Research on Spectrum Denoising Methods Based on the Combination of Wavelet Package Transformation and Mathematical Morphology
LI Hui1, 2, 3, LIN Qi-zhong1, 2, WANG Qin-jun1, 2, LIU Qing-jie1, 2, WU Yun-zhao4
1. Center for Earth Observation and Digital Earth, Chinese Academy of Sciences, Beijing 100086, China 2. Key Laboratory of Digital Earth Sciences, Chinese Academy of Sciences, Beijing 100086, China 3. Graduate University of Chinese Academy of Sciences, Beijing 100049, China 4. School of Geographic and Oceanographic Sciences of Nanjing University, Nanjing 210093, China
Abstract:The present study introduced the generalized morphological filter into the denoising of visible and near infrared spectra for the first time, and provided a new method for denoising the reflectance spectra by combining mathematical morphology methods with the wavelet packet transformation. The authors used vegetable spectra from USGS spectral library as the reference spectra, and obtained the noised spectra by adding noises with different signal-to-noise ratios to the referenced spectra. The results were evaluated by signal-to-noise ratio (SNR), root mean squared error (RMSE), normalized correlation coefficient (NCC) and smoothness ratio (SR) of the denoised spectra. The authors’ results showed that both the thresholding on wavelet packet decomposition best bases method and the generalized morphological filter method could maintain the spectral shape and the spectral smoothness after denoising. The generalized morphological filter method can remove larger amplitude random noise whereas the continuous small amplitude random noise could not be removed well. Hence, the denoised spectra were not smooth. Nevertheless, the denoised spectra using the thresholding on the best base groups of wavelet packet decomposition method were smooth, but the larger amplitude noise could not be removed completely. The authors’ method by combining the two methods has the merits of the two methods but removing their defects. The results showed that both large and small amplitude noise could be removed completely, meanwhile the normalized correlation coefficient (NCC) and smoothness ratio (SR) were improved, which indicated that the authors’ method is superior to other methods in denoising visible and near infrared spectra.
Key words:Visible and near infrared spectra;Denoising;Generalized morphological filter;Thresholding on wavelet packet decomposition best bases
李 慧1,2,3,蔺启忠1,2,王钦军1,2,刘庆杰1,2,吴昀昭4 . 基于小波包变换和数学形态学结合的光谱去噪方法研究[J]. 光谱学与光谱分析, 2010, 30(03): 644-648.
LI Hui1, 2, 3, LIN Qi-zhong1, 2, WANG Qin-jun1, 2, LIU Qing-jie1, 2, WU Yun-zhao4 . Research on Spectrum Denoising Methods Based on the Combination of Wavelet Package Transformation and Mathematical Morphology . SPECTROSCOPY AND SPECTRAL ANALYSIS, 2010, 30(03): 644-648.
[1] LIU Zhi-hong, DENG Bo, ZHOU Yu-rong, et al(刘志宏,邓 波,周玉荣,等). Chinese Journal of Spectroscopy Laboratory(光谱实验室), 2006, 23(4): 815. [2] ZHANG Yin, ZHOU Meng-ran(张 银,周孟然). Infrared Technology(红外技术), 2007, 29(6): 345. [3] Wickerhauser, Mladen Victor. INRIA Lectures on Wavelet Packet Algorithms, 1991. [4] DU Li-zhi, YIN Kun, ZHANG Xiao-pei, et al(杜立志,殷 琨,张晓培,等). Chinese Journal of Engineering Geophysics(工程地球物理学报), 2008, 5(1): 26. [5] DUAN Shan(段 汕). Journal of South-Central University for Nationalities·National Science Edition(中南民族大学·自然科学版), 2007, 26(2): 105. [6] QU Guo-qing, DANG Ya-min, ZHANG Chuan-yin, et al(曲国庆,党亚民,章传银,等). Journal of Geodesy and Geodynamics(大地测量与地球动力学), 2008, 28(4): 102. [7] Donoho D L. IEEE Transaction on Information Theory, 1995, 41(3): 613. [8] CUI Yi(崔 屹). Image Processing and Analysis-Mathematical Morphology Methods and Applications(图像处理与分析-数学形态学方法及应用), Beijing:Science Press(北京:科学出版社), 2000. [9] ZHANG Wen-bin, ZHOU Xiao-jun, LIN Yong(张文斌,周晓军,林 勇). Transactions of the Chinese Society of Agricultural Engineering(农业工程学报), 2008, 24(6). [10] LIU Shu(刘 姝). Applying The Mathematical Morphology in Signal Processing(数学形态学在信号处理方面的应用研究). Dalian:Dalian University of Technology Press(大连:大连理工大学出版社), 2007. [11] Zhou X, Zhou C, Kemp I J. IEEE Transactions on Dielectrics and Electrical Insulation, 2005, 12(3): 586. [12] Tang Ju, Zhou Qian, Tang Ming, Yanbin Xie. IEEE Transactions on Dielectrics and Electrical Insulation, 2007, 14(1): 30-37. [13] Werle P, Akbari A, Borsi H, Gockenbach E. IEEE Transactions on Electrical Insulation, 2002: 195. [14] CHEN Qiang, HUANG Sheng-xiang, WANG Wei(陈 强,黄声享,王 韦). Journal of Geomatics(测绘信息与工程), 2008, 33(5): 31.