A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise.

[1]  Xin Wang Wrap-around effect removal finite ridgelet transform for multiscale image denoising , 2010, Pattern Recognit..

[2]  Jacob Scharcanski,et al.  Adaptive image denoising and edge enhancement in scale-space using the wavelet transform , 2003, Pattern Recognit. Lett..

[3]  KatkovnikVladimir,et al.  From Local Kernel to Nonlocal Multiple-Model Image Denoising , 2010 .

[4]  L. Demanet,et al.  Wave atoms and sparsity of oscillatory patterns , 2007 .

[5]  Xiaoming Huo,et al.  Combined image representation using edgelets and wavelets , 1999, Optics & Photonics.

[6]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[7]  Nasir M. Rajpoot,et al.  Planelets : a new analysis tool for planar feature extraction , 2004 .

[8]  N. Otsu A threshold selection method from gray level histograms , 1979 .

[9]  Zeev Farbman,et al.  Edge-preserving decompositions for multi-scale tone and detail manipulation , 2008, ACM Trans. Graph..

[10]  Haixian Wang,et al.  Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain , 2009, IEEE Transactions on Image Processing.

[11]  Karen O. Egiazarian,et al.  Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images , 2007, IEEE Transactions on Image Processing.

[12]  Balázs Kégl,et al.  Image denoising with complex ridgelets , 2007, Pattern Recognit..

[13]  Zujun Hou,et al.  Adaptive singular value decomposition in wavelet domain for image denoising , 2003, Pattern Recognit..

[14]  Ronald R. Coifman,et al.  Brushlets: A Tool for Directional Image Analysis and Image Compression , 1997 .

[15]  Tolga Tasdizen,et al.  Principal Neighborhood Dictionaries for Nonlocal Means Image Denoising , 2009, IEEE Transactions on Image Processing.

[16]  Mubarak Shah,et al.  Image Diffusion Using Saliency Bilateral Filter , 2008, IEEE Transactions on Information Technology in Biomedicine.

[17]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[18]  Guillermo Sapiro,et al.  Fast image and video denoising via nonlocal means of similar neighborhoods , 2005, IEEE Signal Processing Letters.

[19]  Jaakko Astola,et al.  From Local Kernel to Nonlocal Multiple-Model Image Denoising , 2009, International Journal of Computer Vision.

[20]  Stéphane Mallat,et al.  Wavelets for a vision , 1996, Proc. IEEE.

[21]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[22]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[23]  Minh N. Do,et al.  The finite ridgelet transform for image representation , 2003, IEEE Trans. Image Process..

[24]  L. Villemoes Wavelet packets with uniform time-frequency localization , 2002 .

[25]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[26]  Minh N. Do,et al.  A New Contourlet Transform with Sharp Frequency Localization , 2006, 2006 International Conference on Image Processing.

[27]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[28]  Nasir M. Rajpoot,et al.  Image denoising using multiscale directional cosine bases , 2005, IEEE International Conference on Image Processing 2005.

[29]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[30]  Jack Tumblin,et al.  The Trilateral Filter for High Contrast Images and Meshes , 2003, Rendering Techniques.

[31]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  William T. Freeman,et al.  Presented at: 2nd Annual IEEE International Conference on Image , 1995 .

[33]  D. Alspach A gaussian sum approach to the multi-target identification-tracking problem , 1975, Autom..

[34]  Dimitri Van De Ville,et al.  SURE-Based Non-Local Means , 2009, IEEE Signal Processing Letters.

[35]  Danny Barash,et al.  A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  Daniel Cremers,et al.  Efficient Nonlocal Means for Denoising of Textural Patterns , 2008, IEEE Transactions on Image Processing.

[37]  Shi Zhong-ke,et al.  A multilateral filtering method applied to airplane runway image , 2008, ArXiv.

[38]  Andrew Zisserman,et al.  Representing shape with a spatial pyramid kernel , 2007, CIVR '07.

[39]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[40]  Ming Zhang,et al.  Multiresolution Bilateral Filtering for Image Denoising , 2008, IEEE Transactions on Image Processing.

[41]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[42]  Joachim Weickert,et al.  Relations Between Regularization and Diffusion Filtering , 2000, Journal of Mathematical Imaging and Vision.

[43]  Nasir M. Rajpoot,et al.  Adaptive wavelet restoration of noisy video sequences , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[44]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[45]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

[46]  Charles K. Chui,et al.  A universal noise removal algorithm with an impulse detector , 2005, IEEE Transactions on Image Processing.