A training method and angle super-resolution method for a diffuse magnetic resonance angle super-resolution network

Abstract

This invention relates to the field of image processing technology, and particularly to a training method and a super-resolution method for diffuse magnetic resonance (DWI) angle super-resolution networks. The model training method includes: acquiring training data pairs; constructing an angle super-resolution network, which includes multiple cascaded spatial-angle autoregressive units (SLUs) for incremental prediction and includes a data consistency constraint module; training the angle super-resolution network using the training data pairs to obtain a trained angle super-resolution network. During training, a joint loss function is used to optimize the model parameters, including an unknown angle reconstruction loss and a multi-stage auxiliary supervision loss. By jointly modeling spatial-angle features using multi-stage autoregressive units, introducing geometric and physical constraints and progressive supervision, error accumulation is suppressed, achieving high-fidelity reconstruction of DWI from low angles to high angles, and improving the accuracy of parameter estimation.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a training method and angle super-resolution method for a diffuse magnetic resonance angle super-resolution network. Background Technology

[0002] The principle of diffusion magnetic resonance imaging (dMRI) is as follows: Based on conventional MRI sequences, a pair of symmetrical diffusion-sensitive gradient pulses are applied in specific directions to label the microscopic self-diffusion motion of water molecules within the tissue being tested. When protons undergo diffusion displacement within the tissue, the intensity of the gradient field they experience changes with their position, causing the proton phases to fail to completely refocus, resulting in signal attenuation. By acquiring signals in multiple different directions and with varying gradient intensities, and then using image reconstruction techniques to comprehensively process the different attenuated signals, a diffusion tensor image reflecting the microstructural characteristics and anisotropic information of the tissue being tested can be obtained.

[0003] Existing diffusion magnetic resonance angle super-resolution methods typically suffer from the following significant drawbacks: (1) Difficulty in capturing the global correlation of spatial-angle coupling. Traditional reconstruction networks mainly rely on local convolutional kernels, which are difficult to extract long-range structural consistency patterns across the entire brain when processing DWI data that is highly coupled with "spatial texture" and "angle features". (2) Lack of deep constraints on intermediate features of the sequence. Most existing methods only calculate the loss for the final generated high-angle output data, lacking intermediate supervision and constraints on the multi-stage reconstruction process. This leads to error propagation and accumulation in the inference process of the model in the angle dimension, causing the generated signal to be discontinuous or physically drifted between different diffusion directions. (3) Neglecting the geometric proximity of diffusion gradients. Conventional methods often treat each diffusion channel as an independent feature layer, ignoring the proximity relationship of diffusion gradient vectors in spherical geometric space. Due to the lack of physical geometric prior constraints, the generated data is often not smooth enough in q-space, and is prone to random signal oscillations that contradict physical laws, which in turn affects the accuracy of subsequent parameter estimation in diffusion tensor imaging (DTI) or diffusion kurtosis imaging (DKI). Summary of the Invention

[0004] To address the technical problems of insufficient global space-angle coupling capability, lack of intermediate supervision, and neglect of geometric and physical priors in existing technologies, this invention provides a training method and an angle super-resolution method for diffuse magnetic resonance (DMR) angle super-resolution networks. The technical solution is as follows: On the one hand, a training method for a diffusion magnetic resonance angle super-resolution network is provided. This method includes: acquiring training data pairs, wherein the training data pairs include initial state data as model input and high-angle-resolution diffusion-weighted imaging data as supervision ground truth, wherein the initial state data is obtained by zero-padding low-angle-resolution diffusion-weighted imaging data; constructing an angle super-resolution network, wherein the angle super-resolution network includes multiple cascaded spatial-angle autoregressive units, wherein the spatial-angle autoregressive units generate incremental predictions for the current stage based on the output of the previous stage and update the state by concatenating the channels, and the spatial-angle autoregressive units at least include a data consistency constraint module for forcibly retaining the true signal in the low-angle-resolution diffusion-weighted imaging data to the corresponding angular position of the prediction result; training the angle super-resolution network using the training data pairs to obtain a trained angle super-resolution network, and optimizing the model parameters using a joint loss function during training, wherein the joint loss function at least includes: an unknown angle reconstruction loss, used to supervise the difference between the prediction result of the unsampled angle and the supervision ground truth; and a multi-stage auxiliary supervision loss, used to supervise the difference between the complete angular state output of each stage and the supervision ground truth.

[0005] On the other hand, an angle super-resolution method is provided, which includes: acquiring low-angle resolution diffusion-weighted imaging data to be super-resolution; performing zero-padding on the low-angle resolution diffusion-weighted imaging data to be super-resolution to obtain initial state data to be processed; inputting the initial state data to be processed into a trained angle super-resolution network to obtain super-resolution high-angle resolution diffusion-weighted imaging data, wherein the trained angle super-resolution network is trained according to the training method of the diffusion magnetic resonance angle super-resolution network.

