Accelerated Schemes for the L1/L2 Minimization

In this paper, we consider the L_1/L_2 minimization for sparse recovery and study its relationship with the L_1- \alpha L_2 model. Based on this relationship, we propose three numerical algorithms to minimize this ratio model, two of which work as adaptive schemes and greatly reduce the computation time. Focusing on the two adaptive schemes, we discuss their connection to existing approaches and analyze their convergence. The experimental results demonstrate that the proposed algorithms are comparable to state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. Lastly, we reveal some empirical evidence on the exact L_1 recovery under various combinations of sparsity, coherence, and dynamic ranges, which calls for theoretical justification in the future.