Section: New Results

Augmented Lagrangian for Fast Multi-Sparse Optimization

Participants : Hicham Badri, Hussein Yahia, Khalid Daoudi.

Sparsity has become one of the most important notions in many imaging applications. We address in this paper the problem of multi-sparse optimization, when the energy to minimize contains multiple sparse terms instead of a single one. We show that applying off-the-shelf proximal-based solvers such as ADMM results in a high computational cost due to the complexity of the resulting sub-problems in the case of multi-sparsity. We propose an efficient extension of ADMM for multi-sparse optimization, we study its convergence and complexity and show how it can be applied to computer vision problems. Experiments show that the proposed solver is not only computationally efficient, but also leads quickly to higher-quality results compared to the popular half-quadratic solver.