基于SL0范数的改进稀疏信号重构算法

平滑范数（Smoothed l0，SL0）压缩感知重构算法通过引入平滑函数序列将求解最小l0范数问题转化为平滑函数优化问题，可以有效地用于稀疏信号重构。针对平滑函数的选取和算法稳健性问题，提出一种新的平滑函数序列近似范数，结合梯度投影法优化求解，并进一步提出采用奇异值分解（Singular value decomposition, SVD）方法改进算法的稳健性，实现稀疏度信号的精确重构。仿真结果表明，在相同的测试条件下，本文算法相比OMP算法、SL0算法以及L1-magic算法在重构精度、峰值信噪比方面都有较大改善。

Improved Sparse Signal Reconstruction Algorithm Based on SL0 Norm

The smoothed l0 norm algorithm in compressive sensing introduces smoothed functions to approximate the l0 norm. The problem of minimization of l0 norm can be transferred to a convex optimization problem of the smoothed functions, which could be used efficiently for compressive sensing reconstruction. Aiming at the choice of appropriate smoothed functions and improvement of the robustness of the algorithm, a new smoothed function sequence with gradient projection method has been proposed to solve the optimization problem in this paper. Singular value decomposition (SVD) method has been further proposed to improve the robustness of algorithm,then the accurate reconstruction of sparse signal is realized.Experimental results show that the proposed algorithm improve ignificantly in both the reconstruction accuracy and the peak value signal-to-noise ratio under the same test conditions.