Multi-contrast magnetic resonance reconstruction method based on K-space iteration generation and calibration

Abstract

The invention discloses a multi-contrast magnetic resonance reconstruction method based on K-space iteration generation and calibration, which comprises the following steps of: 1) preparing an image data set, preprocessing the image data set, and dividing the image data set into three parts, namely a training data set, a verification data set and a test data set; 2) constructing a K-space iteration model iKNN, training the K-space iteration model iKNN by using the training data set, verifying a training result of the K-space iteration model iKNN by using the verification data set, and obtaining a trained K-space iteration model iKNN; and 3) introducing an iterative solution algorithm to the K-space iterative model iKNN to test the test data set, and outputting to obtain a reconstructed image. According to the method, for the undersampled part of the magnetic resonance image, reconstruction is carried out by utilizing complementary information in multi-contrast data, so that the structural details of the image are effectively reserved, clear image edges and texture details are obtained, and more efficient and more robust rapid magnetic resonance image reconstruction is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image processing, and particularly relates to a multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration. Background Art

[0002] Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging technology widely used in clinical practice. The reconstruction of magnetic resonance images depends on a large amount of acquired data, and the acquisition of data involves a series of complex physical processes, and each scan takes a long time. The long scan time may not only cause discomfort to patients, but also affect the imaging quality due to factors such as motion artifacts, thereby reducing the accuracy of diagnosis. The research on fast magnetic resonance image reconstruction algorithms, intuitively speaking, is to reduce the amount of data acquisition to achieve the purpose of accelerating the imaging speed. However, the reduction of data acquisition will inevitably bring adverse effects, such as imaging aliasing, artifacts and other problems. Therefore, it is necessary to design an efficient reconstruction algorithm to effectively reconstruct the undersampled part in order to obtain high-quality images while accelerating magnetic resonance scanning.

[0003] Traditional magnetic resonance image reconstruction techniques have made significant progress in the field of image reconstruction and have improved the imaging quality and imaging speed to a certain extent. However, with the continuous growth of the demand for MRI accelerated imaging, especially in high-acceleration scenarios, traditional methods often face problems such as loss of image details, enhanced artifacts, and decreased signal-to-noise ratio, seriously affecting the quality and clinical usability of the reconstructed images. With the continuous breakthroughs of deep learning techniques in the fields of computer vision and natural image processing, fast magnetic resonance imaging reconstruction methods based on deep learning have gradually become a research hotspot.

[0004] Currently, most deep learning-based multi-contrast magnetic resonance image reconstruction methods mainly focus on the reconstruction of single-contrast magnetic resonance images, that is, learning prior information from single-contrast magnetic resonance image data and performing magnetic resonance image reconstruction based on this to achieve the purpose of accelerating imaging. However, such methods largely ignore the complementary information between different-contrast magnetic resonance data, making it impossible for image reconstruction to fully utilize the rich information contained in existing multi-contrast magnetic resonance images, affecting the quality and diagnostic value of the final reconstructed images. Summary of the Invention

[0005] The object of the present invention is to provide a multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration in view of the deficiencies of the prior art, which uses T1WI with a shorter imaging time to accelerate the imaging process of T2WI which takes relatively longer time; and for the under-sampled part of the magnetic resonance image, reconstruction is performed by using complementary information in the multi-contrast data, effectively retaining the structural details of the image, obtaining clear image edges and texture details, and realizing more efficient and robust fast magnetic resonance image reconstruction.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions.

[0007] A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration, comprising the following steps: Step S1, prepare an image data set, and after preprocessing the image data set, divide the image data set into three parts: a training data set, a validation data set and a test data set. The image data set includes the open-source brain data set Brainweb and the open-source data set M4Raw; The open-source brain data set Brainweb initially contains 150 two-dimensional single-coil complex magnetic resonance images, and the open-source data set M4Raw initially contains 1,000 two-dimensional four-coil complex magnetic resonance images; after preprocessing, the open-source brain data set Brainweb is data-augmented to 1,200 two-dimensional single-coil complex magnetic resonance images, and the open-source data set M4Raw is data-augmented to 2,000 two-dimensional four-coil complex magnetic resonance images, and the images in the open-source brain data set Brainweb and the open-source data set M4Raw are uniformly cropped to a size of 256×256 by equal-proportion scaling; Step S2, construct a K-space iterative model iKNN, use the training data set to train the K-space iterative model iKNN, use the validation data set to verify the training result of the K-space iterative model iKNN, and obtain a trained K-space iterative model iKNN after the training result of the K-space iterative model iKNN is fitted; Step S3, introduce an iterative solution algorithm into the trained K-space iterative model iKNN to test the test data set, and output a reconstructed image.

