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.