Joint dictionary learning and recovery algorithms in a jointly sparse framework

We address the general multiple measurement vectors (MMV) problem when signals are jointly sparse, i.e. sharing the same locations of non-zero elements, but are measured by different sensing matrix. We propose practical algorithms to implement joint sparse signal recovery and present its superiority over independent signal recovery. When signals are not sparse themselves, but can be jointly sparsely represented in some basis, we propose a joint dictionary learning algorithm that learns dictionaries in which the joint sparsity is enforced. Simulation study shows that when performing dictionary learning jointly, each of the learned dictionaries achieves improved percentage of successful recovery.