电子学报 ›› 2014, Vol. 42 ›› Issue (11): 2219-2224.DOI: 10.3969/j.issn.0372-2112.2014.11.014

• 学术论文 • 上一篇    下一篇

联合低秩与稀疏先验的高光谱图像压缩感知重建

孙玉宝1,2, 吴泽彬2, 吴敏3, 刘青山1   

  1. 1. 南京信息工程大学信息与控制学院, 江苏南京 210044;
    2. 南京理工大学计算机科学与工程学院与江苏省光谱成像与智能感知重点实验室, 江苏南京 210094;
    3. 南京军区南京总医院医学工程科, 江苏南京 210002
  • 收稿日期:2013-11-08 修回日期:2014-02-07 出版日期:2014-11-25 发布日期:2014-11-25
  • 通讯作者: 刘青山
  • 作者简介:孙玉宝 男,1983年生于江苏连云港.南京信息工程大学讲师.研究方向为多维信号稀疏表示与压缩感知、高光谱图像处理;吴泽彬 男,1981年生于浙江杭州.南京理工大学副教授,研究方向为高光谱图像处理与智能解译、高性能计算技术;吴敏 女,1973年生于江苏南通.南京军区南京总医院,高级工程师,研究方向为压缩感知理论与应用、EEG信号处理.
  • 基金资助:

    国家自然科学基金(No.61300162,No.81201161);江苏省自然科学基金(No.BK2012045,No.BK20131003);中国博士后基金(No.20110491429);江苏省博士后基金(No.1101083C);江苏省光谱成像与智能感知重点实验室基金(No.30920130122003)

Compressed Sensing Reconstruction of Hyperspectral Imagery Jointly Using Low Rank and Sparse Prior

SUN Yu-bao1,2, WU Ze-bin2, WU Min3, LIU Qing-shan1   

  1. 1. Department of Information and Control, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China;
    2. Department of Computer Science and Engineering and Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;
    3. Nanjing General Hospital of Nanjing Area Command, Nanjing, Jiangsu 210002, China
  • Received:2013-11-08 Revised:2014-02-07 Online:2014-11-25 Published:2014-11-25

摘要:

本文建立了一种新的高光谱图像压缩感知重建模型,编码端采用块对角的Noiselet测量矩阵对每一谱带进行独立采样,解码端首先建立高光谱图像低秩稀疏表示模型,分解为低秩与稀疏成分,并对低秩成分在空间维进行稀疏分解,进而构建联合谱间低秩性先验与谱内空间稀疏性先验的凸优化重建模型,并提出模型求解的增广拉格朗日乘子迭代算法,通过引入辅助变量与线性化技巧,使得每一子问题均存在解析解,降低了模型求解的复杂度.实验结果验证了本文模型及其算法的有效性.

关键词: 压缩感知, 低秩先验, 稀疏先验, 增广拉格朗日乘子算法

Abstract:

A new compressed sensing model is proposed to reconstruct hyperspectral image.In the encoder side,block-dialog measurement matrix formed by permuted noiselets transform is used to randomly measure the signal of each channel independently.In the decoder side,the low rank and sparse representation models are firstly constructed to decompose hyperspectral data matrix into low rank and sparse parts,and the low rank part is further sparsely decomposed.Then,the intra-channel low rank prior and the inter-channel sparse prior are jointly utilized to reconstruct the compressed data.A numerical optimization algorithm is also proposed to solve the reconstruction model by augmented lagrange multiplier method.Every sub-problem in the iteration formula admits analytical solution after introducing auxiliary variable and linearization operation.The complexity of the numerical optimization algorithm is reduced.The experimental results verify the effectiveness of our algorithm.

Key words: compressed sensing, low rank prior, sparse prior, augmented Lagrange multiplier method

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