title: Multi-shell diffusion signal recovery from sparse measurements.
abstract: For accurate estimation of the ensemble average diffusion propagator (EAP), traditional multi-shell diffusion imaging (MSDI) approaches require acquisition of diffusion signals for a range of b-values. However, this makes the acquisition time too long for several types of patients, making it difficult to use in a clinical setting. In this work, we propose a new method for the reconstruction of diffusion signals in the entire q-space from highly undersampled sets of MSDI data, thus reducing the scan time significantly. In particular, to sparsely represent the diffusion signal over multiple q-shells, we propose a novel extension to the framework of spherical ridgelets by accurately modeling the monotonically decreasing radial component of the diffusion signal. Further, we enforce the reconstructed signal to have smooth spatial regularity in the brain, by minimizing the total variation (TV) norm. We combine these requirements into a novel cost function and derive an optimal solution using the Alternating Directions Method of Multipliers (ADMM) algorithm. We use a physical phantom data set with known fiber crossing angle of 45° to determine the optimal number of measurements (gradient directions and b-values) needed for accurate signal recovery. We compare our technique with a state-of-the-art sparse reconstruction method (i.e., the SHORE method of Cheng et al. (2010)) in terms of angular error in estimating the crossing angle, incorrect number of peaks detected, normalized mean squared error in signal recovery as well as error in estimating the return-to-origin probability (RTOP). Finally, we also demonstrate the behavior of the proposed technique on human in vivo data sets. Based on these experiments, we conclude that using the proposed algorithm, at least 60 measurements (spread over three b-value shells) are needed for proper recovery of MSDI data in the entire q-space.
authors.affiliation: Brigham and Women's Hospital, Harvard Medical School, Boston, United States. Electronic address: yogesh@bwh.harvard.edu.
authors.forename: Y
authors.initials: Y
authors.lastname: Rathi
authors.affiliation: Department of Electrical Engineering, University of Waterloo, Canada.
authors.forename: O
authors.initials: O
authors.lastname: Michailovich
authors.affiliation: German Cancer Research Center (DKFZ), Dept. of Medical Physics in Radiology, Heidelberg, Germany.
authors.forename: F
authors.initials: F
authors.lastname: Laun
authors.affiliation: Massachusetts General Hospital, Harvard Medical School, Boston, United States.
authors.forename: K
authors.initials: K
authors.lastname: Setsompop
authors.affiliation: Children's Hospital Boston, Harvard Medical School, Boston, United States.
authors.forename: P E
authors.initials: PE
authors.lastname: Grant
authors.affiliation: Brigham and Women's Hospital, Harvard Medical School, Boston, United States.
authors.forename: C-F
authors.initials: CF
authors.lastname: Westin
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D009413:Nerve Fibers, Myelinated; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio
keywords: Compressed sensing; Diffusion MRI; Diffusion propagator; Diffusion spectrum imaging; Kurtosis