[0008] Specifically, the image data set in step S1 includes paired fully sampled T1WI data and under-sampled T2WI data, and the ratio of the training data set, the validation data set and the test data set in the image data set is 8:1:1.

[0009] Specifically, the K-space iterative model iKNN described in step S2 is constructed by replacing the input of the traditional invertible neural network INN with dual-channel data including fully sampled T1WI data and undersampled T2WI data. The invertible neural network INN consists of multiple invertible blocks. Assuming X represents the input, Y represents the output, a set of latent variables Z is introduced, and the latent variables Z follow a normal distribution. The input and output of each invertible block are divided into two parts, respectively represented as and , then the forward calculation path of each invertible block is represented as: ; In the above formula, , , , are learning functions in the neural network; is the Hadamard product; exp(*) is the exponential function; and are the transformation results of the input after passing through the learning function; and are the transformation results of the output after passing through the learning function. The output is transformed from the input through the learning function and coupled in an alternating manner; The reverse calculation path of each invertible block is represented as: .

[0010] Furthermore, the invertible block consists of an affine coupling layer. In each affine coupling layer, d-dimensional input vector is divided into two unequal parts along the channel dimension and , where ; the corresponding output vector is represented as: ; ; In the above formula, and are the scale and dimension transformation function of the dimensional transformation process respectively, represents a d-dimensional vector; To avoid the order of some input channels remaining unchanged in the affine coupling layer and limit the representative learning ability of the K-space iterative model iKNN architecture, a new dimension transformation function is introduced to enhance the affine coupling layer. For the enhanced affine coupling layer, the corresponding output vector v is represented as: ; In the above formula, is the dimensionality conversion function from the dimensionality conversion process; The inverse process of the enhanced affine coupling layer is expressed as: ; ; Next, use the invertible convolution as a learnable permutation function to reverse the channel order of the next affine coupling layer to avoid some input channel orders in the affine coupling layer remaining unchanged.

[0011] Specifically, in step S2, the training dataset is used to train the K-space iterative model iKNN. In order to achieve the detail recovery of the high-frequency region in the K-space during the magnetic resonance imaging reconstruction process, a multi-stage training strategy is adopted for the K-space iterative model iKNN. The K-space iterative models iKNN at different sampling rates are stacked to iteratively refine the undersampled input. The specific training process is as follows: Step S21: Use the undersampled T2WI data at different sampling rates to train N independent K-space iterative models iKNN for image reconstruction. Name these N independent K-space iterative models iKNN as the iKNN model , , for each iKNN model , combine the undersampled T2WI data and the fully sampled T1WI data to construct dual-channel data with a size of 256×256; Step S22: Adopt a variable enhancement method to make the dimensions of the input and output of the K-space iterative model iKNN network consistent, and separate the real and imaginary parts through a weighting strategy to obtain training data of 256×256×4; Step S23: According to the training data obtained in step S22, adopt a two-way training strategy based on a smooth loss function, and optimize and train the K-space iterative model iKNN by minimizing the smooth loss function. The mathematical expression for minimizing the smooth loss function L is: ; In the above formula, is the forward training loss; is the backward training loss; is the real target image; K is the undersampled T2WI image; is the output image reconstructed by the K-space iterative model iKNN based on the undersampled T2WI image; is the undersampled T2WI image obtained by the K-space iterative model iKNN in reverse based on the output image; represents the smooth Loss, assuming represents the error between the predicted value and the real image, then the smoothed loss is expressed as: .

