基于混合优化的平滑l0压缩感知重构算法

研究压缩感知的重构算法，分析了平滑l0（smoothed l0，SL0）的理论基础．SLO算法通过利用平滑的高斯函数去逼近l0范数，将重构中的l0范数最小化问题转化为求解光滑函数最小值的最优化问题．针对算法中最速下降法存在“锯齿现象”和收敛速度慢等缺点，引入数值最优化理论中的混合优化算法，提出了一种基于混合优化的SL0重构算法（HOSL0）．该算法结合了最速下降法和修正牛顿法的优点，提高了算法的重构精度和速度．仿真实验表明，HOSL0算法与同类算法相比性能有明显提高，同时在重构速度上比BP算法快了2个数量级．

Sparse recovery using smoothed l0 based on hybrid optimization algorithm

This paper researches the reconstruction algorithm of compressive sensing, analyzes the theoretical basis of smoothed l0 algorithm （SL0）. Through the use of a sequence of smoothed Gauss functions to approximate the l0 norm, the problem of minimization of the lo norm in the reconstruction can be transformed into a convex optimization problem for the smoothed function. This paper proposes a new reconstruction algorithm to overcome the shortcomings of the gradient method, such as ＂notched effect＂ and the slow convergence. The algorithm using Smoothed l0 based on Hybrid Optimization algorithm （HOSL0） combines the advantages of the gradient method and the revised Newton method to improve the accuracy and speed of sparse recovery. The numerical simulation results show that the proposed algorithm has fast convergence and better accuracy compared with some existing similar methods. It is experimentally shown that HOSL0 algorithm is about two orders of magnitude faster than backpropagation algorithm under the same conditions.