An Evaluation of Regularization Strategies for Subsampled Single-Shell Diffusion MRI

Conventional single-shell diffusion MRI experiments acquire sampled values of the diffusion signal from the surface of a sphere in q-space. However, to reduce data acquisition time, there has been recent interest in using regularization to enable q-space undersampling. Although different regularization strategies have been proposed for this purpose (i.e., sparsity-promoting of the spherical ridgelet representation and Laplace-Beltrami Tikhonov regularization), there has not been a systematic evaluation of the strengths, weaknesses, and potential synergies of the different regularizers. In this work, we use real diffusion MRI data to systematically evaluate the performance characteristics of these different approaches and determine whether one approach is fundamentally more powerful than the other. Results from retrospective subsampling experiments suggest that both regularization strategies offer largely similar reconstruction performance (though with different levels of computational complexity) with some degree of synergy (albeit, relatively minor).