[0012] Furthermore, the variable enhancement method in step S22 maps data points from the input data to the output data by designing a bijective function , and the bijective function consists of a series of invertible and operable Jacobian determinants transformations. m is the number of transformations. The invertible and operable Jacobian determinant is the normalizing flow. For a given input k , through the invertible transformation, the normalized reconstructed data y is obtained to make the dimensions of the input and output of the iKNN model network consistent. The mapping relationship for the invertible transformation to achieve bidirectional conversion between the input and output is as follows: ; ; In the above formula, represents function nesting; is the output of the m-th invertible block, and is the output corresponding to its reverse process.

[0013] Even further, the weighting strategy in step S22 includes the following: Introduce a K-space weighting strategy. By processing the original K-space data and learning prior information in the weighted K-space domain, the influence brought by the problem of uneven dynamic range of the K-space data is eliminated. The mathematical expression of the K-space weighting strategy is: ; In the above formula, is the input data matrix in the K-space domain; is the weight matrix, is the data matrix in the weighted K-space domain; is the frequency-encoding row, is the phase-encoding row; c represents the cut-off value coefficient; is the smoothness coefficient of the weight boundary.

[0014] Specifically, the iterative solution algorithm in step S3 uses multiple trained K-space iterative models iKNN for iterative refinement reconstruction, and embeds data consistency operations between each K-space iterative model iKNN to ensure the reconstruction quality. The specific process is as follows: First, stack the fully sampled T1WI data and the undersampled T2WI data with a sampling rate of R into dual-channel data as the initial input of the K-space iterative model iKNN network, and use the K-space weighting strategy to process the dual-channel data. After passing through a K-space iterative model iKNN, divide the output result by the weighted weight to de-weight; Then perform a data consistency operation for calibration and use it as the input of the next K-space iterative model iKNN; After that, during the iterative reconstruction process, gradually increase the sampling rate R of the undersampled T2WI data, and repeatedly perform the data consistency operation, so as to retain the structural information of the original data to the greatest extent, reduce the errors and distortions introduced during the reconstruction process, obtain high-quality undersampled T2WI data, make the final reconstruction result match the original T2WI information, and finally apply the inverse Fourier transform Perform image reconstruction on the processed data to obtain the reconstruction result 。

[0015] Furthermore, the mathematical expression of the data consistency operation is as follows: ; In the above formula, is the undersampled T2WI data after the data consistency operation; is the data of the observed undersampled T2WI data at the index j ; is the index set of the obtained observed undersampled T2WI data; is the data at the index in the T2WI data; represents the weight coefficient that balances the influence of K-space measurement noise on the reconstruction. Under the noiseless setting , if the data at the -th index position has been sampled, then is replaced with the original weight coefficient.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The method of the present invention utilizes the high-dimensional similarity between different contrast image data to reconstruct magnetic resonance images from highly undersampled K-space data. By fully utilizing the additional information provided by the fully sampled T1WI data, high-quality and fast reconstruction of undersampled T2WI is achieved.

[0017] 2. The method of the present invention combines undersampled T1WI data and fully sampled T1WI data with different sampling rates as input to train a series of iKNN models; subsequently, the trained iKNN models are used for iterative refinement, starting from the low-frequency region of the K-space data that is relatively easier to recover and gradually expanding to the high-frequency region; after the initial reconstruction is completed, by adjusting the sampling rate of the intermediate reconstruction result and passing it to the next model, each adjustment of the sampling rate helps to extract more prior information about the low-frequency region in the K-space image reconstructed by the previous model; through multiple iterations, the recovery range of the undersampled T2WI is gradually expanded from the low-frequency region to the high-frequency region, and finally a high-quality T2WI reconstructed image is obtained.

