Fast and Accurate Multi-tissue Deconvolution Using SHORE and H-psd Tensors

We propose a new regularization for spherical deconvolution in diffusion MRI. It is based on observing that higher-order tensor representations of fiber ODFs should be H-psd, i.e., they should have a positive semidefinite (psd) matrix HT . We show that this constraint is stricter than the currently more widely used non-negativity, and that it can be enforced easily using quadratic cone programming. We demonstrate its use in a multi-tissue deconvolution framework that models the different tissue types in the continuous SHORE basis and can therefore be applied to data with multiple b values that are not organized on shells, such as in Diffusion Spectrum Imaging. Experiments on simulated fiber crossings, data from the Human Connectome Project, and clinical data, demonstrate the improved speed and accuracy of this new method.