Magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning

Abstract

The present invention discloses a magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning. First, paired magnetic resonance images, non-Cartesian sampling k-space data, and polar angles and polar diameters of the polar coordinates of the sampling points are obtained as training sets, a density compensation reconstruction network is constructed, and then the density compensation reconstruction network is trained by the set total loss function. Through coordinate convolution, the sampling point polar coordinate 3D data and the non-Cartesian sampling k-space data are trained together, so that the convolution can perceive the sampling point position, thereby realizing density compensation through the convolution network. After the network training is completed, the non-Cartesian sampling k-space data to be processed and the sampling point polar coordinate 3D data are input into the trained density compensation reconstruction network, and density compensation and reconstruction can be performed quickly. The present invention greatly reduces the consumption of computing resources and time, and the density compensation and reconstruction effects are excellent, and no additional manual optimization is required during application.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence technology, and specifically relates to a magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning, which is suitable for magnetic resonance image reconstruction. Background Art

[0002] Non-Cartesian sampling technology in magnetic resonance imaging (MRI) has many advantages over Cartesian sampling, such as faster imaging speed, insensitivity to motion and fluid, and higher gradient power utilization efficiency.

[0003] A big disadvantage of MRI is that during scanning, slight movements of the subject (such as breathing, heart movement, blood flow, and other voluntary or involuntary movements) can cause blurring and ghost artifacts in the scanned image, which seriously reduces the image quality and affects the accuracy of post-processing operations such as image reading and automatic image segmentation and image registration. Since the traditional Cartesian sampling mode requires repeated application of multiple phase encoding gradients to completely cover the K space, the scanning time is relatively long and it is particularly susceptible to the influence of movement. Many non-Cartesian sampling modes have a high acquisition speed, which reduces the influence of movement on imaging to a certain extent.

[0004] Although non-Cartesian sampling has many advantages, it cannot be quickly promoted. One of the main reasons is that the reconstruction speed of non-Cartesian sampling is not fast enough. Because the non-Cartesian sampling points do not fall on the Cartesian grid points, the traditional fast Fourier transform reconstruction algorithm cannot be directly applied to the reconstruction of non-Cartesian sampling. The grid reconstruction algorithm is the most commonly used reconstruction algorithm for non-Cartesian sampling. The algorithm transforms the unequally spaced MRI data into an equally spaced linear grid through weighting, interpolation, resampling, etc. Compared with other algorithms, it has the advantages of fast calculation speed and simple algorithm.

[0005] Since non-Cartesian sampling often oversamples at the center of k-space and sparsely samples at the edge, the center part will have a greater weight during the interpolation process, so the sampling trajectory must be density compensated in the grid reconstruction algorithm. However, density compensation often takes a long time to calculate and cannot be completed in real time [Johnson KO et al., Magn. Reson. Med., 2009, 61: 439-447]. The commonly used method is to complete the calculation of the sampling density compensation function according to the distribution of the sampling trajectory points before imaging and save it, and then read these values ​​for use in the grid reconstruction process. However, even for the same sampling trajectory, the distribution of the sampling points will not be exactly the same each time the imaging is performed, which requires the calculation of the density compensation function for all possible situations of the sampling point distribution in advance, thereby greatly limiting the use of the grid algorithm. Therefore, in the grid reconstruction algorithm, it is very necessary to improve the calculation speed of density compensation and realize real-time calculation. In addition, sampling density compensation calculation is a difficult task because it is difficult to accurately calculate the sampling density compensation function. On the other hand, if the density compensation is improper, it will cause image blur or artifacts. Therefore, how to design the density compensation function is one of the core issues of non-Cartesian sampling reconstruction.