[0018] 3. The robustness of the method of the present invention is demonstrated by the results of multiple different image reconstruction experiments. Compared with a variety of traditional magnetic resonance image reconstruction methods, the method of the present invention has better performance, which proves its effectiveness and potential in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flowchart of the method of the present invention; Figure 2 is a model architecture diagram of the K-space iterative generation and calibration network of the present invention; Figure 3 is a reconstructed result diagram of the test image in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] To facilitate the understanding and implementation of the present invention by those of ordinary skill in the art, the following provides a detailed description of each step of the method proposed by the present invention. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0021] Embodiment As Figure 1 shown, the present invention discloses a multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration, including the following steps: Step S1. Prepare an image data set, and after preprocessing the image data set, divide the image data set into three parts: a training data set, a validation data set, and a test data set. The image data set includes the open-source brain data set Brainweb and the open-source data set M4Raw; The open-source brain dataset Brainweb initially contains 150 two-dimensional single-coil complex magnetic resonance images, and the open-source dataset M4Raw initially contains 1,000 two-dimensional four-coil complex magnetic resonance images. After preprocessing, the data of the open-source brain dataset Brainweb is augmented to 1,200 two-dimensional single-coil complex magnetic resonance images, and the data of the open-source dataset M4Raw is augmented to 2,000 two-dimensional four-coil complex magnetic resonance images. Moreover, the images in the open-source brain dataset Brainweb and the open-source dataset M4Raw are uniformly cropped to a size of 256×256 through equal-proportion scaling. Step S2: Construct an iterative K-space model iKNN, train the iterative K-space model iKNN using the training dataset, verify the training results of the iterative K-space model iKNN using the validation dataset, and obtain the trained iterative K-space model iKNN after fitting the training results of the iterative K-space model iKNN. Step S3: Introduce an iterative solution algorithm in the trained iterative K-space model iKNN to test the test dataset, and output the reconstructed image.

[0022] Specifically, the image dataset in step S1 includes paired fully sampled T1WI data and undersampled T2WI data, and the ratio of the training dataset, validation dataset, and test dataset in the image dataset is 8:1:1.

[0023] Specifically, in step S2, the construction of the iterative K-space model iKNN is as Figure 2 shown in (c) below. The constructed iterative K-space model iKNN is obtained by replacing the input of the traditional invertible neural network INN with a two-channel data containing fully sampled T1WI data and undersampled T2WI data. As Figure 2 shown in (a) below, the invertible neural network INN consists of multiple invertible blocks. As Figure 2 shown in (b) below, each invertible block consists of an invertible convolutional layer and an affine coupling layer. In the affine coupling layer, the input is divided into two parts along the channel dimension. The significant advantage of this feature is that it can retain the specific structure of images with different contrasts and only learn the potential correlation between them, which helps the learning of multi-contrast MRI imaging. 、 and are transformation functions, which consist of 5 two-dimensional convolutional layers with a size of . Each layer learns a new set of feature maps from the previous layer. The receptive field size of the first four convolutional layers is , and the stride is 2. Finally, there is a rectified linear unit ReLU. The purpose of the ReLU layer is to avoid overfitting the training set, thereby further increasing the non-linearity.

[0024] Assume that X represents the input, Y represents the output, a set of latent variables Z is introduced, and the latent variables Z follow a normal distribution. The input and output of each reversible block are divided into two parts, denoted as and , respectively. Then the forward calculation path of each reversible block is expressed as: ; In the above formula, , , , are learning functions in the neural network; is the Hadamard product; exp(*) is the exponential function; and are the conversion results of the input through the learning function; and are the conversion results of the output through the learning function. The output is converted from the input through the learning function and coupled in an alternating manner; The reverse calculation path of each reversible block is expressed as: .

[0025] Furthermore, the reversible block is composed of an affine coupling layer. In each affine coupling layer, the d-dimensional input vector is divided into two unequal parts along the channel dimension and , where ; the corresponding output vector is expressed as: ; ; In the above formula, and are the dimension conversion process ratio and the dimension conversion function of respectively, represents a d-dimensional vector; To avoid the representative learning ability of the K-space iterative model iKNN architecture being restricted due to the order of some input channels remaining unchanged in the affine coupling layer, a new dimension conversion function is introduced to enhance the affine coupling layer. For the enhanced affine coupling layer, the corresponding output vector v is expressed as: ; In the above formula, is the dimension conversion function from the dimension conversion process; The inverse process of the enhanced affine coupling layer is expressed as: ; ; Next, a reversible convolution is used as a learnable permutation function to reverse the channel order of the next affine coupling layer, so as to avoid some input channel orders in the affine coupling layer remaining unchanged.

