原子集校正及步长可控的稀疏度未知CS 重构

doi:10.3969/j.issn.0255-8297.2014.02.008

应用科学学报 ›› 2014, Vol. 32 ›› Issue (2): 163-169.doi: 10.3969/j.issn.0255-8297.2014.02.008

原子集校正及步长可控的稀疏度未知CS 重构

曾春艳1,2，马丽红1，杜明辉1

1. 华南理工大学电子与信息学院，广州510641
2. 湖北工业大学电气与电子工程学院，武汉430068

收稿日期:2012-09-10 修回日期:2013-06-25 出版日期:2014-03-25 发布日期:2013-06-25
作者简介:曾春艳，博士，讲师，研究方向：压缩感知的重建算法，E-mail: swallow_chunyan@163.com；马丽红，教授，博导，研究方向：数字信号处理、容错编码，E-mail: eelhma@scut.edu.cn；杜明辉，教授，博导，研究方向：生物医学工程、图像重建，E-mail:ecmhdu@scut.edu.cn
基金资助:
国家自然科学基金(No.60972133, No.U0735004)；广东省自然科学基金团队项目基金(No.9351064101000003)；广东省能源技
术重点实验室项目基金(No.2008A060301002)；湖北工业大学博士科研启动基金(No.BSQD13037)资助

Atom Set Calibration and Step Control for Unknown-Sparsity Reconstruction from Compressive Sensing

ZENG Chun-yan1,2, MA Li-hong1, DU Ming-hui1

1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510641, China
2. School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China

Received:2012-09-10 Revised:2013-06-25 Online:2014-03-25 Published:2013-06-25

摘要/Abstract

摘要： 对残差信号用类高斯分布建模，通过分析回溯型自适应正交匹配追踪(backtracking-based adaptive orthogonal matching pursuit, BAOMP) 算法的阈值选择方法与常规信号稀疏度方法的一致性和差异，提出一种改进的BAOMP 算法. 采用80–20 准则判断信号的粗匹配状态，然后对后续匹配步骤引入可变步长阈值，实现
选入原子集容量的精细调整，提高选入原子的正确匹配率，避免了残差信号的准周期性失配. 实验结果表明，与BAOMP算法相比，在500次重复实验中，改进的BAOMP算法对高斯稀疏信号的精确重建概率提高17%-26%，对自然图像的精确重建概率提高70%以上.

关键词: 压缩感知, 正交匹配追踪, 匹配集裁剪, 增量步长控制

Abstract: This paper models residual signals with Gaussian-like distributions, based on which consistency between the Backtracking-based adaptive orthogonal matching pursuit (BAOMP) threshold and signal sparselevel is analyzed. An improved BAOMP (IBAOMP) method is thenproposed. Themethod estimates the
preliminary matching state usingthe 80-20 rule, and introduces a threshold with variable step size to subtly adjust atom set to raise the correct rate of selected atoms and avoid quasi-periodic mismatches of residual signals. Simulation results of 500 tests show that the exact recovery probability of IBAOMP is 17%-26% higher than BAOMP for Gaussian sparse signals, and more than70% higher than BAOMP for natural images.

Key words: compressive sensing (CS), backtracking orthogonal matching pursuit (OMP), matching set calibration, incremental step control

中图分类号:

TN911.7

曾春艳1,2，马丽红1，杜明辉1. 原子集校正及步长可控的稀疏度未知CS 重构[J]. 应用科学学报, 2014, 32(2): 163-169.

ZENG Chun-yan1,2, MA Li-hong1, DU Ming-hui1. Atom Set Calibration and Step Control for Unknown-Sparsity Reconstruction from Compressive Sensing[J]. Journal of Applied Sciences, 2014, 32(2): 163-169.

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原子集校正及步长可控的稀疏度未知CS 重构

Atom Set Calibration and Step Control for Unknown-Sparsity Reconstruction from Compressive Sensing

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