Diffusion compartmentalization using response function groups with cardinality penalization

Spherical deconvolution (SD) of the white matter (WM) diffusion-attenuated signal with a fiber signal response function has been shown to yield high-quality estimates of fiber orientation distribution functions (FODFs). However, an inherent limitation of this approach is that the response function (RF) is often fixed and assumed to be spatially invariant. This has been reported to result in spurious FODF peaks as the discrepancy of the RF with the data increases. In this paper, we propose to utilize response function groups (RFGs) for robust compartmentalization of diffusion signal and hence improving FODF estimation. Unlike the aforementioned single fixed RF, each RFG consists of a set of RFs that are intentionally varied to capture potential signal variations associated with a fiber bundle. Additional isotropic RFGs are included to account for signal contributions from gray matter (GM) and cerebrospinal fluid (CSF). To estimate the WM FODF and the volume fractions of GM and CSF compartments, the RFGs are fitted to the data in the least-squares sense, penalized by the cardinality of the support of the solution to encourage group sparsity. The volume fractions associated with each compartment are then computed by summing up the volume fractions of the RFs within each RFGs. Experimental results confirm that our method yields estimates of FODFs and volume fractions of diffusion compartments with improved robustness and accuracy.