[0006] Currently, the commonly used density compensation functions include: Jackson density compensation function, Pipe iterative density compensation function, Hoge analytical density compensation function and Voronoi diagram density compensation function. The Jackson algorithm uses the inverse of the sampled area density function as the density compensation function [Jackson JL et al., IEEE Trans. Med. Imaging., 1991, 10: 473-2478], which is an approximate compensation. Hoge et al. use the Jacobian determinant as density compensation [Hoge RD et al., Magn. Reson. Med., 1997, 30: 117-128], which is suitable for the case where the sampling trajectory is relatively regular. Pipe et al. proposed to use numerical iteration technology to calculate the sampling density weighting function [Pipe J Get al., Magn. Reson. Med., 1999, 41: 179-186], which is suitable for sampling trajectories of arbitrary shapes, but there are also problems such as long iteration time and difficulty in controlling the iteration convergence standard. Resche proposed a method to use the Voronoi diagram in mathematics to divide the area occupied by randomly distributed sampling points [Rasche V et al., IEEE Trans. Med. Imaging., 1999, 18: 385-392], and used it as a sampling density compensation function. This method is suitable for sampling methods with arbitrary distributions. The disadvantage is that it takes a long time to calculate the Voronoi diagram. In recent years, deep learning methods have shown great potential in the field of magnetic resonance reconstruction. The magnetic resonance reconstruction algorithm based on deep learning can autonomously learn how to extract image features through external data set training and establish a mapping model from input to output. At present, most of the magnetic resonance reconstruction methods based on deep learning study Cartesian reconstruction. In non-Cartesian sampling reconstruction methods, non-Cartesian sampling data also use traditional density compensation algorithms for density compensation. Liu et al. proposed a model for implementing NUFFT using deep learning methods [Yilin Liu et al., MICCAI, 2021, 12906: 161-170]. The model superimposes the non-Cartesian sampling points near the grid points, the distance of the sampling points from the grid points and the sampling point coordinates for processing. However, this method does not directly calculate the density compensation of non-Cartesian sampling points, but infers the value of the grid point through the weights of several sampling points near the grid point through network learning, and indirectly performs density compensation in this process. Because of this, the convolution of the network model cannot obtain a larger receptive field, and it cannot learn the relationship between more sampling points.

[0007] In summary, the prior art has the following problems:

[0008] 1. When the sampling trajectory changes, the density compensation function often needs to be recalculated, which takes a lot of time in practical applications;

[0009] 2. Density compensation calculations often have problems such as long calculation time and insufficient compensation accuracy, which hinder the further application of non-Cartesian sampling reconstruction methods. Summary of the invention

[0010] The purpose of the present invention is to address the above-mentioned problems existing in the prior art and to propose a magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning.

[0011] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0012] A magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning includes the following steps:

[0013] Step 1, obtaining paired magnetic resonance images, non-Cartesian sampling k-space data and corresponding sampling point polar coordinate 3D data as a sample group, wherein the sampling point polar coordinate 3D data includes the polar angle and polar diameter of the sampling point polar coordinate, and dividing the sample group into a training set and a test set;

[0014] Step 2, construct a density compensation reconstruction network, the density compensation reconstruction network includes a density compensation network, a non-uniform Fourier transform and a convolution reconstruction network, the non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data constitute 3D input data, the 3D input data is input into the density compensation network to obtain accurately compensated 2D non-Cartesian sampling k-space data; the accurately compensated 2D non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data are input into the non-uniform Fourier transform to obtain a 2D reconstructed image; the 2D reconstructed image is input into the convolution reconstruction network to obtain a predicted non-Cartesian reconstructed image; wherein the 3D input data dimension is H×W×3, H and W are the length and width of the non-Cartesian sampling k-space data respectively, the third dimension "3" of the 3D input data is 3 channels of the 3D input data, one channel is the non-Cartesian sampling k-space data, one channel is the polar angle of the sampling point polar coordinates, and one channel is the polar diameter of the sampling point polar coordinates;

[0015] Step 3: Set the total loss function L;

[0016] Step 4: According to the total loss function set in step 3, the density compensation reconstruction network constructed in step 2 is trained end-to-end using the training set generated in step 1, and the parameters of the density compensation reconstruction network are saved;

[0017] Step 5: The non-Cartesian sampled k-space data to be processed and the corresponding sampling point polar coordinate 3D data constitute the 3D input data to be reconstructed. The structure of the 3D input data to be reconstructed is consistent with the structure of the 3D input data in step 1. The 3D input data to be reconstructed is input into the density compensation reconstruction network trained in step 4 to obtain a non-Cartesian sampled magnetic resonance reconstructed image.

