信号压缩与重构的交替方向外点持续法

doi:10.3969/j.iss.0372-2012-2014.03.010

电子学报 ›› 2014, Vol. 42 ›› Issue (3): 485-490.DOI: 10.3969/j.iss.0372-2012-2014.03.010

信号压缩与重构的交替方向外点持续法

杨真真^1,2, 杨震²

1. 南京邮电大学通信与信息工程学院, 江苏南京 210003;
2. 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, 江苏南京 210003

收稿日期:2012-09-27 修回日期:2013-10-11 出版日期:2014-03-25
- 作者简介:
- 杨真真 女，1984出生，山东临沂人，南京邮电大学通信与信息工程学院博士研究生.研究方向为压缩感知、现代信号处理.E-mail：2011010101@njupt.edu.cn
- 基金资助:
- 国家重点基础研究发展计划 (973计划） (No.2011CB302903）; 国家自然科学基金 (No.60971129，No.61271335，No.61070234，No.61271240）; 江苏省普通高校研究生科研创新计划资助项目 (No.CXZZ12_0469）; 江苏省高校自然科学研究资助项目 (No.13KJB510020）

Alternating Direction Exterior Point Continuation Method for Signal Compression and Reconstruction

YANG Zhen-zhen^1,2, YANG Zhen²

1. College of Communication & Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210003, China;
2. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210003, China

Received:2012-09-27 Revised:2013-10-11 Online:2014-03-25 Published:2014-03-25
- Supported by:
- National Program on Key Basic Research Project (973 Program) (No.2011CB302903); National Natural Science Foundation of China (No.60971129, No.61271335, No.61070234, No.61271240); Graduate Research Innovation Program of univerities in Jiangsu Province (No.CXZZ12_0469); Supported by Natural Science Research Program of Colleges and Universities of Jiangsu Province (No.13KJB510020)

摘要/Abstract

摘要： 针对压缩感知（Compressed Sensing，CS）中信号重构的l1-正则化问题中的l1-正则项非光滑，求解比较困难，提出了交替方向外点持续法（Alternating Direction Exterior Point Continuation Method，ADEPCM）.该算法首先将信号的稀疏域的l1-正则化问题通过变量分裂（Variable Splitting，VS）技术转化为与之等价的约束优化问题；然后采用一步Gauss-Seidel思想，对优化问题中的变量最小化，并采用持续的思想更新罚参数，重构出信号的稀疏系数；最后进行正交反变换，重构出原始信号.并将ADEPCM用于图像重构，进行了仿真实验及对实验结果进行了分析.实验结果表明：与现有的一些重构算法相比，ADEPCM具有稍高的峰值信噪比（Peak Signal to Noise Ratio，PSNR）和更快速的收敛速度.

关键词: 交替方向外点持续法, 外点法, 信号重构, 压缩感知

Abstract: Alternating direction exterior point continuation method (ADEPCM) is proposed to solve the l1-regularization problem,which is the classic problem of signal compression and reconstruction for compressed sensing (CS).The first step of ADEPCM is to express the l1-regularization problem of the sparse coefficient in the transform domain as an equivalent constrained optimization problem by using variable splitting (VS) technology.Then,by introducing the penalty function,the two variables are alternatively minimized by Gauss-Seidel method,and the penalty variable is updated by a continuation scheme,and then the sparse coefficient in the transform domain is reconstructed.Finally,the original signal is reconstructed by the orthogonal inverse transform.And the experimental simulations demonstrate that the ADEPCM algorithm yields a slightly higher peak signal to noise ratio (PSNR) reconstructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms.

Key words: alternating direction exterior point continuation method, exterior point method, signal reconstruction, compressed sensing

中图分类号:

TN912.3

杨真真, 杨震. 信号压缩与重构的交替方向外点持续法[J]. 电子学报, 2014, 42(3): 485-490.

YANG Zhen-zhen, YANG Zhen . Alternating Direction Exterior Point Continuation Method for Signal Compression and Reconstruction[J]. Acta Electronica Sinica, 2014, 42(3): 485-490.

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信号压缩与重构的交替方向外点持续法

Alternating Direction Exterior Point Continuation Method for Signal Compression and Reconstruction

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