摘要
SL0算法是一种基于近似L0范数的压缩感知信号重建算法,它采用最速下降法和梯度投影原理,逐步逼近最优解,具有匹配度高、重建时间短、计算量低、不需要信号的稀疏度这个先验条件等优点。但是,它的迭代方向为负梯度方向,存在"锯齿效应",并且SL0算法及其改进算法(NSL0)中的连续函数"陡峭性"不大,使近似L0范数的估计不精确、收敛速度慢。本文采用"陡峭性"大的近似双曲正切函数,结合修正牛顿法和阻尼牛顿法,提出一种更快速高效的信号重建算法(ANSL0)。数值计算结果表明,在相同的条件下,相比SL0和NSL0算法,ANSL0算法在匹配度、峰值信噪比和信噪比方面都有了较大提高。
Smoothed l0 norm algorithm（SL0） is a reconstruction algorithm in compressive sensing based on approximate l0 norm.It approches the solution using the specific iteration process with the steepest desent method and gradient projection principle.It has many advantages,such as the high matching degree,the short reconstruction time,the low computation complexity,and no need for the sparsity of a signal.However,it has ＂notched effect＂ due to the negative iterative gradient direction.Moreover,the property of continuous function in SL0 and its improved algorithm（NSL0） is not steep enough,which results in the estimations are not accurate and the convergence is slow.In this paper,we use hyperbolic tangent function as the approximation to the big ＂steep nature＂ in l0 norm.Based on it,we propose a novel reconstruction algorithm named ANSL0 with the Damped Newton method and the Revised Newton method.The numerical simulation results show that the ANSL0 algorithm has great improvement in both matching degree,the peak value signal-to-noise ratio and the signal-to-noise ratio,comparing with the SL0 algorithm and NSL0 algorithm under the same conditions.
出处
《信号处理》
CSCD
北大核心
2012年第6期834-841,共8页
Journal of Signal Processing
基金
江苏省高校自然科学研究重大项目(11KJA510002)
南京邮电大学“宽带无线通信与传感网技术”教育部重点实验室开放研究基金(ZD035001NYKL01)
留学人员科技活动项目(NJ210002)
关键词
压缩感知
重建算法
光滑L0范数
修正牛顿法
阻尼牛顿法
compressive sensing
reconstruction algorithm
smoothed l0 norm
revised Newton method
damped Newton method
