Split Bregman Algorithm for Structured Sparse Reconstruction

Sparse reconstruction has attracted considerable attention in recent years and shown powerful capabilities in many applications. In standard sparse reconstruction, the sparse nonzero elements appear anywhere in a vector. However, in many applications, the nonzero elements usually exhibit additional structure. Structured sparsity can be reconstructed from asymptotically less measurement than standard sparsity. In this paper, a unified framework is given to express the existing sparsity structures. Then efficient algorithm based on split Bregman iteration is proposed to solve the structured sparse reconstruction problem. The convergence of the proposed algorithm is also discussed. Numerical results show the effectiveness of the proposed algorithm for both synthetic and real-world data.