[0026] Specifically, in step S2, the training dataset is used to train the K-space iterative model iKNN. In order to achieve the detail recovery of the high-frequency region of the K-space in the magnetic resonance imaging reconstruction process, a multi-stage training strategy is adopted for the K-space iterative model iKNN, stacking the iKNN models at different sampling rates, and iteratively refining the undersampled input. The specific training process is as follows: Step S21: Undersampled T2WI data with different sampling rates are used to train N independent K-space iterative models iKNN for image reconstruction, and the N independent K-space iterative models iKNN are named iKNN models , respectively. For each iKNN model , the undersampled T2WI data and the fully sampled T1WI data are combined to construct dual-channel data with a size of 256×256; Step S22: A variable enhancement method is adopted to make the dimensions of the input and output of the K-space iterative model iKNN network consistent, and the real and imaginary parts are separated through a weighting strategy to obtain training data of 256×256×4; Step S23: According to the training data obtained in step S22, a two-way training strategy based on a smooth loss function is adopted, and the K-space iterative model iKNN is optimized and trained by minimizing the smooth loss function. The mathematical expression of minimizing the smooth loss function L is: ; In the above formula, is the forward training loss; is the backward training loss; is the real target image; K is the undersampled T2WI image; is the output image reconstructed by the K-space iterative model iKNN according to the undersampled T2WI image; is the undersampled T2WI image obtained by the K-space iterative model iKNN in reverse according to the output image; represents the smooth loss. Assuming represents the error between the predicted value and the real image, then the smooth loss is expressed as: .

[0027] Furthermore, the variable enhancement method in step S22 maps data points from the input data to the output data by designing a bijective function , and the bijective function consists of a series of invertible and operable Jacobian determinants transformations. Here, m is the number of transformations. For a given input k , through an invertible transformation, the normalized reconstructed data y is obtained to make the dimensions of the input and output of the K-space iterative model iKNN network consistent. The mapping relationship of the invertible transformation for bidirectional conversion between the input and output is as follows: ; ; In the above formula, represents function nesting; is the output of the m-th invertible block, and is the output of its reverse process.

[0028] The variable enhancement technology not only simply copies data, but also provides high-dimensional prior information for the K-space iterative model iKNN network. By introducing diversity and complexity, it enhances the K-space iterative model iKNN network's ability to understand and abstract data, and helps the K-space iterative model iKNN network extract the inherent feature information of the data. The introduction of this prior information effectively improves the performance and generalization ability of the K-space iterative model iKNN network, making the K-space iterative model iKNN network perform more robustly and reliably when processing complex medical image data.

[0029] Furthermore, the weighting strategy described in step S22 includes the following: Since the pixel amplitude ranges at various positions in the magnetic resonance image domain data are similar, normalizing the image data has little impact on the overall feature distribution; this characteristic is of great significance in image processing because it means that when normalizing the image, not too much information distortion or deviation will be introduced; in contrast, the features of K-space data exhibit distinct low-frequency and high-frequency components in the frequency spectrum, concentrated in the center and surrounding regions of the frequency spectrum respectively; therefore, there are significant differences in the amplitudes between adjacent pixels in the center and the surrounding; this imbalance in the dynamic range poses certain challenges to K-space data processing, especially when applied in the K-space iterative model iKNN, which may affect the training and generalization capabilities of the model. To overcome these problems, a K-space weighting strategy is introduced in this embodiment. By processing the original K-space data and learning prior information in the weighted K-space domain, the impact brought by the problem of uneven K-space data dynamic range is eliminated. The mathematical expression of the K-space weighting strategy is: ; In the above formula, is the input data matrix in the K-space domain; is the weight matrix, is the data matrix in the weighted K-space domain; is the frequency-encoding row, is the phase-encoding row; c represents the cut-off value coefficient; is the smoothness coefficient of the weight boundary.

[0030] Specifically, for the iterative solution algorithm described in step S3, multiple trained K-space iterative models iKNN are used for iterative refinement reconstruction, and a data consistency operation is embedded between each K-space iterative model iKNN to ensure the reconstruction quality. The specific process is as follows: First, the fully sampled T1WI data and the undersampled T2WI data with a sampling rate of R are stacked into dual-channel data as the initial input of the K-space iterative model iKNN network, and the K-space weighting strategy is used to process the dual-channel data. After passing through a K-space iterative model iKNN, the output result is de-weighted by dividing it by the weighted weights. Then, a data consistency operation is performed for calibration and used as the input of the next K-space iterative model iKNN. After that, during the iterative reconstruction process, the sampling rate R of the undersampled T2WI data is gradually increased, and the data consistency operation is repeatedly performed, so as to retain the structural information of the original data to the greatest extent, reduce the errors and distortions introduced during the reconstruction process, obtain high-quality undersampled T2WI data, make the final reconstruction result match the original T2WI information, and finally apply the inverse Fourier transform to perform image reconstruction on the processed data to obtain the reconstruction result 。

