IEEE Trans Cybern. 2017 Sep;47(9):2651-2663. doi: 10.1109/TCYB.2017.2679705. Epub 2017 Apr 14.
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 l 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 l 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.
稀疏信号重构可以看作是定位信号非零项的问题。在存在测量噪声的情况下，传统的方法，如 l 范数松弛方法和贪婪算法，在准确找到非零项方面表现出了它们的弱点。为了减少噪声的影响并更好地定位非零项，本文提出了一种两阶段算法，以粗到精的方式工作。在第一阶段，应用基于分解的多目标进化算法通过优化解的 l 范数来生成一组稳健的解。为了消除噪声的干扰，从这些解中提取关于每个元素的统计特征，并通过聚类技术确定初始的非零元素集。在第二阶段，提出了一种基于前向的选择方法，根据这些特征进一步更新该集合，并更精确地定位非零元素。最后，通过最小二乘法方法获得重构信号的幅度。我们将所提出的方法与几种最先进的压缩感知恢复方法进行了比较，第一阶段的最佳结果和不使用统计特征的结合了第一阶段和第二阶段的方法。基准信号和随机生成信号的实验结果表明，所提出的方法优于上述方法，实现了更高的恢复精度并保持了更大的稀疏性。