[0006] The beneficial effects of the technical solution provided by the embodiments of the present invention include at least the following: by constructing an angle super-resolution network containing multiple cascaded spatial-angle autoregressive units, each unit generates incremental predictions based on the output of the previous stage and updates the state through channel splicing, thereby realizing joint modeling of the spatial domain and angle domain and effectively capturing long-range structural consistency across regions; the joint loss function used in the training process includes at least unknown angle reconstruction loss and multi-stage auxiliary supervision loss: unknown angle reconstruction loss only supervises unsampled angles, making the model focus on the angles that really need to be predicted; multi-stage auxiliary supervision loss supervises the complete angle state of each stage, effectively suppressing error accumulation in the step-by-step inference process and improving training stability and reconstruction consistency; the angle super-resolution network trained by this method can reconstruct high-angle resolution diffusion signals from low-angle resolution data with high quality, providing a reliable image basis for subsequent diffusion parameter estimation. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 This is a flowchart of a training method for a diffuse magnetic resonance angle super-resolution network provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the training framework and key constraint relationships of a training method for a diffuse magnetic resonance angle super-resolution network provided in an embodiment of the present invention. Figure 3 This is a flowchart of an angle super-resolution method provided in an embodiment of the present invention; Figure 4 This is a visualization result and a comparison chart of the corresponding error residual distribution of the different angle super-resolution methods provided in the embodiments of the present invention for generating high-angle resolution DWI from low-angle resolution DWI. Figure 5 The parameter diagrams obtained by fitting a diffusion tensor model based on reconstructed DWI data, provided by the embodiments of the present invention, include the comparison results of fractional anisotropy, average diffusion rate and axial diffusion rate and their corresponding residual distributions. Detailed Implementation

[0009] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0010] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0011] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0012] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0013] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0014] In the following description of the present invention, the summation subscripts (such as i, j, k, etc.) appearing in each formula are local variables. The same symbols in different formulas do not represent the same value or meaning. The summation range in each formula has been clearly defined in the corresponding formula. When reading, please refer to the value range defined independently by each formula.

[0015] Please see Figure 1 This invention provides a training method for a diffuse magnetic resonance angle super-resolution network, which includes steps S101 to S103.

[0016] Step S101: Obtain training data pairs. The training data pairs include initial state data as input to the model and high-angle resolution diffusion-weighted imaging data as supervision ground truth. The initial state data is obtained by zero-padding the low-angle resolution diffusion-weighted imaging data.

[0017] In this step, the low-angular-resolution diffusion-weighted imaging data can also be called sparse angular-diffusion-weighted imaging data, which can be denoted as S. in ∈R N×H×W (R here is written as in some formulas) Here, the diffusion angle dimension is considered as the channel dimension, N is the total number of sampled angles, and the set of known angle indices can be denoted as Ω. known ={d1,d2,…,d N High-angle resolution diffusion-weighted imaging data can be denoted as Y. gt ∈R M×H×W M represents the total number of angles at high angular resolution. For example, in one specific embodiment, the total number of angles M at the target high angular resolution is 64, and the total number of angles N at the low angular resolution is 16. The known set of angle indices Ω... known ={1,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61}, that is, 16 directions are selected at equal intervals from 64 evenly distributed directions as input sampling directions. At this time, d1=1, d2=5, and so on.

[0018] Optionally, the aforementioned high-angle resolution diffusion-weighted imaging data can be directly acquired using a high-angle resolution diffusion magnetic resonance scanning protocol, such as acquiring complete data in 64 or 90 diffusion gradient directions on a 3T magnetic resonance scanner. Low-angle resolution diffusion-weighted imaging data can be obtained by downsampling the high-angle resolution data, i.e., selecting a subset of angles from the complete high-angle data according to a preset sampling scheme (such as uniform sampling, random sampling, or multi-shell sampling) as input samples. This construction method ensures the physical consistency between the input samples and the ground truth, while fully utilizing existing high-angle data to generate a large number of training sample pairs without the need for additional low-angle data acquisition.

[0019] To align the sparse input to the target angle space, the training data pairs are not in S... in Instead of being the direct input to the network model, S needs to be processed to obtain initial state data, which is then used as the input to the network model. in Process it to construct its zero-filled initialization state X. 0 ∈R M×H×W In layman's terms, it means filling the unsampled angle channels with 0; then, obtaining the initial state data X0=Φ(X) through convolution mapping. 0 ), where Φ() represents the convolution mapping operator, used to map the input channel to a preset hidden feature space, providing a basic representation for subsequent coupling modeling across spatial locations and across angular channels.