[0018] As described above, the density compensation network in the density compensation reconstruction network includes an input layer, multiple coordinate convolution blocks and multiple k-space convolution blocks in order:

[0019] The input layer includes 3D convolution layer, batch normalization layer and activation layer in sequence;

[0020] The coordinate convolution block includes a 3D convolution layer, a batch normalization layer, and an activation layer;

[0021] The k-space convolution block includes a 2D convolution layer, a batch normalization layer, and an activation layer;

[0022] Except for the last coordinate convolution block, the number of input channels and output channels of each coordinate convolution block are equal to the number of output channels of the input layer;

[0023] The number of input channels of the last coordinate convolution block is equal to the number of output channels of the input layer, and the number of output channels of the last coordinate convolution block is equal to the number of input channels of the input layer;

[0024] The 3D input data is fed into a density compensation network to obtain accurately compensated 2D non-Cartesian sampled k-space data.

[0025] As shown above, the input data of the non-uniform Fourier transform is the accurately compensated 2D non-Cartesian sampled k-space data and the corresponding sampling point polar coordinate 3D data. The non-uniform Fourier transform uses the NUFFT grid algorithm to interpolate the accurately compensated 2D non-Cartesian sampled k-space data onto the Cartesian grid, and then performs a Fourier transform to obtain a 2D reconstructed image.

[0026] As mentioned above, the convolutional reconstruction network in the density compensation reconstruction network includes multiple image convolution blocks and an output layer in sequence:

[0027] The image convolution block includes a 2D convolution layer, a batch normalization layer, and an activation layer;

[0028] The output layer includes a 2D convolutional layer, a batch normalization layer, and an activation layer;

[0029] The number of input channels of the first image convolution block is 2;

[0030] Except for the first image convolution block, the number of input channels and the number of output channels of other image convolution blocks are equal to the number of output channels of the first image convolution block;

[0031] The number of input channels of the output layer is equal to the number of output channels of the first image convolution block; the number of output channels of the output layer is equal to 2.

[0032] The 2D reconstructed image is input into the convolutional reconstruction network to obtain the predicted non-Cartesian reconstructed image.

[0033] As mentioned above, the convolution kernel size of the 3D convolution layer of the coordinate convolution block is 3×1×H or 3×1×W.

[0034] As mentioned above, the total loss function L is:

[0035] L=L2(f θ (k,c),x)

[0036] Where L2 is the mean square error calculation, x is the magnetic resonance image, k is the non-Cartesian sampled k-space data, c is the polar coordinate 3D data of the sampling point corresponding to the non-Cartesian sampled k-space data, and f is the θ (k,c) represents the predicted non-Cartesian reconstructed image output by the density compensation reconstruction network, and θ is the network parameter of the density compensation reconstruction network.

[0037] As described above, the paired MRI images in step 1 are fully sampled and the non-Cartesian sampled k-space data are undersampled.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention builds a density compensation reconstruction network, uses the set total loss function to train the network to learn the density compensation of non-Cartesian data, performs non-Cartesian sampling reconstruction, and can ensure the performance of magnetic resonance image reconstruction. Ordinary convolution has translation invariance and cannot perceive spatial coordinates, while the density compensation calculation depends on the position of the sampling points. Coordinate convolution adds the coordinate information of two channels to the original convolution, giving the convolution kernel the ability to perceive the coordinate position, thereby realizing the density compensation of the sampling points learned through the convolution network. Compared with traditional density compensation methods, the present invention trains data with different sampling trajectories through coordinate convolution, and can use the convolution network to quickly complete the density compensation and reconstruction of non-Cartesian sampling data. It is no longer necessary to calculate all possible density compensation functions in advance according to the sampling trajectory. No additional optimization is required during application, and it has practical application value;

[0040] 2. The present invention uses a convolutional neural network to learn density compensation of sampling points, and can quickly perform density compensation on multiple sampling trajectories when applied. Compared with the traditional density compensation method, the method of the present invention does not require additional parameter adjustment after the density compensation reconstruction network training is completed. The density compensation calculation speed is faster, the image details can be better preserved, and the image reconstruction effect is better.

