Deep learning techniques for magnetic resonance image reconstruction

1. A method, comprising:

generating a magnetic resonance (MR) image from input MR spatial frequency data using a neural network model comprising one or more neural network blocks including a first neural network block, wherein the first neural network block is configured to perform processing using a non-uniform Fourier transformation for transforming image domain data to spatial frequency domain data; and

applying the first neural network block to image domain data, wherein the applying comprises:

applying, to the image domain data, the non-uniform Fourier transformation followed by an adjoint non-uniform Fourier transformation to obtain first output;

applying the adjoint non-uniform Fourier transformation to the input MR spatial frequency data to obtain second output; and

providing the image domain data, the first output, and the second output as inputs to a plurality of convolutional layers.

2. The method of claim 1 , wherein each of the one or more neural network blocks is configured to perform processing using the non-uniform Fourier transformation.

3. The method of claim 1 , further comprising:

obtaining the input MR spatial frequency data;

generating an initial image from the input MR spatial frequency data using the non-uniform Fourier transformation; and

applying the neural network model to the initial image at least in part by using the first neural network block to perform the processing using the non-uniform Fourier transformation.

4. The method of claim 1 , wherein the first neural network block is configured to perform processing using the non-uniform Fourier transformation at least in part by performing the non-uniform Fourier transformation on data by applying a gridding interpolation transformation, a Fourier transformation, and a de-apodization transformation to the data.

5. The method of claim 4 , wherein applying the gridding interpolation transformation to the data is performed using sparse graphical processing unit (GPU) matrix multiplication.

6. The method of claim 1 , wherein the first neural network block comprises:

the plurality of convolutional layers.

7. The method of claim 6 , wherein the plurality of convolutional layers include one or more convolutional layers and one or more transposed convolutional layers.

8. The method of claim 6 , wherein the plurality of convolutional layers have a U-net structure.

9. The method of claim 1 , wherein the plurality of convolutional layers is configured to generate the MR image using the image domain data, the first output, and the second output.

10. The method of claim 1 , further comprising:

applying a convolutional neural network to a result of applying the non-uniform Fourier transformation to the image domain data to obtain an intermediate output; and

applying the adjoint non-uniform Fourier transformation to the intermediate output to obtain the first output.

11. The method of claim 1 , wherein points in the input MR spatial frequency data were obtained using a non-Cartesian sampling trajectory.

12. The method of claim 11 , wherein the non-uniform Fourier transformation is determined at least in part by using the non-Cartesian sampling trajectory.

13. At least one non-transitory computer-readable storage medium storing processor-executable instructions that, when executed by at least one computer hardware processor, cause the at least one computer hardware processor to perform a method comprising:

generating a magnetic resonance (MR) image from input MR spatial frequency data using a neural network model comprising one or more neural network blocks including a first neural network block, wherein the first neural network block is configured to perform processing using a non-uniform Fourier transformation for transforming image domain data to spatial frequency domain data; and

applying the first neural network block to image domain data, wherein the applying comprises:

applying, to the image domain data, the non-uniform Fourier transformation followed by an adjoint non-uniform Fourier transformation to obtain first output;

applying the adjoint non-uniform Fourier transformation to the input MR spatial frequency data to obtain second output; and

providing the image domain data, the first output, and the second output as inputs to a plurality of convolutional layers.

14. The at least one non-transitory computer-readable storage medium of claim 13 , wherein the method further comprises:

obtaining the input MR spatial frequency data;

generating an initial image from the input MR spatial frequency data using the non-uniform Fourier transformation; and

applying the neural network model to the initial image at least in part by using the first neural network block to perform the processing using the non-uniform Fourier transformation.

15. The at least one non-transitory computer-readable storage medium of 13 , wherein applying the first neural network block further comprises:

performing processing using the non-uniform Fourier transformation at least in part by performing the non-uniform Fourier transformation on data by applying a gridding interpolation transformation, a Fourier transformation, and a de-apodization transformation to the data.

16. The at least one non-transitory computer-readable storage medium of 13 , wherein the method further comprises:

applying a convolutional neural network to a result of applying the non-uniform Fourier transformation to the image domain data to obtain an intermediate output; and

applying the adjoint non-uniform Fourier transformation to the intermediate output to obtain the first output.

17. A magnetic resonance imaging (MRI) system, comprising:

a magnetics system comprising:

a B 0 magnet configured to provide a B 0 field for the MRI system;

gradient coils configured to provide gradient fields for the MRI system;

at least one RF coil configured to detect magnetic resonance (MR) signals; and

a controller configured to:

control the magnetics system to acquire MR spatial frequency data using a non-Cartesian sampling trajectory;

generate an MR image from the acquired MR spatial frequency data using a neural network model comprising one or more neural network blocks including a first neural network block, wherein the first neural network block is configured to perform processing using a non-uniform Fourier transformation; and

apply the first neural network block to image domain data, wherein the applying comprises:

applying, to the image domain data, the non-uniform Fourier transformation followed by an adjoint non-uniform Fourier transformation to obtain first output;

applying the adjoint non-uniform Fourier transformation to the input MR spatial frequency data to obtain second output; and

providing the image domain data, the first output, and the second output as inputs to a plurality of convolutional layers.

18. The MRI system of claim 17 , wherein the B 0 magnet is a permanent magnet.

19. The MRI system of claim 17 , wherein the controller is further configured to:

obtain the input MR spatial frequency data;

generate an initial image from the input MR spatial frequency data using the non-uniform Fourier transformation; and

apply the neural network model to the initial image at least in part by using the first neural network block to perform the processing using the non-uniform Fourier transformation.

20. The MRI system of claim 17 , wherein the first neural network block is configured to perform processing using the non-uniform Fourier transformation at least in part by performing the non-uniform Fourier transformation on data by applying a gridding interpolation transformation, a Fourier transformation, and a de-apodization transformation to the data.