[0020] This step aligns the sparsely sampled low-angle data to the target high-angle space using zero-padding, ensuring consistency between the model's input and output dimensions, which facilitates subsequent stage-by-stage reconstruction. The convolutional mapping operator Φ() maps the input channels to a pre-defined hidden feature space, providing a basic representation for subsequent coupled modeling of cross-spatial and cross-angle channels. This preprocessing method preserves the true signals of known angles while reserving padding space for unknown angles, forming the basis for subsequent progressive reconstruction.

[0021] Please see Figure 2 Step S102: Construct an angle super-resolution network. The angle super-resolution network includes multiple cascaded spatial-angle autoregressive units. The spatial-angle autoregressive units generate incremental predictions for the current stage based on the output of the previous stage and update the state by splicing through the channel dimension. The spatial-angle autoregressive units also include at least a data consistency constraint module to force the real signal in the low-angle resolution diffusion-weighted imaging data to be retained at the corresponding angle position of the prediction result.

[0022] In this step, the update process in the t-th stage can be written as: , , The first formula above corresponds to "the spatial-angle autoregressive unit generates the incremental prediction for the current stage based on the output of the previous stage" in step S102, and the second formula corresponds to "updating the state by splicing the channel dimensions". t Let t represent the t-th spatial-angle autoregressive unit, and DC represent the data consistency constraint module. Let T be the feature concatenation operator representing the channel dimension, where t = 1, 2, ..., T. Through these T stages, X can ultimately be obtained. T At the same time, an X can be obtained at each stage. t .

[0023] Spatial-angle autoregressive unit output incremental prediction Δ t Instead of directly outputting the complete state X t This is to reduce the learning difficulty at each stage. Incremental prediction allows each unit to learn only the "missing part" of the current state compared to the previous state. The increment is larger when the state is sparse in the early stages and smaller when the state is more complete in the later stages, forming a progressive residual learning strategy. At the same time, updating the state through channel splicing not only retains all historical information from the previous stage but also adds new predictive information, avoiding information loss and facilitating the smooth propagation of gradients across multiple stages.

[0024] Optionally, the spatial-angle autoregressive unit generates the incremental prediction for the current stage based on the output of the previous stage, specifically including the following steps: (2.1) Compressing and encoding the output of the previous stage using the encoder to obtain a spatial feature map, which can be represented as: E t =Enc t (X t-1 (2.2) The global context modeling module is used to capture the long-range dependencies between the spatial and angular dimensions of the spatial feature map, so as to achieve deep aggregation of cross-regional structural and angular information, which can be expressed as: (2.3) The features output by the global context modeling module are restored to a prediction signal with the same spatial resolution as the input using the decoder, which can be expressed as: (2.4) The predicted signal is corrected using the data consistency constraint module, that is, the Y signal is corrected. t After making corrections, we get Y. corr,t (2.5) Map the corrected prediction results to the incremental prediction of the current stage, that is, Y corr,t Mapped to Δ t .

[0025] This processing flow forms a complete link: encoder-global context-decoder-data consistency constraint. The encoder compresses and encodes the input state, extracting multi-scale spatial features; the global context modeling module captures the long-range dependencies between spatial and angular dimensions; the decoder restores the features to full-angle prediction signals; the data consistency constraint module enforces the retention of true signals for known angles; and finally, the corrected results are mapped to incremental predictions. This "compression-global modeling-restoration-constraint" structure ensures computational efficiency, achieves deep coupling of spatial and angular information, and ensures the physical fidelity of the reconstruction results through data consistency constraints.

[0026] Optionally, step 2.2 above specifically includes: (1) using pixel unshuffle and reshape operations to transform the spatial feature map from spatial to sequential to obtain serialized features (Z). t (2) Using a selective scanning mechanism to perform global context modeling on the serialized features, the updated sequence features are obtained. (3) Utilize the inverse reshape operation (Reshape) -1 The pixel shuffle operation restores the updated sequence features to a two-dimensional spatial topology and performs residual connections with the spatial feature map to obtain the output features of the global context modeling module. ).

[0027] These steps can be expressed by the following formula: , , , , In the formula, r is the serialization factor, and the sequence length L and feature dimension D are respectively: , .

[0028] This processing flow transforms 2D spatial features into long sequences through patch serialization, utilizes a selective scanning mechanism to achieve global context modeling with linear computational complexity, and finally restores the spatial structure through inverse operations and connects it to the input residuals. Compared to the quadratic computational complexity of traditional Transformers, this method significantly reduces computational overhead while maintaining the global receptive field. Residual connections ensure that original feature information is not lost, enabling the model to learn the residual mapping from input to output, resulting in more stable training. This design allows the model to capture the consistency of spatial structure and the coupling relationships between angles across the entire brain.

