Acquisition time in diffusion MRI increases with the number of diffusion-weighted images that need to be acquired. Particularly in clinical settings, scan time is limited and only a sparse coverage of the vast q-space is possible. In this paper, we show how non-local self-similar information in the x-q space of diffusion MRI data can be harnessed for q-space upsampling. More specifically, we establish the relationships between signal measurements in x-q space using a patch matching mechanism that caters to unstructured data. We then encode these relationships in a graph and use it to regularize an inverse problem associated with recovering a high q-space resolution dataset from its low-resolution counterpart. Experimental results indicate that the high-resolution datasets reconstructed using the proposed method exhibit greater quality, both quantitatively and qualitatively, than those obtained using conventional methods, such as interpolation using spherical radial basis functions (SRBFs).
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