Iterative Weighted Method of Sparse Decomposition and Preliminary Application

FU Ting; YAO De-zhong

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Iterative Weighted Method of Sparse Decomposition and Preliminary Application

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- Iterative Weighted Method of Sparse Decomposition and Preliminary Application
- Acta Electronica Sinica Vol. 32, Issue 4, Pages: 567-570(2004)
- 作者机构：
  
  电子科技大学生命科学与技术学院,四川,成都,610054
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP301
- Published：2004
- 稿件说明：
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FU Ting, YAO De-zhong. Iterative Weighted Method of Sparse Decomposition and Preliminary Application[J]. Acta Electronica Sinica, 2004, 32(4): 567-570.
DOI：

FU Ting, YAO De-zhong. Iterative Weighted Method of Sparse Decomposition and Preliminary Application[J]. Acta Electronica Sinica, 2004, 32(4): 567-570. DOI：

摘要

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.

Abstract

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

-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

-1 problem

proposed is the difference of

-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.

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