[0041] 3. In the coordinate convolution of the present invention, a 1D convolution kernel with an expanded dimension is used, and convolution is performed with the data of the first dimension of the 3D input data or the data of the second dimension of the 3D input data. In non-Cartesian sampling, multiple sampling spokes are usually used to form a data matrix. Compared with the commonly used square convolution kernels such as 3×3 or 5×5, the 1D convolution with an expanded dimension can simultaneously convolve with all points on a sampling spoke or the same point on all sampling spokes, which improves the receptive field and enables the network to better learn the distance relationship between sampling points. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of the present invention;

[0043] Figure 2 Schematic diagram of the structure of the density compensation reconstruction network: (a) is a schematic diagram of the overall structure of the density compensation reconstruction network, (b) is a schematic diagram of the structure of the input layer, (c) is a schematic diagram of the structure of the output layer, and (d) is a schematic diagram of the structure of the convolution block (including the coordinate convolution block, the k-space convolution block and the image convolution block);

[0044] Figure 3 The reconstruction results of the traditional density compensation algorithm for non-Cartesian sampling magnetic resonance brain image data and the reconstruction results of the magnetic resonance non-Cartesian sampling density compensation reconstruction network based on deep learning of the present invention: (a) is the final output result of the convolutional reconstruction network, (b) is the output result of the non-uniform Fourier transform, (c) is the reconstruction result using the Voronoi diagram density compensation algorithm, and (d) is the reconstruction result using the Pipe iterative density compensation algorithm;

[0045] Table 1 is a comparison table of the reconstruction time of the present invention and different traditional density compensation methods, recording Figure 3 The time required to reconstruct a 256×256 magnetic resonance image using different methods, in seconds. DETAILED DESCRIPTION

[0046] In order to facilitate those skilled in the art to understand and implement the present invention, the following embodiments and Figure 1-Figure 3 , Table 1 further describes the present invention in detail. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0047] Example 1

[0048] The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning specifically includes the following steps:

[0049] Step 1: Acquire paired magnetic resonance images, non-Cartesian sampling k-space data, and corresponding sampling point polar coordinate 3D data as a sample group, wherein the magnetic resonance image is a fully sampled image, the non-Cartesian sampling k-space data is under-sampled data, and the sampling point polar coordinate 3D data includes the polar angle and polar diameter of the sampling point polar coordinates, and divide the sample group into a training set and a test set.

[0050] In this example, the magnetic resonance images obtained are 2250 magnetic resonance 2D brain images obtained from the magnetic resonance brain public data set cc359, and the NUFFT gridding algorithm is used to simulate and generate the corresponding under-sampled non-Cartesian sampling k-space data according to the written Radial sampling trajectory. The magnetic resonance images, the simulated non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data are used as a sample group, and then the sample group is divided into a training set and a test set. In this embodiment, 1500 magnetic resonance images and the generated under-sampled non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data are used as a training set, and 750 magnetic resonance images and the generated under-sampled non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data are used as a test set. The size of the magnetic resonance images is 256×256. The radial sampling trajectory of each MRI image includes 256 spokes, each spoke has 256 sampling points, the spokes are distributed in a golden angle distribution (i.e., each spoke is 137.51° apart), and the initial angle of the spoke is randomly set to ensure that the sampling trajectory of each MRI image is different.

[0051] In this example, the simulated non-Cartesian sampling k-space data is generated from a public data set, or the fully sampled non-Cartesian sampling k-space data obtained by sampling during the nuclear magnetic resonance imaging process can be selected, and then the fully sampled non-Cartesian sampling k-space data is transformed by non-uniform Fourier transform to obtain the corresponding magnetic resonance image, and the non-Cartesian sampling k-space data obtained by retrospective undersampling, the corresponding sampling point polar coordinate 3D data, and the corresponding fully sampled magnetic resonance image obtained by non-uniform Fourier transform are paired as a sample group. In this step, the radial sampling trajectory is selected, and other sampling methods can also be selected. In addition, the method of the present invention is not limited to 2D magnetic resonance image reconstruction, and can be very conveniently extended to magnetic resonance 3D imaging reconstruction.

[0052] Step 2: Construct a density compensation reconstruction network, which includes a density compensation network, a non-uniform Fourier transform and a convolution reconstruction network.