[0029] Optionally, step 2.4 above can be expressed by the formula: m=1,2,…,N; , i∈Ω known ; The core function of the data consistency constraint module is to enforce the retention of the true acquired signal at a known angle at each stage. For a known angle position, the original input S is used directly. in The actual signal in the data overlays the network's predicted values; for unknown angle positions, the network's prediction results are retained. This hard constraint mechanism ensures that the reconstruction results are strictly consistent with the original observation data, avoiding the drift of known angle values ​​caused by multiple iterations, and is the key to ensuring the physical rationality of the reconstruction results.

[0030] Step S103: Train the angle super-resolution network using training data to obtain a well-trained angle super-resolution network. During training, optimize the model parameters using a joint loss function, which includes at least the unknown angle reconstruction loss and the multi-stage auxiliary supervision loss. The unknown angle reconstruction loss supervises the difference between the predicted result of the unsampled angle and the ground truth; the multi-stage auxiliary supervision loss supervises the difference between the complete angle state output at each stage and the ground truth. This step optimizes the network end-to-end using the joint loss function. The unknown angle reconstruction loss only supervises the unsampled angle, allowing the model to focus on the task that truly needs prediction; the multi-stage auxiliary supervision loss supervises the complete state of all intermediate stages, effectively requiring the output to be close to the ground truth at each stage. This dual mechanism of "process supervision + result supervision" effectively suppresses error accumulation, ensuring the model optimizes in the correct direction at each step during training, improving training efficiency and final reconstruction quality.

[0031] Optionally, the joint loss function may also include any one or more of the following losses: orientation consistency regularization loss, spherical harmonic coefficient domain constraint loss, and hard example angle loss. The orientation consistency regularization loss is used to supervise the differences between the prediction results of each angle within the nearest neighbor set in the spherical neighborhood graph; the spherical harmonic coefficient domain constraint loss is used to supervise the differences between the spherical harmonic coefficients of the predicted signal and the spherical harmonic coefficients of the supervised ground truth, and to suppress the energy of higher-order spherical harmonic coefficients; the hard example angle loss is used to supervise the differences between the prediction results and the supervised ground truth in a preset subset of the most difficult unknown angles selected based on the reconstruction error scores of each unknown angle. These three losses, as optional regularization constraints, improve the reconstruction quality from different perspectives. The directional consistency regularization loss utilizes the spherical geometric proximity of the diffusion gradient direction to constrain the smooth transition of prediction results in adjacent directions, enhancing the continuity of the q-space. The spherical harmonic coefficient domain constraint loss transforms the signal to the physical domain and eliminates non-physical high-frequency oscillations through higher-order energy suppression, improving the physical rationality of the reconstruction results. The hard example angle loss adaptively weights the reconstruction errors of each angle, focusing model training on the most difficult-to-reconstruct angles and improving the reconstruction fidelity of complex tissue regions (such as fiber intersection areas). These three loss functions can be used individually or in any combination, flexibly configured according to specific application scenarios.

[0032] Optionally, in a specific embodiment of the present invention, the joint loss function includes all five losses simultaneously, and its calculation formula is as follows: , In the formula, L total For joint losses, L rec L aux L angle L sh L hard These are the losses for unknown angle reconstruction, multi-stage auxiliary supervision, direction consistency regularization, spherical harmonic coefficient domain constraint, and hard example angle, respectively, λ. rec , λ aux , λ angle , λ sh , λ hard These are the weighting coefficients for these losses. Of course, some loss terms may further contain multiple sub-losses. In this case, their weighting coefficients can be set to 1, and the weighting coefficients of the entire loss term can be adjusted by adjusting the weighting coefficients of these sub-loss terms. This will be described in detail later.

[0033] This joint loss function weights and sums five losses to form a multi-objective optimization framework. The unknown angle reconstruction loss and multi-stage auxiliary supervision loss ensure basic reconstruction accuracy and process stability; the orientation consistency regularization loss, spherical harmonic coefficient domain constraint loss, and hard example angle loss improve reconstruction quality from three dimensions: geometric consistency, physical rationality, and hard example focusing, respectively. This hierarchical loss function design guarantees the model's basic reconstruction capability while providing a flexible regularization mechanism to adapt to different application scenarios.

[0034] Optionally, the reconstruction loss L from the unknown angle rec Defined as: , In the formula, Ω u Let Ω be the set of unknown angles. u and the known set of angles Ω known Together they form the set of all angles, X T,i Let Y be the predicted value of the i-th angle by the angle super-resolution network. gt,i Let ||i|| be the truth value of the i-th angle, and ||i||1 be the L1 norm. Let be the Charbonnier function, and ε be the smoothing parameter. Unknown angle reconstruction loss is the core objective of supervised learning. This loss applies only to the set of unknown angles Ω. u The calculations are performed without further supervision because the known angles have been forcibly replaced with true values ​​by the data consistency constraint module. The Charbonnier function is used as the loss form, which is smoother near zero compared to L1 loss and more robust to outliers than L2 loss, making it suitable for handling potentially noisy diffuse magnetic resonance (DMR) data. By minimizing this loss, the model learns the mapping relationship from low-angle input to high-angle output, which is fundamental to ensuring reconstruction accuracy.

