is achieved by using a convolutional layer with a stride of 1, a size of 1×1, and half the number of channels, and nearest neighbor interpolation sampling to halve the number of feature channels before inputting them into the next step. The downsampling of the last step of the contraction path and the upsampling of the last layer of the expansion path are connected through an intermediate layer with an attention mechanism; the operation of the intermediate layer is represented as follows: ； Here, Q, K, and V all come from the downsampled output of the last step. Let be the dimension of the vector; This is the input for upsampling.

6. The undersampled nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 1, characterized in that, The process of training and testing a network model using a simulation dataset to obtain a trained nuclear magnetic resonance spectrum reconstruction network includes the following steps: The simulated dataset is input into the network, the loss value between the output result and the actual noise is calculated, the gradient is calculated using the backpropagation algorithm, and the network parameters are updated using the Adam optimization algorithm. This process iteratively updates the network parameters until the loss value converges or a preset number of training rounds is reached, at which point training stops. The loss value is calculated using the following loss function, expressed as: ； Where n is the number of data points. and These represent the i-th point of the label data and the i-th point of the prediction data, respectively. Used to select the peak region; set the peak region to 1, and all other settings to 0.

7. The undersampled nuclear magnetic resonance spectrum reconstruction method based on the conditional diffusion probability model according to claim 5, characterized in that, The method of using a trained NMR spectrum reconstruction network to achieve rapid NMR spectrum reconstruction specifically involves: inputting a preprocessed, undersampled NMR spectrum test set of arbitrary size as a condition into the trained network model; guiding the inverse denoising process to gradually generate a recovery result that is close to the full-sampled spectrum; simultaneously, the undersampled spectrum is also processed for data consistency with the results of each iteration in the inverse denoising process, thereby effectively constraining the inverse inference process and ensuring that the denoising result gradually approaches the full-sampled spectrum.

8. An undersampled nuclear magnetic resonance spectrum reconstruction system based on a conditional diffusion probability model, characterized in that, include: The simulation data generation module uses a mathematical model to simulate the nuclear magnetic resonance FID signal based on the characteristics of the nuclear magnetic resonance spectrum signal and adds random Gaussian noise to construct a simulation dataset for training. The model building module constructs a nuclear magnetic resonance spectrum reconstruction network based on the conditional diffusion probability model and sets the relevant training parameters. The model training module uses a simulation dataset to train and test the network model, resulting in a trained nuclear magnetic resonance spectrum reconstruction network. The model application module utilizes a trained nuclear magnetic resonance spectrum reconstruction network to achieve rapid nuclear magnetic resonance spectrum reconstruction. The nuclear magnetic resonance spectrum reconstruction network consists of a forward process and a backward process. The forward process takes a high-resolution fully sampled simulated spectrum as input, while the backward process takes a noisy image as input. The noise is gradually removed through a reverse Markov chain to restore the image to a distribution similar to the fully sampled spectrum data, generating the desired image. In the backward denoising process, an undersampled spectrum is introduced as a condition to guide the generated result to approximate the target fully sampled spectrum.

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