Systems and methods of processing magnetic resonance images using phase-sensitive structural similarity index measure

1. A computer-implemented method of processing complex magnetic resonance (MR) images, comprising:

receiving a pair of corrupted complex data and pristine complex images corresponding to the corrupted complex data; and

training a neural network model using the pair of corrupted complex data and pristine complex images by:

inputting the corrupted complex data to the neural network model;

setting the pristine complex images as target outputs of the neural network model;

processing the corrupted complex data using the neural network model to derive output complex images of the corrupted complex data;

comparing the output complex images with the target outputs by computing a phase-sensitive structural similarity index measure (PS-SSIM) between each of the output complex images and its corresponding target complex image, wherein the PS-SSIM is real-valued and varies with phases of the output complex image and phases of the target complex image; and

adjusting the neural network model based on the comparison.

2. The method of claim 1 , wherein the PS-SSIM includes a luminance comparison function, the luminance comparison function varying with the phases of the output complex image and the phases of the target complex image.

3. The method of claim 2 , wherein the luminance comparison function reaches a maximum when means of image patches in the output complex image are equal to means of image patches in the target complex image.

4. The method of claim 2 , wherein the luminance comparison function reaches a maximum when means of real components of image patches in the output complex image are equal to means of real components of image patches in the target complex image and means of imaginary components of image patches in the output complex image are equal to means of imaginary components of image patches in the target complex image.

5. The method of claim 1 , wherein the PS-SSIM includes a contrast comparison function, the contrast comparison function varying with the phases of the output complex image and the phases of the target complex image.

6. The method of claim 5 , wherein the contrast comparison function reaches a maximum when standard deviations of image patches in the output complex image are equal to standard deviations of image patches in the target complex image.

7. The method of claim 5 , wherein the contrast comparison function reaches a maximum when standard deviations of real components of image patches in the output complex image are equal to standard deviations of real components of image patches in the target complex image and standard deviations of imaginary components of image patches in the output complex image are equal to standard deviations of imaginary components of image patches in the target complex image.

8. The method of claim 1 , wherein the PS-SSIM includes a structure comparison function, the structure comparison function varying with phases of the output complex image and phases of the target complex image.

9. The method of claim 8 , wherein the structure comparison function reaches a maximum when real components of image patches in the output complex image are linearly dependent upon real components of image patches in the target complex image and imaginary components of image patches in the output complex image are linearly dependent upon imaginary components of image patches in the target complex image.

10. The method of claim 8 , wherein the structure comparison function reaches a maximum when image patches in the output complex image are linearly dependent upon image patches in the target complex image.

11. The method of claim 8 , wherein the structure comparison function reaches a maximum when real components of image patches in the output complex image are positively fully correlated with real components of image patches in the target complex image and imaginary components of image patches in the output complex image are positively fully correlated with imaginary components of image patches in the target complex image.

12. The method of claim 8 , wherein the structure comparison function reaches a maximum when image patches in the output complex image are positively fully correlated with image patches in the target complex image.

13. An image processing system, comprising an image processing computing device, the image processing computing device comprising at least one processor in communication with at least one memory device, and the at least one processor programmed to:

receive a pair of corrupted complex data and pristine complex images corresponding to the corrupted complex data; and

train a neural network model using the pair of corrupted complex data and pristine complex images by:

inputting the corrupted complex data to the neural network model;

setting the pristine complex images as target outputs of the neural network model;

processing the corrupted complex data using the neural network model to derive output complex images of the corrupted complex data;

comparing the output complex images with the target outputs by computing a phase-sensitive structural similarity index measure (PS-SSIM) between each of the output complex images and its corresponding target complex image, wherein the PS-SSIM is real-valued and varies with phases of the output complex image and phases of the target complex image; and

adjusting the neural network model based on the comparison.

14. The system of claim 13 , wherein the PS-SSIM includes a luminance comparison function, the luminance comparison function varying with the phases of the output complex image and the phases of the target complex image.

15. The system of claim 14 , wherein the luminance comparison function reaches a maximum when means of image patches in the output complex image are equal to means of image patches in the target complex image.

16. The system of claim 13 , wherein the PS-SSIM includes a contrast comparison function, the contrast comparison function varying with the phases of the output complex image and the phases of the target complex image.

17. The system of claim 16 , wherein the contrast comparison function reaches a maximum when standard deviations of image patches in the output complex image are equal to standard deviations of image patches in the target complex image.

18. The system of claim 13 , wherein the PS-SSIM include a structure comparison function, the structure comparison function varying with phases of the output complex image and phases of the target complex image.

19. The system of claim 18 , wherein the structure comparison function reaches a maximum when real components of image patches in the output complex image are linearly dependent upon real components of image patches in the target complex image and imaginary components of image patches in the output complex image are linearly dependent upon imaginary components of image patches in the target complex image.

20. An image processing system, comprising an image processing computing device, the image processing computing device comprising at least one processor in communication with at least one memory device, and the at least one processor programmed to:

receive crude complex data;

process the crude complex data using a neural network model, wherein the neural network model was trained with a pair of corrupted complex data and pristine complex images with the corrupted complex data as inputs and the pristine complex images as target outputs, and a loss function of the neural network model that compares outputs of the neural network model and the target outputs of the neural network model includes a phase-sensitive structural similarity index measure (PS-SSIM) between each of the output complex images and its corresponding target complex image, wherein the PS-SSIM is real-valued and varies with phases of the output complex image and phases of the target complex image;

generate a predicted image of the crude complex data based on the processing; and

output the predicted image.