[0053] The non-Cartesian sampled k-space data and the corresponding sampling point polar coordinate 3D data constitute the 3D input data. The 3D input data is input into the density compensation reconstruction network to obtain the predicted non-Cartesian reconstructed image, wherein the 3D input data dimension is H×W×3, H and W are the length and width of the non-Cartesian sampled k-space data, respectively. The third dimension "3" of the 3D input data is the three channels of the 3D input data, one channel is the non-Cartesian sampled k-space data, one channel is the polar angle of the sampling point polar coordinates, and one channel is the polar diameter of the sampling point polar coordinates.

[0054] The density compensation network includes an input layer, multiple coordinate convolution blocks and multiple k-space convolution blocks in order. In the density compensation network: the input layer includes 3D convolution layer, batch normalization layer and activation layer in sequence; the coordinate convolution block includes 3D convolution layer, batch normalization layer and activation layer; the k-space convolution block includes 2D convolution layer, batch normalization layer and activation layer. The 3D input data is preliminarily density compensated through the coordinate convolution block, and multiple k-space convolution blocks are cascaded to further adjust the density compensation results to obtain accurately compensated 2D non-Cartesian sampling k-space data.

[0055] The input data of the non-uniform Fourier transform is the output of the density compensation network, namely the accurately compensated 2D non-Cartesian sampled k-space data and the corresponding sampling point polar coordinate 3D data. The non-uniform Fourier transform uses the NUFFT gridding algorithm for approximate calculation, interpolates the density-accurately compensated 2D non-Cartesian sampled k-space data onto the Cartesian grid, and then performs a Fourier transform to quickly obtain a 2D reconstructed image.

[0056] The convolutional reconstruction network includes multiple image convolution blocks and an output layer in order. In the convolutional reconstruction network: the image convolution block includes a 2D convolution layer, a batch normalization layer, and an activation layer; the output layer includes a 2D convolution layer, a batch normalization layer, and an activation layer. The convolutional reconstruction network further removes artifacts from the 2D reconstructed image and improves the reconstruction quality by cascading multiple image convolution blocks.

[0057] In this embodiment, the density compensation network includes an input layer, two coordinate convolution blocks and three k-space convolution blocks in order. Both the input layer and the coordinate convolution block use coordinate convolution:

[0058] The input layer includes a 3D convolution layer, a batch normalization layer, and an activation layer. The convolution kernel of the 3D convolution layer of the input layer uses a 1D convolution kernel with an expanded dimension. The convolution kernel size of the 3D convolution layer is 3×1×256. The first dimension "3" of the convolution kernel of the 3D convolution layer of the input layer corresponds to the three channels of the 3D input data, namely, the non-Cartesian sampled k-space data of one channel, the polar angle of the polar coordinates of the sampling points of one channel, and the polar radius of the polar coordinates of the sampling points of one channel. The second dimension of the convolution kernel of the 3D convolution layer of the input layer is 1, and the third dimension of the convolution kernel of the 3D convolution layer of the input layer is the first dimension of the convolution kernel of the 3D convolution layer. Each channel corresponds to the first dimension or second dimension of the input 3D input data (the first dimension and the second dimension of the 3D input data are H and W respectively, so the second dimension of the convolution kernel of the 3D convolution layer of the input layer is 1, and the third dimension is W or H). The number of input channels of the input layer is 2, the number of output channels is 16, the input feature map size is 3×256×256, and the output feature map size is 3×256×256.

[0059] The convolution kernel of the 3D convolution layer in the coordinate convolution block also uses a 1-dimensional convolution kernel with an expanded dimension, and except for the last coordinate convolution block, the number of input channels and the number of output channels of each of the remaining coordinate convolution blocks are equal to the number of output channels of the input layer; the number of input channels of the last coordinate convolution block is equal to the number of output channels of the input layer, and the number of output channels of the last coordinate convolution block is equal to the number of input channels of the input layer. This embodiment is specifically set as follows: the convolution kernel size in the 3D convolution layer of the first coordinate convolution block is 3×1×256, the number of input channels is 16, the number of output channels is 16, the input feature map size is 3×256×256, and the output feature map size is 256×256; the convolution kernel size in the 3D convolution layer of the second coordinate convolution block is 3×256×1, the number of input channels is 16, the output channel is 2, the input feature map size is 256×256, and the output feature map size is 256×256.

