A quest for deep learning MR image reconstruction loss functions in k-space

Motivation: Existing loss functions are not optimal for measuring similarity in k-space. Goal(s): To develop an improved k-space loss function that accounts for the k-space characteristics. Approach: We propose a magnitude-phase-energy loss (MPE-loss), which employs separated magnitude and phase losses to improve the accuracy of complex-valued predictions, along with an additional energy term to account for the overall k-space energy. Results: The proposed MPE-loss provides a symmetric loss landscape for each complex k-space sample, creating a quasi-convex loss that facilitates convergence under variations in image brightness and contrast. Experiments demonstrate that MPE-loss outperforms other standard loss functions in k-space reconstruction. Impact: We propose a loss function that is more suitable for k-space, taking into account its characteristics and enhancing the accuracy of k-space regression. This loss function can be applied to any tasks that require calibration of k-space similarity.