[0035] Optionally, multi-stage auxiliary supervision loss L aux Defined as: , In the formula, s(e) is the scheduling function that gradually increases with each training round, and W rep The image represents the spatially adaptive weighted graph replicated along the channel dimension; P is the prediction tensor composed of intermediate prediction results from each stage of the angle super-resolution network, i.e., X1, X2, ..., X... T Together they form P; This represents the copied truth tensor corresponding to the prediction tensor, which is equivalent to copying Y... gt The result is obtained by copying T times; ⊙ represents element-wise multiplication, || ||1 is the L1 norm, λ grad These are the weighting coefficients of the gradient constraint term. x and yThese represent the horizontal and vertical gradient operators, respectively.

[0036] Multi-stage auxiliary supervision loss for the complete state X at each stage t Supervision is applied to ensure that the model outputs predictions close to the true value at each step during training. The scheduling function s(e) gradually increases with each training epoch e, with smaller weights in the early stages to allow the model to learn basic reconstruction capabilities; the weights increase in the later stages to enhance the output quality in the intermediate stages, forming a progressive training strategy from "relaxed exploration" to "strict constraints". The loss also includes gradient constraint terms to supervise the image gradients in the horizontal and vertical directions, enhancing the spatial structure fidelity of the reconstruction results and preserving edge and texture details.

[0037] As we mentioned before, the multi-stage auxiliary supervision loss L aux The formula for calculating the joint loss function includes a weighting coefficient λ. aux Meanwhile, the multi-stage auxiliary supervision loss L aux It consists of two sub-losses, corresponding to the auxiliary supervision term and the gradient constraint term, respectively. Looking at the joint loss function, the weight coefficient of the gradient constraint term is actually λ. aux ×s(e)×λ grad Of course, we can also consider the multi-stage auxiliary supervision loss L. aux Defined as: , And in the joint loss formula, L aux The weighting coefficients are set to 1. They are essentially similar, both being weighted sums of various losses.

[0038] Optionally, the directional consistency regularization loss L angle Defined as: , , , In the formula, S is the set of angles for which graph constraints need to be applied, which is a subset of the set of unknown angles; N(i) is the set of nearest neighbors of angle i in the spherical neighborhood graph; X T,i and X T,j , respectively, are the predicted values ​​of the i-th and j-th angles by the angle super-resolution network; ||||1 is the L1 norm; ρ() is the Charbonnier function; a ij θ ij These are the neighborhood weights before and after normalization, respectively; σ is the Gaussian kernel width parameter; clip() is the truncation operation.

[0039] In this embodiment, the set Ω is from an unknown perspective. uIn selecting the subset S of angles to which graph constraints need to be applied, a common approach is to directly select the set of unknown angles Ω. u As a subset of angles S, a spherical K-nearest neighbor graph based on the bvec angle is constructed using the neighborhood relations of the diffusion gradient direction vectors on the sphere. This yields the nearest neighbor set N(i) for each angle i in the spherical neighborhood graph. For angles i and j, the unnormalized neighborhood weight θ can be obtained by calculating the dot product of their normalized diffusion gradient direction vectors (unit vectors). ij (Corresponding to the third formula above), and during calculation, it is truncated to [-1, 1] to prevent numerical errors. Then, according to the second formula above, the neighborhood weight θ is... ij Normalization is performed to obtain the normalized neighborhood weights a. ij Finally, the directional consistency regularization loss L is calculated using the first formula mentioned above. angle .

[0040] The directional consistency regularization loss leverages the physical prior of diffuse magnetic resonance: geometrically similar diffusion gradient directions should result in smoothly varying measured signals. This loss constructs a spherical K-nearest neighbor graph, applying weighted constraints to the differences in predictions between each angle and its geometric neighbors. The weights are determined by a Gaussian kernel of the directional angle—the smaller the angle, the stronger the constraint. This design enhances the continuity and smoothness of the q-space, avoiding signal jitter caused by independent processing of different angle channels in traditional methods. Furthermore, K-nearest neighbor and weight normalization prevent over-smoothing, preserving necessary angular details.

[0041] Optionally, the spherical harmonic coefficient domain constraint loss L sh Defined as: , , In the formula, λ lb c represents the higher-order energy suppression weighting coefficient. pred c gt These are the spherical harmonic coefficients corresponding to the predicted signal and the ground truth supervision signal output by the angle super-resolution network, respectively. pred,k ω represents the spherical harmonic coefficients corresponding to the predicted value of the k-th angle by the angle super-resolution network. k The order weight of the k-th coefficient, n k Let be the order corresponding to the k-th spherical harmonic coefficient.