[0060] In the k-space convolution block: the convolution kernel size of the 2D convolution layer in the first k-space convolution block is 3×3, the input channel is 2, the output channel is 16, the input feature map size is 256×256, and the output feature map size is 256×256; the convolution kernel size of the 2D convolution layer in the second k-space convolution block is 3×3, the input channel is 16, the output channel is 16, the input feature map size is 256×256, and the output feature map size is 256×256; the convolution kernel size of the 2D convolution layer in the third k-space convolution block is 3×3, the input channel is 16, the output channel is 2, the input feature map size is 256×256, and the output feature map size is 256×256; the activation layer function of each activation layer in the density compensation network (including the input layer, coordinate convolution block and k-space convolution block) is the ReLU function.

[0061] In this example, two coordinate convolution blocks and three k-space convolution blocks are used. In actual applications, the number of coordinate convolution blocks or the number of k-space convolution blocks can be modified and increased according to needs.

[0062] The non-uniform Fourier transform uses the NUFFT gridding algorithm for approximate calculations, and passes the data to the GPU for acceleration. The input data of the non-uniform Fourier transform is the output of the density compensation network and the corresponding sampling point polar coordinate 3D data: the size of the precisely compensated 2D non-Cartesian sampling k-space data output by the density compensation network is 256×256, and the size of the sampling point polar coordinate 3D data is 2×256×256. The "2" in the first dimension of the sampling point polar coordinate 3D data represents 2 channels, corresponding to the polar angle and polar diameter of the polar coordinates. After the non-uniform Fourier transform is completed, a 2D reconstructed image of size 256×256 is output.

[0063] In this example, the convolutional reconstruction network includes 4 image convolution blocks and 1 output layer in sequence. The convolution kernel size of the 2D convolution layer in the first image convolution block is 3×3, the number of input channels is 2, the number of output channels is 16, the input feature map size is 256×256, and the output feature map size is 256×256; the convolution kernel size of the 2D convolution layer in the second image convolution block, the 2D convolution layer in the third image convolution block, and the 2D convolution layer in the fourth image convolution block are all 3×3, the number of input channels is 16, the number of output channels is 16, the input feature map size is 256×256, and the output feature map size is 256×256; the convolution kernel size of the 2D convolution layer in the output layer is 3×3, the number of input channels is 16, the number of output channels is 2, the input feature map size is 256×256, and the output feature map size is 256×256; in the convolution reconstruction network (including the image convolution block and the output layer), the activation layer function is the ReLU function.

[0064] Step 3, set the total loss function. In this example, the total loss function is the mean square error between the predicted non-Cartesian reconstructed image (i.e., the result obtained by inputting 3D input data into the density compensation reconstruction network) and the magnetic resonance image. The total loss function L is set as:

[0065] L=L2(f θ (k,c),x)

[0066] Where L2 is the mean square error calculation, x is the magnetic resonance image, k is the non-Cartesian sampled k-space data, c is the polar coordinate 3D data of the sampling point corresponding to the non-Cartesian sampled k-space data, and f is the θ(k,c) represents the predicted non-Cartesian reconstructed image output by the density compensation reconstruction network, wherein the input of the density compensation reconstruction network is: the non-Cartesian sampled k-space data paired with the magnetic resonance image and the polar coordinate 3D data of the sampling points corresponding to the non-Cartesian sampled k-space data, and θ is the network parameter of the density compensation reconstruction network.

[0067] Step 4: According to the total loss function set in step 3, the density compensation reconstruction network constructed in step 2 is trained end-to-end using the training set generated in step 1, and the parameters of the density compensation reconstruction network are saved;

[0068] According to the density compensation reconstruction network built in step 2, the network learning rate is initialized to 0.0001, the batch size is set to 16, and the network training is performed on the PyTroch platform using the Adam optimizer. The data in the training set generated in step 1, in this example, the non-Cartesian sampling k-space data generated by the radial sampling trajectory simulation and the corresponding sampling point polar coordinate 3D data are input into the density compensation reconstruction network to obtain the predicted non-Cartesian sampling reconstructed image, and the network training is performed according to the total loss function set in step 4. The training is stopped after the total number of iterations of the network training reaches 100, and the parameters of the corresponding density compensation reconstruction network are saved.