[0031] Furthermore, the mathematical expression of the data consistency operation is as follows: ; In the above formula, is the undersampled T2WI data after the data consistency operation; is the data of the observed undersampled T2WI data at index j ; is the index set of the acquired observed undersampled T2WI data; is the data at index in the T2WI data; represents the weight coefficient for balancing the influence of K-space measurement noise on reconstruction. Under the setting of no noise , if the data at the -th index position has been sampled, then is replaced with the original weight coefficient.

[0032] Next, through a specific magnetic resonance imaging reconstruction experiment, the technical effects of the method of the present invention will be further described.

[0033] The experimental implementation configuration and settings are as follows: Under the PyTorch framework, 2 NVIDIA Titan XP GPUs are used for training and reconstruction to implement the method of the present invention. For the reversible neural network INN, its core module is the reversible block, which consists of a reversible 1×1 convolution and an affine coupling layer; in the affine coupling layer, the input is divided into two parts along the channel dimension, and multi-contrast features are extracted through 5 layers of dense convolution blocks, with the convolution kernel size of each layer being 3×3 and the activation function being LeakyReLU. During the training process, the Adam optimizer is adopted, with an initial learning rate of 1×10 -5 , decaying to half value every 25 epochs, the batch size is 1, and the total number of training rounds is 300. During the reconstruction process, the total number of iteration steps is 4 times, and each iteration corresponds to different sampling rates (10%→20%→40%→60%).

[0034] To reflect the magnetic resonance image reconstruction quality of the method of the present invention, the method of the present invention is compared with the traditional P-LORAKS algorithm, the K-space interpolation algorithm ACNN, and U-net in terms of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the images, and their reconstruction performances under different sampling modes and sampling rates are evaluated. As Figure 3As shown in (a), the results of magnetic resonance image reconstruction indicate that there are still obvious aliasing artifacts and blurred lesion areas (such as tumor boundaries) in the traditional P-LORAKS algorithm at high acceleration factors. The K-space interpolation algorithm ACNN has insufficient noise suppression and loses image texture details. Although U-net retains some structures, there is a loss of spatial resolution. The method of the present invention can effectively suppress artifacts and retain clear tissue boundaries and textures.

[0035] To evaluate the performance stability of the method of the present invention at different sampling rates, taking the radial sampling mode as an example, the present invention sets sampling rates of 10%, 20%, 40%, and 60%, and compares the differences in the performance of magnetic resonance image reconstruction between the method of the present invention and traditional methods in the radial sampling mode with a sampling rate of 10%, as Figure 3 As shown in (b), the image reconstruction results in the radial sampling mode with a sampling rate of 10% are presented, and the comparison results of image reconstruction performance are shown in Table 1 below.

[0036] Table 1. Comparison of Image Reconstruction Performance 。

[0037] It can be clearly seen from the data in Table 1 above that in each sampling mode, the average PSNR value of the reconstructed images of the K-space iterative model iKNN proposed by the present invention on the Brainweb dataset is higher than that of other models. Compared with the U-net model, the PSNR of the K-space iterative model iKNN proposed by the present invention in the radial sampling mode is increased by 1.62 dB. In addition, in the radial sampling mode, the average PSNR and SSIM results of 20 test images reconstructed by the K-space iterative model iKNN are 3.94 dB and 0.095 higher than those of the P-LORAKS model respectively. And compared with the existing ACNN model based on K-space reconstruction method, in the random sampling mode, the K-space iterative model iKNN increases the PSNR from 22.28 dB to 25.03 dB. On the M4Raw dataset, although the PSNR value of the K-space iterative model iKNN is slightly lower than that of the P-LORAKS model, the SSIM value is higher than that of the P-LORAKS model, which indicates that the reconstruction results of the K-space iterative model iKNN and the real images have good structural similarity. Using different reconstruction methods may result in a certain trade-off between peak signal-to-noise ratio and structural similarity. Although the K-space iterative model iKNN is slightly inferior in terms of PSNR, its reconstruction results are superior to the P-LORAKS model in terms of image structure preservation and blurring degree. This means that the K-space iterative model iKNN proposed by the present invention can reconstruct in a way closer to the real image, and the generated images have clearer and more accurate details and content. This is of great significance for application fields that require maintaining structural similarity.

