稀疏分解的加权迭代方法及其初步应用

为了在强噪声背景下提取信号,本文发展了一种加权迭代稀疏分解方法.从一个完备库中寻找观测信号的稀疏成分表达问题的目标函数,可以取残差的l-2模和稀疏成分的l-1模的加权和最小,通过分析噪声信号在多分辨小波分解下的性质,得到了二尺度小波框架下不同尺度空间的加权系数的表达式;通过分析最小l-1模问题的求解过程,提出了用两次迭代得到的信号成分的l-1模的差作为迭代的收敛条件.最后用仿真试验和真实信号验证了方法的有效性.

Iterative Weighted Method of Sparse Decomposition and Preliminary Application

A weighted algorithm of sparse decomposition is developed for recovery of signal in strong background noise. To find the real components in a complete dictionary, the cost function can be constructed by a weighted sum of the / - 2 norm of residual errors and l-1 norm of sparse components. Taking complete dictionary as the multiresolution wavelets, a feasible penalty formula is deduced according to two-scale relation of additive noise in wavelets dictionary. Analyzing the resolving process of minimum l -1 problem, proposed is the difference of l - 1 norm of signal components as converge condition, where the difference is derived from the results of successive two iterative steps.The method is confirmed by both simulated and real data.