WAVELET FRAMES ON THE SPHERE, HIGH ANGULAR RESOLUTION DIFFUSION IMAGINING AND L_1-REGULARIZED OPTIMIZATION ON STIEFEL MANIFOLDS

Abstract

Motivated by sparser representations of signals for High Angular Resolution Diffusion Imaging (HARDI), we first construct wavelet frames for the space of symmetric, square-integrable functions defined on the unit sphere. These wavelet frames are then applied to denoise HARDI signals, with superior performances over approaches based on spherical harmonics and spherical ridgelets. Denoising performances can be enhanced by optimization models on Stiefel manifolds. To solve such models, we propose a proximal alternating minimized augmented Lagrangian method (with convergence analysis) for a class of l1-regularized optimization problems with orthogonality constraints, which also include the problem of compressed modes.