Leveraging EAP-Sparsity for Compressed Sensing of MS-HARDI in $({\mathbf {k}},{\mathbf {q}})$-Space

Abstract

Compressed Sensing (CS) for the acceleration of MR scans has been widely investigated in the past decade. Lately, considerable progress has been made in achieving similar speed ups in acquiring multi-shell high angular resolution diffusion imaging (MS-HARDI) scans. Existing approaches in this context were primarily concerned with sparse reconstruction of the diffusion MR signal $S({\mathbf {q}})$ in the ${\mathbf {q}}$-space. More recently, methods have been developed to apply the compressed sensing framework to the 6-dimensional joint $({\mathbf {k}},{\mathbf {q}})$-space, thereby exploiting the redundancy in this 6D space. To guarantee accurate reconstruction from partial MS-HARDI data, the key ingredients of compressed sensing that need to be brought together are: (1) the function to be reconstructed needs to have a sparse representation, and (2) the data for reconstruction ought to be acquired in the dual domain (i.e., incoherent sensing) and (3) the reconstruction process involves a (convex) optimization.

In this paper, we present a novel approach that uses partial Fourier sensing in the 6D space of $({\mathbf {k}},{\mathbf {q}})$ for the reconstruction of $P({\mathbf {x}},{\mathbf {r}})$. The distinct feature of our approach is a sparsity model that leverages surfacelets in conjunction with total variation for the joint sparse representation of $P({\mathbf {x}}, {\mathbf {r}})$. Thus, our method stands to benefit from the practical guarantees for accurate reconstruction from partial $({\mathbf {k}},{\mathbf {q}})$-space data. Further, we demonstrate significant savings in acquisition time over diffusion spectral imaging (DSI) which is commonly used as the benchmark for comparisons in reported literature. To demonstrate the benefits of this approach, we present several synthetic and real data examples.

This research was funded in part by the AFOSR FA9550-12-1-0304 and NSF CCF-1018149 grants to Alireza Entezari and the NIH grant NS066340 to Baba C. Vemuri.