AN ADAPTIVE l1-l2-TYPE MODEL WITH HIERARCHIES FOR SPARSE SIGNAL RECONSTRUCTION PROBLEM

This paper addresses solving an adaptive l(1)-l(2) regularized model in the framework of hierarchical convex optimization for sparse signal reconstruction. This is realized in the framework of bi-level convex optimization, we can also turn the challenging bi-level model into a single-level constrained optimization problem through some priori information. The l(1)-l(2 )norm regularized least-square sparse optimization is also called the elastic net problem, and numerous simulation and real-world data show that the elastic net often outperforms the Lasso. However, the elastic net is suitable for handling Gaussian noise in most cases. In this paper, we propose an adaptive and robust model for reconstructing sparse signals, say l(p-)l(1)-l(2), where the l(p)-norm with p >= 1 measures the data fidelity and l(1)-l(2)-term measures the sparsity. This model is robust and flexible in the sense of having the ability to deal with different types of noises. To solve this model, we employ an alternating direction method of multipliers (ADMM) based on introducing one or a pair of auxiliary variables. From the point of view of numerical computation, we use numerical experiments to demonstrate that both of our proposed model and algorithms outperform the Lasso model solved by ADMM on sparse signal reconstruction problem.