[Deep parallel MRI reconstruction based on a complex-valued loss function]

To propose a new method for fast MRI reconstruction based on deep learning in parallel MRI data using a new loss function defined as the summation of the mean squared errors of the magnitude and phase.

The multicoil image data were combined into single-coil image data to eliminate the correlation between noises and used as a label in the training process. Considering the importance of the phase information in some applications, where the phase information was lost when combining multicoil data using sum of square method, a new loss function was introduced, defined as the weighted sum of the mean squared error (MSE) of the magnitude and phase. The single weight in the loss function was used to balance the importance of the magnitude and phase in different applications. To validate the proposed method, real brain and knee data in FastMRI dataset were used for training and testing. We also compared this proposed method with two other methods that used MSE or mean absolute error (MAE) as a loss function.

The experimental results showed that the proposed method was capable of accurate reconstruction of multicoil MR images with significantly reduced artifacts compared with the other two methods. Quantitative analysis showed that the propose method increased the peak signal-to-noise ratio (PSNR) of the reconstructed images by about 1 dB.

The proposed deep MRI reconstruction method using a new loss function to fit the noise in parallel MRI data can accelerate MRI reconstruction and significantly improve the quality of the reconstructed images.