SVD-UNET based ground magnetic resonance fast imaging method

Abstract

The application belongs to the field of ground magnetic resonance imaging interpretation, and particularly relates to a ground magnetic resonance rapid imaging method based on SVD-UNET. The method comprises the following steps: adopting a gate integral method to perform dimension reduction processing on collected magnetic resonance data; utilizing a truncated singular value decomposition method to decompose a kernel function; utilizing a generalized inverse algorithm to inversely solve the processed magnetic resonance data and the decomposed kernel function, so as to obtain a characteristic parameter matrix containing water content and relaxation time information; and finally using a trained U-Net network to infer the water content and relaxation time distribution information of the underground space position by using the characteristic parameter matrix. The method effectively improves the inversion imaging efficiency by combining a traditional algorithm and an intelligent algorithm, and solves the time-consuming problem of the traditional imaging method.

Description

Technical Field

[0001] This invention belongs to the field of ground magnetic resonance imaging interpretation, specifically a ground magnetic resonance rapid imaging method based on SVD-UNET. Background Technology

[0002] Ground magnetic resonance imaging (GMR) is a technique for detecting groundwater, offering advantages such as directness, quantification, and unique interpretability. GMR imaging enables quantitative assessment and detection of water sources and is now widely used in groundwater exploration, hydrogeological surveys, and water-related disaster detection. However, current traditional inversion methods often employ iterative algorithms, requiring massive amounts of data and consuming considerable time. Therefore, researching a rapid GMR imaging method based on SVD-UNet is of great significance.

[0003] CN103984033A discloses a two-dimensional inversion method for ground-based nuclear magnetic resonance (NMR). This method uses a straightening transformation to reduce the dimensionality of the two-dimensional forward model, abstracting it into a matrix equation solution model. It then uses a combination of least squares singular value decomposition and an improved stochastic gradient descent method for inversion to achieve two-dimensional inversion. However, this method uses an improved stochastic gradient descent method, making the inversion process relatively time-consuming.

[0004] CN105785455A discloses a two-dimensional ground nuclear magnetic resonance inversion method based on B-spline interpolation. This method deploys fewer coils, collects signals from only a few measurement points, and combines the inversion method with spline interpolation to obtain the interpretation results obtained by half-covering with an array of coils. It is suitable for detecting non-layered, inhomogeneous water bodies. Furthermore, it improves the computational speed by searching for the optimal regularization factor using a bisection method. However, its use of the Gauss-Newton iteration method to solve the inversion objective function makes the inversion process time-consuming.

[0005] CN110515131A discloses a ground magnetic resonance inversion method based on time-lapse technology. This method utilizes the QT inversion method to perform inversion on the first measurement. The water content was obtained by inverting the ground magnetic resonance signal corresponding to the time; then, according to the measurement time sequence, the water content was analyzed separately. The three-dimensional ground magnetic resonance signals obtained from the previous measurement were used for QT inversion, and the inversion results from the previous measurement time were used as prior constraint information for the next measurement time. By utilizing inversion results from multiple different measurement times, the imaging accuracy was improved, and the changes in groundwater over time could be depicted. However, because multiple sets of measurement data were repeatedly inverted, the processing was relatively time-consuming. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a ground magnetic resonance imaging method based on SVD-UNET, which can improve the inversion speed and realize rapid inversion imaging.

[0007] This invention is implemented as follows:

[0008] A ground-based rapid magnetic resonance imaging method based on SVD-UNET, the method comprising:

[0009] Gate integration is performed on the magnetic resonance data acquired in ground magnetic resonance imaging.

[0010] The model is forward modeled based on the measured parameters, the kernel function is calculated, and then the kernel function is decomposed using SVD.

[0011] The generalized inverse algorithm is used to invert the magnetic resonance data after gate integration and the decomposed kernel function to obtain the feature parameter matrix containing water content and relaxation time information.

[0012] Using the U-Net network, the water content and relaxation time of underground spatial locations are inferred from the feature parameter matrix.

[0013] Furthermore, the gate integration process includes:

[0014] Step 1a: Write the measured magnetic resonance data in the matrix form shown in equation (1):

[0015] ,

[0016] in for 1-th order matrix, The number of pulse moments. The number of receiving coils, It is the product of the number of pulse moments and the number of receiving coils. The number of sampling points;

[0017] Step 1b: In Take the real part from the middle and the virtual part According to the sampling time point Generate a set of logarithmically spaced points And then according to The log-interval points will and Divided into The data in each group is integrated and the mean is calculated, as shown in equation (2):

[0018] ,

[0019] in , For the first The sampling point and the first One sampling point, and Between contains the first All sampling points of the group data, represent or The gate integrals are then performed to obtain the results. and The data after combining to form the gate integral :

[0020] ,

[0021] in for 1-order matrix.