[0042] In this embodiment, the spherical harmonic coefficient c (regardless of c) pred Still C gt The value c(p) for each voxel p in the calculation (which uses the same method) can be obtained through fitting with smoothing regularization: , In the formula, s(p) represents the signal vector composed of samples from all angles, and B∈R N×C L represents the smoothing regularization matrix related to the spherical harmonic order, and λ is the regularization coefficient.

[0043] The spherical harmonic coefficient domain constraint loss transforms the signal into the physical representation space of the spherical harmonic domain. The first term constrains the predicted signal's spherical harmonic coefficients to match the true values, ensuring the accuracy of the predicted signal in the physical domain; the second term uses order weights ω... k A penalty is imposed on higher-order spherical harmonic coefficients, with the penalty increasing as the order increases. Since the real diffused signal is a smooth low-pass signal in the angular dimension, excessively large higher-order spherical harmonic coefficients imply non-physical high-frequency oscillations. This loss effectively suppresses abnormal jitter in the reconstruction results, improving the robustness and physical plausibility of the model under different noise levels.

[0044] Optionally, the difficult example angle loss L hard Defined as: , , , In the formula, Ω u Ω is a set of unknown angles. K To select the Top-K most difficult subsets of unknown angles based on error scores, Ω K =TopK({e i} i∈Ωu );w i Let X be the weight of the i-th angle. T,i Let Y be the predicted value of the i-th angle by the angle super-resolution network. gt,i Let ||i||1 be the truth value of the i-th angle, ||i||1 be the L1 norm, and ρ() be the Charbonnier function; i Let τ be the error score for the i-th angle, and τ be the temperature coefficient; H and W be the tensor sizes (i.e., X and W) of the angle super-resolution network's prediction of the i-th angle. T,i (size), p represents the spatial location index.

[0045] The difficult example angle loss employs an adaptive difficult example mining strategy, focusing model training on angles that are difficult to reconstruct. First, the spatial average reconstruction error e for each unknown angle is calculated. i As an error score, the top-K angles with the highest errors are then selected to form the difficult example set Ω. KFinally, a softmax function adjusted by a temperature coefficient τ is used to calculate the weights of each difficult example, applying weighted supervision to the angles of the difficult examples. The smaller the temperature coefficient τ, the more concentrated the weights are on the most difficult angles; the larger τ, the more evenly the weights are distributed. This strategy allows the model to focus on the reconstruction quality of complex tissue regions in the later stages of training, improving the model's generalization ability on difficult samples.

[0046] Please see Figure 3 This invention provides an angular super-resolution method, which includes: S301, acquiring low-angular resolution diffusion-weighted imaging data to be super-resolution, corresponding to S in the above training method. in S302. Perform zero-padding on the low-angle resolution diffusion-weighted imaging data to be super-resolution to obtain the initial state data to be processed, corresponding to X0 in the above training method; S303. Input the initial state data to be processed into the trained angle super-resolution network to obtain the super-resolution high-angle resolution diffusion-weighted imaging data, corresponding to X0 in the above training method. T The trained angle super-resolution network is obtained by training the angle super-resolution network of diffusion magnetic resonance as described above.

[0047] This angle super-resolution method directly reuses the data preprocessing workflow and network structure from the training phase, forming a complete inference pipeline. The input low-angle data is zero-padded to obtain the initial state X0, which is then fed into the trained angle super-resolution network. After successive reconstruction through T spatial-angle autoregressive units, the final output is high-angle resolution data X. T The entire inference process requires no iterative optimization and can be completed in a single forward propagation, resulting in high computational efficiency and suitability for practical clinical applications. The trained network parameters are fixed, enabling fast inference and real-time processing of diffusion MRI data from individual patients.

[0048] Please see Figure 4 and Figure 5 To further verify the superior performance of the angle super-resolution method in this invention, this invention (Proposed) was compared with common super-resolution methods in the prior art (SH, SVL, MLP, 2DCNN, 3DUnet, 3DRCNN).

[0049] In these two images, GT (Ground Truth) represents the actual high-angle resolution diffusion-weighted imaging data or a parameter map calculated based on it, serving as a reference standard for comparison. The b-value is the diffusion-sensitive gradient intensity, measured in s / mm². Different b-values ​​in the image correspond to different degrees of diffusion weighting: lower b-values ​​(e.g., b=1000) have a higher signal-to-noise ratio, making reconstruction relatively easy; higher b-values ​​(e.g., b=2000) have a lower signal-to-noise ratio, significant signal attenuation, and a significantly increased reconstruction difficulty. The Residual map shows the difference between the reconstruction results of each method and GT; the smaller the residual value and the more uniform the distribution, the higher the reconstruction accuracy. FA (fractional anisotropy), MD (mean diffusivity), and AD (axial diffusivity) are the core parameters of diffusion tensor imaging, reflecting the directionality of water molecule diffusion, the overall diffusion rate, and the diffusion capacity along fiber bundles, respectively. They are important quantitative indicators for clinical diagnosis and scientific research analysis.

