基于光滑l0范数和修正牛顿法的压缩感知重建算法

基于光滑l0范数最小的压缩感知重建算法——SL0算法,通过引入光滑函数序列去逼近l0范数,从而将l0范数最小的问题转化为光滑函数的最优化问题.针对光滑函数的选取以及求解该函数的最优化问题,提出一种基于光滑l0范数和修正牛顿法的重建算法——NSL0算法.首先采用双曲正切函数序列来逼近l0范数,得到一个新的最优化问题;为了提高该优化问题的计算效率,推导出针对双曲正切函数的修正牛顿方向,并采用修正牛顿法进行求解.实验结果表明,在相同的测试条件下,NSL0算法无论在重建效果还是在计算时间方面都明显优于其他同类算法.

Reconstruction Algorithm for Compressive Sensing Based on Smoothed l0 Norm and Revised Newton Method

The SL0 algorithm for compressive sensing(CS) reconstruction uses smoothed l0 norm and introduces a sequence of smoothed functions to approximate the l0 norm.Therefore,the NP-hard problem of minimization of the l0 norm can be transferred to a convex optimization problem for smoothed functions.In order to choose an appropriate sequence of smoothed functions and solve the optimization problem effectively,we propose a new reconstruction algorithm based on smoothed l0 norm and revised Newton method,called NSL0 algorithm.We employ the hyperbolic tangent sequence to approximate the l0 norm,yielding a new optimization problem.To improve the computational performance,we utilize the revised Newton method to solve the optimization problem by deriving the new revised Newton directions for the sequence of hyperbolic tangent functions.Experimental results show that the proposed NSL0 algorithm is superior to existing methods both in terms of the reconstruction quality and the performance.