[0022] Furthermore, the step of performing SVD decomposition on the kernel function includes:

[0023] Step 2a: For the kernel function Perform singular value decomposition:

[0024] ,

[0025] in for Kernel function of order, The number of grids to divide the underground space. For matrix of eigenvector matrix of order, For matrix of eigenvector matrix of order, Composed of singular values A diagonal matrix of order 1;

[0026] Step 2b: Truncate singular values, discarding small singular values ​​and their corresponding eigenvectors:

[0027] ,

[0028] in The number of singular values ​​to be retained. for eigenvector matrix of order, for eigenvector matrix of order, for A singular value diagonal matrix of order 1;

[0029] Furthermore, the inversion solution using the generalized inverse algorithm for the gate-integrated magnetic resonance data and the decomposed kernel function includes:

[0030] Step 3a: Based on the gate-integrated magnetic resonance data and the kernel function after truncating singular value decomposition The expression for the ground-based nuclear magnetic resonance signal is obtained as follows:

[0031] ,

[0032] The generalized inverse solution yields:

[0033] ,

[0034] in for 1-order matrix;

[0035] Step 3b: Based on the two-dimensional matrix Transform into a three-dimensional matrix : 2D matrix Each column of data Restored to its corresponding mesh position A two-dimensional matrix of order will eventually be Convert to Three-dimensional matrix .

[0036] Furthermore, using the U-Net network, the water content and relaxation time of underground spatial locations are inferred from the feature parameter matrix, including:

[0037] Step 4a: Generate dataset based on simulation model Each set of data includes a feature parameter matrix of water content information. and its corresponding water content and relaxation time matrix ;

[0038] Step 4b: Optimize the U-Net network by selecting the loss function and optimization strategy;

[0039] Step 4c: Training the U-Net network: on the dataset Randomly select 80% as the training set and 20% as the validation set, train for E epochs to stabilize the loss, and retain the optimal model parameters. ;

[0040] Step 4d: Utilize the optimal model parameters trained Based on the water content information feature parameter matrix The water content and relaxation time of the underground space can be deduced:

[0041] ,

[0042] in Represents the complex functions used to construct the network model. The matrix represents the water content and relaxation time inferred by the network model.

[0043] Compared with existing technologies, the advantages of this invention are as follows: This invention achieves rapid imaging. By combining the advantages of traditional algorithms and artificial intelligence algorithms, it solves the time-consuming problem of traditional inversion methods. Inversion imaging using this method only takes 4 seconds, while simultaneously improving imaging resolution, especially in terms of layered structures and water content information in boundary regions, resulting in higher fitting accuracy. In the engineering field, adopting this rapid imaging method can accelerate project progress and improve economic efficiency. Attached Figure Description

[0044] Figure 1 A flowchart of a ground-based rapid magnetic resonance imaging method based on SVD-UNET provided for embodiments of the present invention;

[0045] Figure 2 An improved U-Net network framework diagram provided for embodiments of the present invention;

[0046] Figure 3 The provided method simulation data test result diagram is shown in the embodiment of the present invention;

[0047] Figure 4 The figure shows the simulation data test results of the method provided in the embodiment of the present invention at different noise levels. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0049] like Figure 1 As shown, a rapid ground magnetic resonance imaging method based on singular value decomposition and U-Net network (SVD-UNET) is proposed. Addressing the time-consuming nature of traditional inversion methods, this method combines the advantages of traditional inversion methods with artificial intelligence methods, achieving rapid imaging while ensuring applicability and accuracy. The invention specifically includes the following steps:

[0050] Step 1: Perform gate integration on the acquired ground magnetic resonance data. The specific steps are as follows:

[0051] Step 1a: Write the magnetic resonance data in the matrix form shown in equation (1):

[0052] ,

[0053] in for Order matrix, number of impulse moments Number of receiving coils , Number of sampling points ;

[0054] Step 1b: In Take the real part from the middle and the virtual part According to the time point Generate a set of logarithmically spaced points Then, based on 50 log-interval points, and The data were divided into 49 groups, and the mean of each group was calculated by integration, as shown in equation (2):

[0055] ,

[0056] in , Representing the The sampling point and the first One sampling point, and Between contains the first All sampling points of the group data, represent or The gate integrals are then performed to obtain the results. and The data after combining to form the gate integral : ,in for 1-order matrix;

[0057] Step 2: Calculate the forward kernel function based on the measured parameters and perform truncated singular value decomposition on it. Specific steps include:

[0058] Step 2a: For the kernel function Perform singular value decomposition:

[0059] ,

[0060] in for Kernel function of order, The number of grids to divide the underground space. For matrix of eigenvector matrix of order, For matrix of eigenvector matrix of order, Composed of singular values A diagonal matrix of order 1;

[0061] Step 2b: Truncate singular values, discarding smaller singular values ​​and their corresponding eigenvectors to improve the stability of the algorithm.

