1. 北京理工大学光电学院, 北京 100081 2. 北京理工大学光电成像技术与系统教育部重点实验室，北京 100081 3. Polytechnic Institute of New York University, Brooklyn, NY, USA 11201
A Noise Reduction Algorithm of Hyperspectral Imagery Using Double-Regularizing Terms Total Variation
LI Ting1，2, CHEN Xiao-mei1，2*, CHEN Gang1，3, XUE Bo1，2, NI Guo-qiang1，2
1. School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China 2. Key Laboratory of Photoelectronic Imaging Technology and System (Beijing Institute of Technology), Ministry of Education of China, Beijing 100081, China 3. Polytechnic Institute of New York University, Brooklyn, NY, USA 11201
Abstract：In the present paper, an effective total variation denoising algorithm is proposed based on hyperspectral imagery noise characteristics. The new algorithm generalizes the classical total variation denoising algorithm for two-dimensional images to a three-dimensional formulation. Considering the fact that the noise of hyperspectral imagery shows different characteristics in spatial domain and spectral domain respectively, the objective function of the proposed total variation algorithm is improved by utilizing double-regularizing terms (spatial term and spectral term) and separate regularization parameters respectively. Then, the new objective function is discretized via approximating the gradient of the regularizing terms by three orthogonal local differences, and further majorized by a convex quadratic function. Thus, noise in spatial and spectral domain could be removed independently by minimizing the majorizing function with a majorization-minimization (MM) based iteration. The performance of the proposed algorithm is experimented on a set of Hyperion imageries acquired in 2007. Experiment results show that, properly choosing the values of regularization parameters, the new algorithm has a similar improvement of signal-to-noise-ratio as minimum noise fraction (MNF) method and Savitzky-Golay filter, but a better performance in removing the indention and restoring the spectral absorption peaks.
[1] Othman H, Qian S-E. IEEE Trans. Geosci. Remote Sens., 2006, 44(2): 397. [2] SUN Lei, GU De-feng, LUO Jian-shu(孙 蕾, 谷德峰, 罗建书). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2009, 29(7): 1954. [3] Donoho D L. IEEE Trans. Inf. Theory, 1995, 41(3): 613. [4] WU Chuan-qing, TONG Qing-xi, ZHENG Lan-fen(吴传庆, 童庆禧, 郑兰芬). Remote Sensing Information(遥感信息), 2005, 4: 10. [5] David G G, Han T. First Workshop on Hyperspectral Image and Signal Processing (WHISPERS), IEEE, Piscataway NJ USA, 2009. 1. [6] WANG Qiang, SHU Jiong, YIN Qiu(王 强, 束 炯, 尹 球). J. Infrared Millim. Waves(红外与毫米波学报), 2006, 25(1): 29. [7] Rudin L, Osher S, Fatemi E. Physica. D, 1992, 60: 259. [8] Chan T, Esedoglu S, Park F, et al. In Mathematical Models of Computer Vision, by Paragios N, Chen Y, Faugeras O, Editors, Springer Verlag, 2005. [9] Figuered M, Dias J, Oliveira J, et al. In Proc. IEEE Conf. on Image Processing(ICIP), 2006. 2633. [10] Hunter D, Lange K. The American Statistician, 2004, 58： 30. [11] Chambolle A. Journal of Math Imaging and Vision, 2004, 20: 89. [12] Strang G. Introduction to Applied Mathematics, Wellesley-Cambridge Press, 1986. [13] Pearlman J, Segal C, Liao L, et al. Proc. SPIE, 2000, 4135: 243. [14] Roger R E, Arnold J F. Int. J. Remote Sens., 2001, 17(10): 1951.
