Structured sparsity through reweighting and application to diffusion MRI

We consider the problem of multiple correlated sparse signals reconstruction and propose a new implementation of structured sparsity through a reweighting scheme. We present a particular application for diffusion Magnetic Resonance Imaging data and show how this procedure can be used for fibre orientation reconstruction in the white matter of the brain. In that framework, our structured sparsity prior can be used to exploit the fundamental coherence between fibre directions in neighbour voxels. Our method approaches the $\ell_0$ minimisation through a reweighted $\ell_1$-minimisation scheme. The weights are here defined in such a way to promote correlated sparsity between neighbour signals.