[0062] ,

[0063] in The number of singular values ​​to be retained. for eigenvector matrix of order, for eigenvector matrix of order, for A singular value diagonal matrix of order 1;

[0064] Step 3: Solve using the generalized inverse algorithm. Specific steps include:

[0065] Step 3a: Based on the gate-integrated magnetic resonance data and the kernel function after truncating singular value decomposition Write the expression for the ground-based nuclear magnetic resonance signal:

[0066] ,

[0067] The generalized inverse solution yields:

[0068] ,

[0069] in for 1-order matrix;

[0070] Step 3b: Two-dimensional matrix Convert to a three-dimensional matrix : 2D matrix Each column of data Restored to its corresponding mesh position A two-dimensional matrix of order will eventually be Convert to Three-dimensional matrix ;

[0071] Step 4: Use the U-Net network to infer the water content and relaxation time of the underground spatial location:

[0072] Step 4a: Generate a dataset containing 100,000 data points based on the simulation model. Each set of data contains a feature parameter matrix of water content information. and its corresponding water content and relaxation time matrix ;

[0073] Step 4b: Optimize the U-Net network, such as... Figure 2As shown, RepVGGBlock modules are used to replace the basic convolutional layer modules, increasing the network's branching structure and improving its representational ability. Three different RepVGGBlock modules are employed to handle situations where the input and output data sizes differ. Smooth L1 loss is chosen as the loss function, and its expression is as follows:

[0074] ,

[0075] in It is the actual value. It is a predicted value. For hyperparameters, when the prediction bias is less than When the prediction error is greater than 1, the squared error, or L2 loss, is used. In this case, linear error is used, similar to L1 loss;

[0076] Step 4c: Training the network: Dataset 80% of the data is used as the training set and 20% as the validation set; 200 training iterations are performed to stabilize the loss and retain the optimal model parameters. ;

[0077] Step 4d: Utilize the optimal model parameters trained Based on the water content information feature parameter matrix The water content and relaxation time of the geological layer can be deduced:

[0078] ,

[0079] in Represents the complex functions used to construct the network model. The matrix represents the water content and relaxation time inferred by the network model.

[0080] The simulation data were verified using the above implementation method, and the results were obtained. Figure 3 and Figure 4 The experimental results shown are as follows, in which Figure 3 The experimental results for different simulation models, Figure 4 These are experimental results for different noise levels.

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rapid ground magnetic resonance imaging method based on SVD-UNET, characterized in that, The method includes: The magnetic resonance data acquired during ground-based magnetic resonance imaging (MRI) is subjected to gate integration processing; the gate integration processing includes: Step 1a: Write the measured magnetic resonance data in the matrix form shown in equation (1): ， in for 1-th order matrix, The number of pulse moments. The number of receiving coils, It is the product of the number of pulse moments and the number of receiving coils. The number of sampling points; Step 1b: In Take the real part from the middle and the virtual part According to the sampling time point Generate a set of logarithmically spaced points And then according to The log-interval points will and Divided into The data in each group is integrated and the mean is calculated, as shown in equation (2): ， in , For the first The sampling point and the first One sampling point, and Between contains the first All sampling points of the group data, represent or The gate integrals are then performed to obtain the results. and The data after combining to form the gate integral : , in for 1-order matrix; The model is forward modeled based on the measured parameters, the kernel function is calculated, and then the kernel function is decomposed using SVD. The generalized inverse algorithm is used to invert and solve the gate-integrated magnetic resonance data and the decomposed kernel function to obtain a feature parameter matrix containing water content and relaxation time information. The inversion and solution process using the generalized inverse algorithm includes: Step 3a: Based on the gate-integrated magnetic resonance data and the kernel function after truncating singular value decomposition The expression for the ground-based nuclear magnetic resonance signal is obtained as follows: ， The generalized inverse solution yields: , in for 1-order matrix; Step 3b: Based on the two-dimensional matrix Transform into a three-dimensional matrix : 2D matrix Each column of data Restored to its corresponding mesh position A two-dimensional matrix of order will eventually be Convert to Three-dimensional matrix ; Using the U-Net network, the water content and relaxation time of underground spatial locations are inferred from the feature parameter matrix.

2. The method according to claim 1, characterized in that, The step of performing SVD decomposition on the kernel function includes: Step 2a: For the kernel function Perform singular value decomposition: ， in for Kernel function of order, The number of grids to divide the underground space. For matrix of eigenvector matrix of order, For matrix of eigenvector matrix of order, Composed of singular values A diagonal matrix of order 1; Step 2b: Truncate singular values, discarding small singular values ​​and their corresponding eigenvectors: ， in The number of singular values ​​to be retained. for eigenvector matrix of order, for eigenvector matrix of order, for A diagonal matrix of singular values ​​of order 1.

3. The method according to claim 1, characterized in that, Using the U-Net network, the water content and relaxation time of underground spatial locations are inferred from the feature parameter matrix, including: Step 4a: Generate dataset based on simulation model Each set of data includes a feature parameter matrix of water content information. and its corresponding water content and relaxation time matrix ; Step 4b: Optimize the U-Net network by selecting the loss function and optimization strategy; Step 4c: Training the U-Net network: on the dataset Randomly select 80% as the training set and 20% as the validation set, train for E epochs to stabilize the loss, and retain the optimal model parameters. ; Step 4d: Utilize the optimal model parameters trained Based on the water content information feature parameter matrix The water content and relaxation time of the underground space can be deduced: ， in Represents the complex functions used to construct the network model. The matrix represents the water content and relaxation time inferred by the network model.

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