非凸稀疏低秩约束的高光谱解混方法

doi:10.3969/j.issn.1001-2400.2016.06.020

西安电子科技大学学报

非凸稀疏低秩约束的高光谱解混方法

孔繁锵1;卞陈鼎1;李云松2;郭文骏1

(1. 南京航空航天大学航天学院，江苏南京 210016;
2. 西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071)

收稿日期:2015-11-09 出版日期:2016-12-20 发布日期:2017-01-19
作者简介:孔繁锵(1980-)，男，讲师， E-mail: kongfq@nuaa.edu.cn．
基金资助:
国家自然科学基金资助项目(61401200，61201365)

Hyperspectral unmixing method based on the non-convex sparse and low-rank constraints

KONG Fanqiang1;BIAN Chending1;LI Yunsong2;GUO Wenjun1

(1. College of Astronautics, Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China;
2. State Key Lab. of Integrated Service Networks, Xidian Univ., Xi'an 710071, China)

Received:2015-11-09 Online:2016-12-20 Published:2017-01-19

摘要/Abstract

摘要：

针对高光谱混合像元的丰度矩阵具有行稀疏特性，提出一种非凸稀疏低秩约束的高光谱解混方法．首先，建立高光谱图像非凸稀疏低秩约束模型，将丰度系数矩阵的非凸p范数作为稀疏约束，并将丰度系数矩阵奇异值的非凸p范数作为低秩约束；其次，构建联合低秩性先验与稀疏性先验的非凸极小化模型，并提出求解的增广拉格朗日交替极小化算法，将复合正则化问题分解成多个单一正则化问题，交替迭代求解．实验仿真结果表明，该算法比贪婪算法和凸优化算法能获得更高的解混精度，并且适用于信噪比较高的高光谱数据．

关键词: 图像处理, 稀疏解混, 稀疏表示, 低秩, 凸优化

Abstract:

Aiming at the row sparse feature of the abundance matrix of hyperspectral mixed pixels, a hyperspectral unmixing method based on the non-convex sparse and low-rank constraints is presented. The non-convex sparse representation and non-convex low-rank models are first constructed, which take the non-convex p-norm of the abundance matrix as the sparse constraint and the non-convex p-norm of the singular values of the abundance matrix as the low-rank constraint. Then the low-rank prior and the sparse prior are jointly utilized to construct a non-convex minimization model. An augmented lagrange alternating minimization method is proposed to solve the unmixing model, the compound regularization problem is decomposed into multiple single regularization problems solved by the variable separation method. Experimental results demonstrate that the proposed method outperforms the greedy algorithm and the convex algorithms with a better spectral unmixing accuracy, and is suitable for high signal-to-noise ratio hyperspectral data.

Key words: image processing, sparse unmixing, sparse representation, low-rank, convex optimization

孔繁锵;卞陈鼎;李云松;郭文骏. 非凸稀疏低秩约束的高光谱解混方法[J]. 西安电子科技大学学报, 2016, 43(6): 116-121.

KONG Fanqiang;BIAN Chending;LI Yunsong;GUO Wenjun. Hyperspectral unmixing method based on the non-convex sparse and low-rank constraints[J]. Journal of Xidian University, 2016, 43(6): 116-121.

参考文献

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非凸稀疏低秩约束的高光谱解混方法

Hyperspectral unmixing method based on the non-convex sparse and low-rank constraints

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