Abstract The nonlocal means (NLM) is a spatial domain image denoising method, and it exploits long range similarities between pixels of natural images. Notably, the similarity between true pixel values in original NLM is estimated based on patch information of noise-corrupted input image. In this paper, the pixel similarities in NLM are estimated based on Log-Gabor features to achieve good denoising results. Moreover, the mixed similarity combining the Log-Gabor features with intensity information is exploited to get better adaptivity to local image characteristics andfurther improve the denoising quality. In addition, the random projection-based NLM speed-up method is studied based on Johnson-Lindenstrauss lemma. Extensive tests including the running time comparison before and after dimensionality reduction, the impact of types of projection matrices and the extent of dimensionality reduction on final denoising performances are carried out. The experimental results confirm the effectiveness of the proposed acceleration scheme.
[1] Buades A, Coll B, Morel J M. A Non-local Algorithm for Image Denoising // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Diego, USA, 2005, II: 60-65 [2] Buades A, Coll B, Morel J M. A Review of Image Denoising Algorithms, with a New One. SIAM Journal on Multiscale Modeling and Simulation, 2005, 4(2): 490-530 [3] Buades A, Coll B, Morel J M. Denoising Image Sequences Does Not Require Motion Estimation // Proc of the IEEE Conference on Advanced Video and Signal Based Surveillance. Como, Italy, 2005: 70-74 [4] Ji Z X, Chen Q, Sun Q S, et al. A Moment-Based Nonlocal-Means Algorithm for Image Denoising. Information Processing Letters, 2009, 109(23/24): 1238-1244 [5] Grewenig S, Zimmer S, Weickert J. Rotationally Invariant Similarity Measures for Nonlocal Image Denoising. Journal of Visual Communication and Image Representation, 2011, 22(2): 117-130 [6] Hu M K. Visual Pattern Recognition by Moment Invariants. IRE Transactions on Information Theory, 1962, 8(2): 179-187 [7] Wang S S, Xia Y, Liu Q G, et al. Gabor Feature Based Nonlocal Means Filter for Textured Image Denoising. Journal of Visual Communication and Image Representation, 2012, 23(7): 1008-1018 [8] Field D J. Relations between the Statistics of Natural Images and the Response Properties of Cortical Cells. Journal of the Optical Society of America A, 1987, 4(12): 2379-2394 [9] Johnson W B, Lindenstrauss J. Extensions of Lipschitz Mappings into a Hilbert Space. Contemporary Mathematics, 1984, 26(12): 18-25 [10] Cachier P, Bardinet E, Dormont D, et al. Iconic Feature Based Nonrigid Registration: The PASHA Algorithm. Computer Vision and Image Understanding, 2003, 89(2/3): 272-298 [11] Xiong G, Ding T H. ADWA: A Filtering Paradigm for Signal′s Noise Removal and Feature Preservation. Signal Processing, 2012, 93(5): 1172-1191 [12] Azzabou N, Paragios N, Guichard F. Image Denoising Based on Adapted Dictionary Computation // Proc of the IEEE International Conference on Image Processing. San Antonio, USA, 2007, III: 109-112 [13] Tasdizen T. Principal Neighborhood Dictionaries for Nonlocal Means Image Denoising. IEEE Trans on Image Processing, 2009, 18(12): 2649-2660 [14] Zhang L, Dong W S, Zhang D, et al. Two-Stage Image Denoising by Principal Component Analysis with Local Pixel Grouping. Pattern Recognition, 2010, 43(4): 1531-1549 [15] Indyk P, Motwani R. Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality // Proc of the 30th Annual ACM Symposium on Theory of Computing. Dallas, USA, 1998: 604-613 [16] Achlioptas D. Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins. Journal of Computer and System Sciences, 2003, 66(4): 671-687 [17] Ailon N, Chazelle B. The Fast Johnson-Lindenstrauss Transform and Approximate Nearest Neighbors. SIAM Journal of Computing, 2009, 39(1): 302-322
2015, Vol. 28 