[0038] In summary, the experimental results of multiple different image reconstructions demonstrate the robustness of the K-space iterative model iKNN proposed by the present invention. Moreover, by comparing with a variety of traditional magnetic resonance image reconstruction methods, it is proved that the K-space iterative model iKNN proposed by the present invention is effective and has potential in practical applications.

[0039] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration, characterized in that, It includes the following steps: Step S1: Prepare an image dataset. After preprocessing the image dataset, divide the image dataset into three parts: a training dataset, a validation dataset, and a test dataset. The image dataset includes the open-source brain dataset Brainweb and the open-source dataset M4Raw; The open-source brain dataset Brainweb initially contains 150 two-dimensional single-coil complex magnetic resonance images, and the open-source dataset M4Raw initially contains 1,000 two-dimensional four-coil complex magnetic resonance images. After preprocessing, the open-source brain dataset Brainweb is data-augmented to 1,200 two-dimensional single-coil complex magnetic resonance images, and the open-source dataset M4Raw is data-augmented to 2,000 two-dimensional four-coil complex magnetic resonance images. Moreover, the images in the open-source brain dataset Brainweb and the open-source dataset M4Raw are uniformly cropped to a size of 256×256 through equal-proportion scaling; Step S2: Construct a K-space iterative model iKNN. Use the training dataset to train the K-space iterative model iKNN, use the validation dataset to verify the training results of the K-space iterative model iKNN, and obtain a trained K-space iterative model iKNN after the training results of the K-space iterative model iKNN are fitted; Step S3: Introduce an iterative solution algorithm into the trained K-space iterative model iKNN to test the test dataset, and output a reconstructed image.

2. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 1, characterized in that In Step S1, the image dataset includes paired fully sampled T1WI data and undersampled T2WI data, and the ratio of the training dataset, the validation dataset, and the test dataset in the image dataset is 8:1:

1.

3. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 1, characterized in that, In step S2, the K-space iterative model iKNN is constructed. The constructed K-space iterative model iKNN is obtained by replacing the input of the traditional invertible neural network INN with dual-channel data including fully sampled T1WI data and undersampled T2WI data. The invertible neural network INN is composed of multiple invertible blocks. Assuming that X represents the input, Y represents the output, a set of latent variables Z is introduced, and the latent variable Z follows a normal distribution. The input and output of each invertible block are divided into two parts, which are respectively represented as and , then the forward calculation path of each invertible block is expressed as: ； In the above formula, , , , are learning functions in the neural network; is the Hadamard product; exp(*) is the exponential function; and are the conversion results of the input passing through the learning function; and are the conversion results of the output passing through the learning function, and the output is converted from the input passing through the learning function and coupled in an alternating manner; The reverse calculation path of each reversible block is expressed as: 。 4. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 3, characterized in that, The reversible block consists of affine coupling layers. In each affine coupling layer, The input vector of dimension is divided into two unequal parts along the channel dimension and , where ; the corresponding output vector is expressed as: ； ； In the above formula, and are respectively the ratio and the dimensionality conversion function of the dimensionality conversion process, represents a d-dimensional vector; To avoid the situation where the order of some input channels in the affine coupling layer remains unchanged, which restricts the representative learning ability of the K-space iterative model iKNN architecture, a new dimension transformation function is introduced to enhance the affine coupling layer. For the enhanced affine coupling layer, the corresponding output vector v is expressed as: ； In the above formula, is the dimensionality conversion function of the dimensionality conversion process; The inverse process of the enhanced affine coupling layer is expressed as: ； ； Next, use an invertible convolution as a learnable permutation function to reverse the channel order of the next affine coupling layer, so as to avoid that the order of some input channels in the affine coupling layer always remains unchanged.

5. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 1, wherein In Step S2, when using the training dataset to train the K-space iterative model iKNN, in order to realize the detail recovery of the high-frequency region of the K-space in the magnetic resonance imaging reconstruction process, a multi-stage training strategy is adopted for the K-space iterative model iKNN. Stack the K-space iterative models iKNN at different sampling rates, and iteratively refine the undersampled input. The specific training process is as follows: Step S21: Use undersampled T2WI data with different sampling rates to train N independent K-space iterative models iKNN for image reconstruction, and name these N independent K-space iterative models iKNN as iKNN models in sequence. , For each iKNN model , combine the undersampled T2WI data and the fully sampled T1WI data to construct dual-channel data with a size of 256×256. Step S22: Adopt a variable enhancement method to make the dimensions of the input and output of the K-space iterative model iKNN network consistent, and separate the real part and the imaginary part through a weighting strategy to obtain training data of 256×256×4; Step S23: According to the training data obtained in step S22, adopt a two-way training strategy based on a smoothed loss function, and optimize and train the K-space iterative model iKNN by minimizing the smoothed loss function, minimizing the smoothed loss function L The mathematical expression of which is: ； In the above formula, is the forward training loss; is the backward training loss; is the real target image; K is the undersampled T2WI image; is the output image reconstructed by the K-space iterative model iKNN from the undersampled T2WI image; is the undersampled T2WI image obtained backward by the K-space iterative model iKNN from the output image; represents smoothed loss. Assuming represents the error between the predicted value and the real image, then the smoothed loss is expressed as: 。 6. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 5, characterized in that The variable enhancement method in step S22 maps data points from the input data to the output data by designing a bijective function , and the bijective function consists of a series of invertible and operable Jacobian determinants transformations. m is the number of transformations. The invertible and operable Jacobian determinant, for a given input k , obtains the normalized reconstructed data y through an invertible transformation, so that the dimensions of the input and output of the K-space iterative model iKNN network are consistent. The mapping relationship of the invertible transformation to achieve a two-way conversion between the input and output is as follows: ； ； In the above formula, represents function nesting; is the output of the m-th reversible block, is the output corresponding to its reverse process.

7. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 5, characterized in that, The weighting strategy described in Step S22 includes the following content: Introduce a K-space weighting strategy. By processing the original K-space data and learning prior information in the weighted K-space domain, eliminate the influence brought by the problem of uneven dynamic range of the K-space data. The mathematical expression of the K-space weighting strategy is: ； In the above formula, is the input data matrix in the K-space domain; is the weight matrix, is the weighted data matrix in the K-space domain; is the frequency encoding row, is the phase encoding row; c represents the cut-off value coefficient; is the smoothness coefficient of the weight boundary.

8. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 1, characterized in that In Step S3, the iterative solution algorithm uses multiple trained K-space iterative models iKNN for iterative refinement reconstruction, and embeds a data consistency operation between each K-space iterative model iKNN to ensure the reconstruction quality. The specific process is as follows: First, the fully sampled T1WI data and the undersampled T2WI data with a sampling rate of R are stacked into dual-channel data as the initial input of the K-space iterative model iKNN network, and the dual-channel data is processed using the K-space weighting strategy. After passing through a K-space iterative model iKNN, the output result is divided by the weighted weight to remove the weight; Then, a data consistency operation is performed for calibration and used as the input of the next K-space iterative model iKNN; After that, during the iterative reconstruction process, gradually increase the sampling rate R of the undersampled T2WI data, and repeatedly perform the data consistency operation, so as to retain the structural information of the original data to the greatest extent, reduce the errors and distortions introduced during the reconstruction process, obtain high-quality undersampled T2WI data, make the final reconstruction result match the original T2WI information, and finally apply the inverse Fourier transform Perform image reconstruction on the processed data to obtain the reconstruction result .

9. A multi-contrast magnetic resonance reconstruction method based on K-space iterative generation and calibration according to claim 8, characterized in that, The mathematical expression of the data consistency operation is as follows: ； In the above formula, is the undersampled T2WI data after data consistency operation; is the data of the observed undersampled T2WI data at the index j ; is the index set of the obtained observed undersampled T2WI data; is the data at the index in the T2WI data; represents the weight coefficient for balancing the influence of the K-space measurement noise on the reconstruction. Under the noise-free setting , if the data at the -th index position has been sampled, then is replaced with the original weight coefficient.

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