q-Space Learning with Synthesized Training Data

q-Space learning has been developed to improve tissue microstructure estimation on diffusion magnetic resonance imaging (dMRI) scans when only a limited number of diffusion gradients are applied. However, the training samples for q-space learning are obtained from high-quality diffusion signals densely sampled in the q-space, which are acquired on the same scanner of the test scans with a large number of diffusion gradients, and they may not be available for existing or ongoing datasets. In this work, we explore q-space learning with synthesized training data so that it can be applied to datasets where training signals are not available. We seek to synthesize diffusion signals densely sampled in the q-space, whose corresponding undersampled signals should match the distribution of observed undersampled diffusion signals. Specifically, by drawing samples from a simple distribution and feeding them into a generator defined by a multiple layer perceptron, we synthesize the continuous SHORE signal representation, from which both densely sampled and undersampled synthesized diffusion signals can be computed. The weights in the generator are learned by minimizing the distribution difference, which is measured by the maximum mean discrepancy, between the synthesized and observed undersampled signals. In addition, regularization terms are added to discourage unrealistic synthetic signals. With the learned generator, densely sampled diffusion signals can be synthesized for q-space learning. The proposed approach was applied to microstructure estimation on dMRI scans acquired with a limited number of diffusion gradients. The results demonstrate the benefit of using synthetic training signals for q-space learning when actual training data are not acquired.