Sparse signal reconstruction can be regarded as a problem of locating the nonzero entries of the signal. In presence of measurement noise, conventional methods such as l₁ norm relaxation methods and greedy algorithms, have shown their weakness in finding the nonzero entries accurately. In order to reduce the impact of noise and better locate the nonzero entries, in this paper, we propose a two-phase algorithm which works in a coarse-to-fine manner. In phase 1, a decomposition-based multiobjective evolutionary algorithm is applied to generate a group of robust solutions by optimizing l₁ norm of the solutions. To remove the interruption of noise, the statistical features with respect to each entry among these solutions are extracted and an initial set of nonzero entries are determined by clustering technique. In phase 2, a forward-based selection method is proposed to further update this set and locate the nonzero entries more precisely based on these features. At last, the magnitudes of the reconstructed signal are obtained by the method of least squares. We conduct the comparison of our proposed method with several state-of-the-art compressive sensing recover methods, the best result in phase 1 and the approach combining phases 1 and 2 without the statistical features. Experimental results on benchmark signals as well as randomly generated signals demonstrate that our proposed method outperforms the above methods, achieving higher recover precision and maintaining larger sparsity.
Bibliographical noteThis work was supported in part by the Hong Kong RGC General Research Fund GRF under Grant 9042038 (CityU 11205314), and in part by the National Natural Science Foundation of China under Grant 61672443 and Grant 61473241.
- Compressive sensing
- greedy randomized adaptive search procedure (GRASP)
- k-means clustering
- multiobjective evolutionary algorithm (MOEA)
- sparse reconstruction