为了更有效地去除图像噪声，同时更好地保留图像边缘细节信息，提出了一种基于shearlet 域各向异性扩散和稀疏表示的图像去噪方法. 首先对含噪图像进行非下采样shearlet 变换(nonsubsampled shearlet transform, NSST)，将图像分解为低频分量和多个高频分量. 低频分量中包含图像信号的主要能量以及少量的噪
声，而高频分量中含有大部分噪声和图像边缘信息. 然后，利用K-奇异值分解(K-singular value decomposition,K-SVD) 算法去除低频分量中的噪声，各个方向的高频分量则通过核各向异性扩散(kernel anisotropic diffusion,KAD) 算法进行去噪. 最后，对处理过的低频分量和高频分量进行非下采样shearlet 反变换(inverse nonsubsampled shearlet transform, INSST)，得到重构图像，从而有效地去除图像噪声，保留图像边缘细节. 实验结果表明，与小波扩散去噪法、shearlet 硬阈值去噪法、K-SVD 稀疏去噪法、小波域稀疏去噪法相比，该方法的去噪能力更强，并能更好地保留图像纹理细节特征，改善图像视觉效果.
To suppress image noise effectively and better preserve edge details, an image denoising method
based on anisotropic diffusion and sparse representation in the shearlet domain is proposed. The noisy image is
first decomposed into a low frequency component and several high frequency components by non-subsampled
shearlet transform (NSST). The main energy of the image information is contained in the low frequency
component, while the edge information and most of noise are contained in high frequency components. The K-singular value decomposition (K-SVD) algorithm is used to remove noise in low frequency component. The kernel anisotropic diffusion (KAD) algorithm is used to reduce noise in each high frequency component. The reconstructed image is obtained by inverse non-subsampled shearlet transform (INSST) for the processed low frequency and high frequency components. Noise in the image is effectively suppressed, and edge details are preserved satisfactorily. Experimental results show that, compared with the denoising methods such as wavelet combining with nonlinear diffusion method, shearlet hard threshold method, K-SVD sparse denoising method and sparse redundant denoising method in wavelet domain, the proposed method has better performance both in noise reduction and detail preservation.
[1] 余锦华, 汪源源. 基于各向异性扩散的图像降噪算法综述[J]. 电子测量与仪器学报. 2011, 25(2): 105-116.
YU Jinhua, WANG Yuanyuan. Image noise reduction based on anisotropic diffusion: a survey[J]. Journal of Electronic Measurement and Instrument. 2011, 25(2):
105-116. (in Chinese)
[2] 郭德全, 杨红雨, 刘东权, 何文森. 基于稀疏性的图像去噪综述[J]. 计算机应用研究. 2012, 29(2): 406-413.
GUO Dequan, YANG Hongyu, LIU Dongquan, HE Wensen. Overview on sparse image denoising[J]. Application Research of Computers. 2012, 29(2): 406-413. (in Chinese)
[3] LIM W Q. The discrete Shearlets transform: a new directional transform and compactly supported Shearlets frams[J]. IEEE Transactions on Image Processing. 2010,19(5): 1166-1180.
[4] 刘帅奇, 胡绍海, 肖扬. 基于Shearlet变换的SAR图像去噪[J]. 应用科学学报, 2012, 30(6): 629-634.
LIU Shuaiqi, HU Shaohai, XIAO Yang. De-noising of SAR images based on Shearlets transform[J]. Journal of Applied Sciences—Electronics and Information Engineering, 2012, 30(6): 629-634. (in Chinese)
[5] GILBOA G, SOCHEN N, ZEEVI Y Y. Forward-and-backward diffusion processes for adaptive image enhancement and denoising[J]. IEEE Transactions on Image Processing. 2002, 11(7): 689-703.
[6] ZHANG F, YOO Y M, KOH L M. Nonlinear diffusion in Laplacian pyramid domain for ultrasonic speckle reduction[J]. IEEE Transactions on Medical Imaging. 2007, 26(2): 200-211.
[7] YU J H, WANG Y Y, SHEN Y Z. Noise reduction and edge detection via kernel anisotropic diffusion[J]. Pattern Recognition Letters. 2008, 29(10): 1496-1503.
[8] AHARON M, ELAD M, BRUCKSTEIN A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Transations on Image Processing. 2006, 54(11): 4311-4322.
[9] 邓承志. 基于多尺度脊波字典的图像去噪算法[J]. 计算机工程. 2010, 36(23): 207-209.
DENG Chengzhi. Image denoising algorithm based on multiscale ridgelet dictionary[J]. Computer Engineering.
2010, 36(23): 207-209. (in Chinese)
[10] 曾军英, 甘俊英, 翟懿奎. Gabor字典及l0范数快速稀疏表示的人脸识别算法[J]. 信号处理. 2013, 29(2): 256-261. ZENG Junying, GAN Junying, ZHAI Yikui. Face recognition based on fast sparse representation of Gabor dictionary and l0 norm[J]. Journal of Signal Processing. 2013, 29(2): 256-261. (in Chinese)
[11] TROPP J A, GIBERT A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory. 2007, 53(12): 4655-4666.
[12] MANCERA L, PORTILLA J. L0-norm-based sparse representation through alternate projection[C]. IEEE International Conference on Image Processing. Atlanta. USA, 2006: 2089-2092.
[13] SZLAM A, KAVUKCOUGLU K, YANN L C. Convolutional matching pursuit and dictionary training [EB/OL]. [2010-10-3]. http: //arxiv.org/abs/1010.0422.
[14] 胡海智, 孙辉, 邓承志, 陈习, 柳枝华. 全变差正则化的Shearlet收缩去噪[J]. 中国图象图形学报. 2011, 16(2):
168-173.
HU Haizhi, SUN Hui, DENG Chengzhi, CHEN Xi, LIU Zhihua. Shearlet shrinkage de-noising based total variation regularization[J]. Journal of Image and Graphics. 2011,
16(2): 168-173. (in Chinese)
[15] 李慧斌, 刘峰. 小波变换和稀疏冗余表示的混合图像去噪[J]. 中国图象图形学报. 2012, 17(9): 1061-1068.
LI Huibin, LIU Feng. Hybrid image denosing method based on wavelet transform as well as on a sparse and redundant reprseentations model[J]. Journal of Image and Graphics. 2012, 17(9): 1061-1068. (in Chinese)
[16] 刘帅奇, 胡绍海, 肖扬. 基于稀疏表示的Shearlet域SAR图像去噪[J]. 电子与信息学报. 2012, 34(9): 2110-2115.
LIU Shuaiqi, HU Shaohai, XIAO Yang. Shearlet domain SAR image de-noising via sparse representation[J]. Journal
of Electronics & Information Technology. 2012, 34(9): 2110-2115. (in Chinese)
[17] 吴亚东, 孙世新. 基于二维小波收缩与非线性扩散的混合图像去噪算法[J]. 电子学报, 2006, 34(1): 163-166.
WU Yadong, SUN Shixin. A new hybrid image de-noising algorithm based on 2D wavelet shrinkage and nonlinear
diffusion[J]. Acta Electronica Sinica. 2006, 34(1): 163-166. (in Chinese)
