Sparse Blind Spherical Deconvolution of diffusion weighted MRI

Diffusion-weighted magnetic resonance imaging provides invaluable insights into in-vivo neurological pathways. However, accurate and robust characterization of white matter fibers microstructure remains challenging. Widely used spherical deconvolution algorithms retrieve the fiber Orientation Distribution Function (ODF) by using an estimation of a response function, i.e., the signal arising from individual fascicles within a voxel. In this paper, an algorithm of blind spherical deconvolution is proposed, which only assumes the axial symmetry of the response function instead of its exact knowledge. This algorithm provides a method for estimating the peaks of the ODF in a voxel without any explicit response function, as well as a method for estimating signals associated with the peaks of the ODF, regardless of how those peaks were obtained. The two stages of the algorithm are tested on Monte Carlo simulations, as well as compared to state-of-the-art methods on real in-vivo data for the orientation retrieval task. Although the proposed algorithm was shown to attain lower angular errors than the state-of-the-art constrained spherical deconvolution algorithm on synthetic data, it was outperformed by state-of-the-art spherical deconvolution algorithms on in-vivo data. In conjunction with state-of-the art methods for axon bundles direction estimation, the proposed method showed its potential for the derivation of per-voxel per-direction metrics on synthetic as well as in-vivo data.