Comparing k-space versus image domain loss functions in joint learning of sampling pattern and deep-learning reconstruction

Motivation: Joint learning of sampling pattern (SP) and deep-learning (DL) reconstruction can have their loss functions in the k-space or image domain. It is not clear which approach is better. Goal(s): Investigate this question by comparing the results of both loss functions, exploiting the flexibility of k-space domain loss functions for joint learning. Approach: We modify the training of DL reconstructions to compare image or k-space domain losses. We tested on two DL networks and two different datasets, always using raw k-space as input. Results: The differences in image quality are very small, but there are visual differences in the learned SPs. Impact: This investigation shows that image loss is also a good option, but k-space loss is more flexible to control the shape of the SP. Interestingly, different learned SPs, with slightly different distributions of k-space samples, led to similar quality results.