A Multi-phase Multiobjective Approach Based on Decomposition for Sparse Reconstruction

Solving sparse optimization problems via regularization frameworks is the dominant methodology for reconstructing sparse signals in the area of compressive sensing. In recent a few years, the use of multiobjective evolutionary algorithms (MOEAs) for sparse optimization has also attracted some research interests. Under the multiobjective framework, the loss term (error) and the regularization term (sparsity) are treated as two separate objective functions. So far, two popular multiobjective frameworks, NSGA-II and MOEA/D, have been used for sparse optimization. In this paper, we further develop a new MOEA/D variant for sparse reconstruction and sparsity detection, which involves three phases - approximating Pareto front (PF) in a chain order (phase 1) and in a random order (phase 2), and exploiting a knee region (phase 3 - optional). Our experimental results show that our proposed method is more effective than the earlier version of MOEA/D and the HALF solver in sparse signal reconstruction and sparsity detection.