[0050] As can be seen from the figure, the method of this invention achieves the best reconstruction results under all b-value conditions and all diffusion parameters. In the visualization results, the residual plot of the method of this invention is the darkest with the fewest highlighted areas, indicating the smallest reconstruction error. In the parameter plot comparison, the FA, MD, and AD parameter plots of the method of this invention are closest to GT, with uniform residual distribution and the smallest amplitude. In contrast, existing methods all exhibit varying degrees of blurring, artifacts, or parameter estimation bias. Especially under high noise conditions of b=2000 and in complex tissue regions such as white matter fiber intersections, the advantages of the method of this invention are more obvious, verifying that the invention can indeed improve the reconstruction fidelity, stability, and reliability of subsequent diffusion characterization in complex tissue regions.

[0051] In summary, this invention models the diffusion magnetic resonance angle super-resolution problem as a multi-stage progressive reconstruction process, jointly modeling the coupling dependency between the spatial and angular domains within a unified framework through a space-angle autoregressive unit. Addressing the problem of existing methods' difficulty in capturing global correlations, this invention designs a global context modeling module incorporating patch serialization and selective scanning mechanisms. This achieves cross-regional and cross-angle information propagation with linear computational complexity, enabling the model to capture long-range structural consistency across the entire brain. Addressing the problem of existing methods' lack of intermediate supervision, this invention introduces a multi-stage auxiliary supervision loss, supervising the complete angular state at each stage, and combining this with a scheduling function that increases with each training epoch to form a progressive training strategy from lenient to strict, effectively suppressing error accumulation. Addressing the problem of existing methods' neglect of geometric and physical priors, this invention introduces constraints in both the angular and physical domains: in the angular domain, a K-nearest neighbor graph is constructed based on the spherical geometric proximity of the diffusion gradient direction to constrain the consistency of prediction results in adjacent directions; in the physical domain, the signal is transformed to the spherical harmonic coefficient domain, and non-physical high-frequency oscillations are eliminated through high-order energy suppression. Furthermore, this invention employs an optimization strategy that prioritizes unknown cases and weights difficult examples, focusing model training on the truly needed unknown angles and angles that are difficult to reconstruct. Through the synergistic effect of these designs, this invention can reconstruct high-angle-resolution diffusion signals from low-angle-resolution data with high fidelity, significantly improving the accuracy and reliability of diffusion tensor parameter estimation, and providing strong technical support for clinical diagnosis and scientific research analysis.

[0052] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0053] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0054] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0055] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0056] 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 each specific application, but such implementations should not be considered beyond the scope of this invention.

[0057] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0058] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of 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 device, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0059] 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.

[0060] In addition, the functional units in the various embodiments of the present invention 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.

[0061] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0062] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for training a diffusion magnetic resonance angle super-resolution network, characterized in that, The method includes: Acquire training data pairs, which include initial state data as input to the model and high-angle resolution diffusion-weighted imaging data as supervised ground truth, wherein the initial state data is obtained by zero-padding low-angle resolution diffusion-weighted imaging data; An angle super-resolution network is constructed, which includes multiple cascaded spatial-angle autoregressive units. The spatial-angle autoregressive units generate incremental predictions for the current stage based on the output of the previous stage and update the state by splicing through the channel dimension. The spatial-angle autoregressive units also include at least a data consistency constraint module to force the real signal in the low-angle resolution diffusion-weighted imaging data to be retained at the corresponding angle position of the prediction result. The angle super-resolution network is trained using the training data to obtain a trained angle super-resolution network. During the training process, a joint loss function is used to optimize the model parameters. The joint loss function includes at least the following: Unknown angle reconstruction loss is used to supervise the difference between the predicted results of unsampled angles and the supervised ground truth. Multi-stage auxiliary supervision loss is used to supervise the difference between the complete angle state output at each stage and the supervision truth value. The spatial-angle autoregressive unit generates incremental predictions for the current stage based on the output of the previous stage, including: The output of the previous stage is compressed and encoded using an encoder to obtain a spatial feature map; The global context modeling module is used to capture the long-range dependencies between the spatial and angular dimensions of the spatial feature map, so as to achieve deep aggregation of cross-regional structural and angular information; The decoder is used to recover the features output by the global context modeling module into a prediction signal with the same spatial resolution as the input; The predicted signal is corrected using the data consistency constraint module. The corrected forecast results are mapped to the incremental forecast for the current stage.