[0069] Step 5: The non-Cartesian sampling k-space data to be reconstructed and the corresponding sampling point polar coordinate 3D data constitute the 3D input data to be reconstructed. The structure of the 3D input data to be reconstructed is consistent with the structure of the 3D input data in step 1. The 3D input data to be reconstructed is input into the density compensation reconstruction network trained in step 4 to obtain the non-Cartesian sampling magnetic resonance reconstructed image.

[0070] In this example, the non-Cartesian sampling k-space data to be reconstructed and the corresponding sampling point polar coordinate 3D data in the test set generated in step 1 are used to form the 3D input data to be reconstructed, and the 3D input data to be reconstructed is input into the density compensation reconstruction network trained in step 4 to obtain the corresponding non-Cartesian sampling magnetic resonance reconstruction image. In addition, the non-Cartesian sampling k-space data obtained by sampling during nuclear magnetic resonance imaging and the corresponding sampling point polar coordinate 3D data to be reconstructed can also be selected as the input of step 5.

[0071] The non-Cartesian sampling MRI reconstructed image obtained in step 5 is compared with the MRI image of the test set, and the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) indicators between the two are calculated.

[0072] Figure 3This is a comparison between the method of the present invention and different traditional density compensation algorithms. (a) is the final reconstruction result of the network of the present invention, (b) is the output result of the data output by the density compensation network after non-uniform Fourier transform, (c) is the reconstruction result using the Voronoi diagram density compensation algorithm, and (d) is the reconstruction result using the Pipe iterative density compensation algorithm, with 10 iterations. Comparing (a) and (b) with (c) and (d), it can be seen that the strip artifacts in the background part of (a) and (b) are better removed. The difference between (a) and (b) is that (a) has been further removed by the convolutional reconstruction network. The reconstruction results prove the role of the density compensation network and the convolutional reconstruction network, as well as the effectiveness of the present invention.

[0073] Table 1 lists the reconstruction time of the present invention and different traditional density compensation methods. It can be seen that compared with the traditional algorithm, the reconstruction speed of the present invention is increased by more than 30 times.

[0074] Table 1 Comparison of reconstruction time of the present invention and different traditional density compensation methods

[0075]

[0076] The present invention performs density compensation on multi-channel 3D input data composed of non-Cartesian sampling k-space data and sampling point polar coordinate 3D data through convolution, and then interpolates it to the Cartesian grid through the NUFFT grid algorithm and performs Fourier transform, and then obtains the artifact-free predicted non-Cartesian reconstructed image through image domain convolution. On the one hand, the present invention adds coordinate information corresponding to the polar coordinate 3D data on the basis of ordinary convolution, giving the convolution kernel the ability to perceive the coordinate position. In addition, the convolution kernel uses a 1-dimensional convolution kernel with an extended dimension to convolve each spoke of the non-Cartesian k-space data or the same position of all spokes, while expanding the receptive field, so that the network can better learn the relationship between the sampling points, thereby realizing density compensation of the sampling points through the convolution network; on the other hand, the method first performs density compensation, then adjusts the density compensation result, interpolates, and then adjusts the result in the image domain, uses a convolutional neural network to learn the density compensation of the sampling points, and can quickly perform density compensation on a variety of sampling trajectories when applied. Compared with the traditional density compensation method, the method of the present invention does not require additional adjustment parameters after the density compensation reconstruction network training is completed, and the density compensation calculation speed is faster, which can better retain image details.

[0077] Example 2

[0078] The magnetic resonance non-Cartesian sampling density compensation reconstruction device based on deep learning utilizes the magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning described in Example 1, including an acquisition module, a network building module, a total loss function setting module, a training module, and a use test module:

[0079] Wherein, the acquisition module is used to implement step 1 in embodiment 1;

[0080] The network building module is used to implement step 2 in embodiment 1;

[0081] The total loss function setting module is used to implement step 3 in Example 1;

[0082] The training module is used to implement step 4 in Example 1;

[0083] The test module was used to implement step 5 in Example 1.

