XQ-SR: Joint x-q space super-resolution with application to infant diffusion MRI

Diffusion MRI (DMRI) is a powerful tool for studying early brain development and disorders. However, the typically low spatio–angular resolution of DMRI diminishes structural details and limits quantitative analysis to simple diffusion models. This problem is aggravated for infant DMRI since (i) the infant brain is significantly smaller than that of an adult, demanding higher spatial resolution to capture subtle structures; and (ii) the typically limited scan time of unsedated infants poses significant challenges to DMRI acquisition with high spatio–angular resolution. Post–acquisition super–resolution (SR) is an important alternative for increasing the resolution of DMRI data without prolonging acquisition times. However, most existing methods focus on the SR of only either the spatial domain (x–space) or the diffusion wavevector domain (q–space). For more effective resolution enhancement, we propose a framework for joint SR in both spatial and wavevector domains. More specifically, we first establish the signal relationships in x–q space using a robust neighborhood matching technique. We then harness the signal relationships to regularize the ill–posed inverse problem associated with the recovery of high–resolution data from their low–resolution counterpart. Extensive experiments on synthetic, adult, and infant DMRI data demonstrate that our method is able to recover high–resolution DMRI data with remarkably improved quality.