2. The method of claim 1, wherein, The global context modeling module is used to capture the long-range dependencies between the spatial and angular dimensions of the spatial feature map, including: The spatial feature map is transformed from spatial to sequential by using pixel unshuffling and rearrangement operations to obtain serialized features; The serialized features are modeled globally using a selective scanning mechanism to obtain updated sequence features. The updated sequence features are restored to a two-dimensional spatial topology using inverse rearrangement and pixel shuffling operations, and residual connections are made with the spatial feature map to obtain the output features of the global context modeling module.

3. The training method for the diffuse magnetic resonance angle super-resolution network according to claim 1, characterized in that, The joint loss function also includes any one or more of the following losses: The orientation consistency regularization loss is used to supervise the differences between predictions for each angle within the nearest neighbor set in the spherical neighborhood graph; The spherical harmonic coefficient domain constraint loss is used to supervise the difference between the spherical harmonic coefficients of the predicted signal and the spherical harmonic coefficients of the supervised true value, and to suppress the energy of higher-order spherical harmonic coefficients. The difficult angle loss is used to supervise the difference between the prediction results and the supervised ground truth in a preset subset of the most difficult unknown angles selected based on the reconstruction error scores of each unknown angle.

4. The method of claim 1 or 3, wherein, The unknown angle reconstruction loss L rec is defined as: ， In the formula, Ω u is a set of unknown angles, X T,i is a predicted value of the i-th angle by the angle super-resolution network, Y gt,i is a true value of the i-th angle, and || ||1 is an L1 norm, is a Charbonnier function, and ε is a smoothing parameter.

5. The method of claim 1 or 3, wherein, The multi-stage auxiliary supervision loss L aux Defined as: ， In the formula, s(e) is the scheduling function that gradually increases with each training round, and W rep The image represents the spatially adaptive weighted graph copied along the channel dimension, and P is the prediction tensor composed of intermediate prediction results from each stage of the angle super-resolution network. This represents the replicated truth tensor corresponding to the predicted tensor, ⊙ denotes element-wise multiplication, |||1 is the L1 norm, and λ grad These are the weighting coefficients of the gradient constraint term. x and y These represent the horizontal and vertical gradient operators, respectively.

6. The method of claim 3, wherein, the direction consistency regular loss L angle is defined as: ， ， ， In the formula, S is the set of angles for which graph constraints need to be applied, which is a subset of the set of unknown angles; N(i) is the set of nearest neighbors of angle i in the spherical neighborhood graph; X T,i and X T,j , respectively, are the predicted values ​​of the angle super-resolution network for the i-th and j-th angles; ||||1 is the L1 norm; ρ() is the Charbonnier function; a ij θ ij These are the neighborhood weights before and after normalization, respectively; σ is the Gaussian kernel width parameter; clip() is the truncation operation.

7. The method of claim 3, wherein the method further comprises: determining a plurality of diffusion magnetic resonance angles; and training the diffusion magnetic resonance angle super-resolution network using the plurality of diffusion magnetic resonance angles. the spherical harmonic coefficient domain constraint loss L sh is defined as: ， ， In the formula, λ sh , λ lb These are the spherical harmonic coefficient consistency loss weighting coefficient and the higher-order energy suppression weighting coefficient, respectively; c pred c gt c represents the spherical harmonic coefficients corresponding to the predicted signal and the supervision ground truth signal output by the angle super-resolution network, respectively. pred,k ω represents the spherical harmonic coefficient corresponding to the predicted value of the k-th angle by the angle super-resolution network; k The order weight of the k-th coefficient, n k Let be the order corresponding to the k-th spherical harmonic coefficient.

8. The method of claim 3, wherein, The difficult example angle loss L hard is defined as: ， ， ， In the formula, Ω u Ω is a set of unknown angles. K To select the Top-K most difficult subsets of unknown angles based on error scores, w i Let X be the weight of the i-th angle. T,i Y is the predicted value of the angle super-resolution network for the i-th angle. gt,i Let ||i||1 be the truth value of the i-th angle, ||i||1 be the L1 norm, and ρ() be the Charbonnier function; i The error score for the i-th angle is given by τ, where τ is the temperature coefficient; H and W are the tensor sizes of the prediction value of the i-th angle by the angle super-resolution network, and p represents the spatial location index.

9. An angular super-resolution method, characterized in that, The method includes: Acquire low-angle resolution diffusion-weighted imaging data to be super-resolution; The low-angle resolution diffusion-weighted imaging data to be super-resolution is subjected to zero-filling processing to obtain the initial state data to be processed. The initial state data to be processed is input into the trained angle super-resolution network to obtain high-angle resolution diffusion-weighted imaging data after super-resolution, wherein the trained angle super-resolution network is trained according to the training method of diffusion magnetic resonance angle super-resolution network according to any one of claims 1 to 8.

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