[0084] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning, characterized in that: The following steps are involved: Step 1, obtaining paired magnetic resonance images, non-Cartesian sampling k-space data and corresponding sampling point polar coordinate 3D data as a sample group, wherein the sampling point polar coordinate 3D data includes the polar angle and polar diameter of the sampling point polar coordinate, and dividing the sample group into a training set and a test set; Step 2, construct a density compensation reconstruction network, the density compensation reconstruction network includes a density compensation network, a non-uniform Fourier transform and a convolution reconstruction network, the non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data constitute 3D input data, the 3D input data is input into the density compensation network to obtain accurately compensated 2D non-Cartesian sampling k-space data; the accurately compensated 2D non-Cartesian sampling k-space data and the corresponding sampling point polar coordinate 3D data are input into the non-uniform Fourier transform to obtain a 2D reconstructed image; the 2D reconstructed image is input into the convolution reconstruction network to obtain a predicted non-Cartesian reconstructed image; wherein the 3D input data dimension is H×W×3, H and W are the length and width of the non-Cartesian sampling k-space data respectively, the third dimension "3" of the 3D input data is 3 channels of the 3D input data, one channel is the non-Cartesian sampling k-space data, one channel is the polar angle of the sampling point polar coordinates, and one channel is the polar diameter of the sampling point polar coordinates; Step 3: Set the total loss function L; Step 4: According to the total loss function set in step 3, the density compensation reconstruction network constructed in step 2 is trained end-to-end using the training set generated in step 1, and the parameters of the density compensation reconstruction network are saved; Step 5: The non-Cartesian sampled k-space data to be processed and the corresponding sampling point polar coordinate 3D data constitute the 3D input data to be reconstructed. The structure of the 3D input data to be reconstructed is consistent with the structure of the 3D input data in step 1. The 3D input data to be reconstructed is input into the density compensation reconstruction network trained in step 4 to obtain a non-Cartesian sampled magnetic resonance reconstructed image.

2. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 1, characterized in that: The density compensation network in the density compensation reconstruction network includes an input layer, multiple coordinate convolution blocks and multiple k-space convolution blocks in order: The input layer includes 3D convolution layer, batch normalization layer and activation layer in sequence; The coordinate convolution block includes a 3D convolution layer, a batch normalization layer, and an activation layer; The k-space convolution block includes a 2D convolution layer, a batch normalization layer, and an activation layer; Except for the last coordinate convolution block, the number of input channels and output channels of each coordinate convolution block are equal to the number of output channels of the input layer; The number of input channels of the last coordinate convolution block is equal to the number of output channels of the input layer, and the number of output channels of the last coordinate convolution block is equal to the number of input channels of the input layer.

3. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 1, characterized in that: The non-uniform Fourier transform uses the NUFFT grid algorithm to interpolate the accurately compensated 2D non-Cartesian sampling k-space data onto a Cartesian grid, and then performs Fourier transform to obtain a 2D reconstructed image.

4. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 1, characterized in that: The convolutional reconstruction network in the density compensation reconstruction network includes multiple image convolution blocks and an output layer in sequence: The image convolution block includes a 2D convolution layer, a batch normalization layer, and an activation layer; The output layer includes a 2D convolutional layer, a batch normalization layer, and an activation layer; The number of input channels of the first image convolution block is 2; Except for the first image convolution block, the number of input channels and the number of output channels of other image convolution blocks are equal to the number of output channels of the first image convolution block; The number of input channels of the output layer is equal to the number of output channels of the first image convolution block; the number of output channels of the output layer is equal to 2.

5. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 2, characterized in that: The convolution kernel size of the 3D convolution layer of the coordinate convolution block is 3×1×H or 3×1×W.

6. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 1, characterized in that: The total loss function L is: L=L2(f θ (k,c),x) Where L2 is the mean square error calculation, x is the magnetic resonance image, k is the non-Cartesian sampled k-space data, c is the polar coordinate 3D data of the sampling point corresponding to the non-Cartesian sampled k-space data, and f is the θ (k,c) represents the predicted non-Cartesian reconstructed image output by the density compensation reconstruction network, and θ is the network parameter of the density compensation reconstruction network.

7. The magnetic resonance non-Cartesian sampling density compensation reconstruction method based on deep learning according to claim 1, characterized in that: The paired magnetic resonance images in step 1 are fully sampled, and the non-Cartesian sampled k-space data are under-sampled.

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