[1]郑晓,薄华,孙强.QR分解与特征值优化观测矩阵的算法研究[J].智能系统学报,2015,10(1):149-155.[doi:10.3969/j.issn.2013-0934.201309034]
ZHENG Xiao,BO Hua,SUN Qiang.An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio[J].CAAI Transactions on Intelligent Systems,2015,10(1):149-155.[doi:10.3969/j.issn.2013-0934.201309034]
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ZHENG Xiao,BO Hua,SUN Qiang.An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio[J].CAAI Transactions on Intelligent Systems,2015,10(1):149-155.[doi:10.3969/j.issn.2013-0934.201309034]
QR分解与特征值优化观测矩阵的算法研究
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
10
期数:
2015年第1期
页码:
149-155
栏目:
学术论文—机器学习
出版日期:
2015-03-25
- Title:
- An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio
- Keywords:
- compressed sensing; sparse basis; measurement matrix; reconstruction algorithm; QR decomposition; eigenvalue; column independence; incoherenc
- 分类号:
- TP391.9
- 文献标志码:
- A
- 摘要:
- 观测矩阵的构造是压缩感知中的核心部分之一,观测矩阵的列独立性,观测矩阵与稀疏基的非相干性,对重构图像的质量有重要影响,基于此提出了一种优化算法。该算法实现对观测矩阵进行QR分解以增大其列独立性,同时对格拉姆矩阵进行优化,使其归一化后的特征值逼近N/M,从而增大观测矩阵与稀疏基的非相干性。仿真结果显示,算法在提高图像重构质量,以及重构结果稳定性上都有较好的结果,尤其是在观测值个数较少的情况下,有比其他算法更明显的优势。
- Abstract:
- Measurement matrix is a core part of compressed sensing. The column independence of measurement matrix and the incoherence between measurement matrix and sparse basis have a major impact on the quality of a reconstructed image. This paper proposes a new algorithm of measurement matrix based on QR decomposition and eigenvalue. The column independence of the measurement matrix is increased by QR decomposition and at the same time the Gram matrix is optimized. Therefore, the eigenvalue of the normalized Gram matrix approximates to N/M so as to increases the incoherence between measurement matrix and sparse basis. The simulation results showed that the proposed method has excellent results on the aspects of increasing the quality of reconstructed image. In addition, the stability of the reconstructed results had more apparent advantages than other algorithms in the case of less number of observed values.
- 参考文献/References:
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备注/Memo
收稿日期:2013-9-12;改回日期:。
基金项目:国家自然科学基金资助项目(61001140).
作者简介:郑晓,女,1989年生,硕士研究生,主要研究方向为图像处理与模式识别;薄华,女,1971年生,副教授,主要研究方向为遥感图像处理、模式识别、人工智能。曾主持上海市教委项目,参加国家“863”计划国家自然科学基金项目多项,并以第二完成人获军队科技进步奖三等奖2次;孙强,男,1979年生,博士,副教授。主要研究方向为遥感图像处理与解译、机器学习、机器视觉和专用集成系统主持国家自然科学基金项目1项、陕西省教育厅自然科学专项2项;参加国家“973”计划、“863”计划、国家自然科学基金和国防部委资助的科研项目多项。
通讯作者:郑晓.E-mail:gofishingwan@163.com.
更新日期/Last Update:
2015-06-16