Affine Non-Local Means Image Denoising

This paper presents an extension of the Non-Local Means denoising method, that effectively exploits the affine invariant self-similarities present in the images of real scenes. Our method provides a better image denoising result by grounding on the fact that in many occasions similar patches exist in the image but have undergone a transformation. The proposal uses an affine invariant patch similarity measure that performs an appropriate patch comparison by automatically and intrinsically adapting the size and shape of the patches. As a result, more similar patches are found and appropriately used. We show that this image denoising method achieves top-tier performance in terms of PSNR, outperforming consistently the results of the regular Non-Local Means, and that it provides state-of-the-art qualitative results.

[1]  Michael Elad,et al.  Generalizing the Nonlocal-Means to Super-Resolution Reconstruction , 2009, IEEE Transactions on Image Processing.

[2]  Laurent D. Cohen,et al.  Non-local Regularization of Inverse Problems , 2008, ECCV.

[3]  Jean-Michel Morel,et al.  Multiscale Image Blind Denoising , 2015, IEEE Transactions on Image Processing.

[4]  Guillermo Sapiro,et al.  DCT image denoising: a simple and effective image denoising algorithm , 2011, Image Process. Line.

[5]  Jean-Michel Morel,et al.  Non-local dual image denoising , 2014, 2014 IEEE International Conference on Image Processing (ICIP).

[6]  Charles-Alban Deledalle,et al.  Non-local Methods with Shape-Adaptive Patches (NLM-SAP) , 2012, Journal of Mathematical Imaging and Vision.

[7]  E. Schiavi,et al.  Iterated Rician Denoising , 2011 .

[8]  Gabriele Facciolo,et al.  Linear Multiscale Analysis of Similarities between Images on Riemannian Manifolds: Practical Formula and Affine Covariant Metrics , 2015, SIAM J. Imaging Sci..

[9]  E. Nadaraya.  On Estimating Regression , 1964 .

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

[11]  Vicent Caselles,et al.  Multiscale Analysis of Similarities between Images on Riemannian Manifolds , 2014, Multiscale Model. Simul..

[12]  Gabriel Peyré,et al.  Manifold models for signals and images , 2009, Comput. Vis. Image Underst..

[13]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[14]  Jean-Michel Morel,et al.  Implementation of the "Non-Local Bayes" (NL-Bayes) Image Denoising Algorithm , 2013, Image Process. Line.

[15]  Gabriele Facciolo,et al.  Affine Invariant Self-similarity for Exemplar-based Inpainting , 2016, VISIGRAPP.

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

[17]  C. Stein.  Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

[18]  David Zhang,et al.  Two-stage image denoising by principal component analysis with local pixel grouping , 2010, Pattern Recognit..

[19]  Karl Kunisch,et al.  Total Generalized Variation , 2010, SIAM J. Imaging Sci..

[20]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

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

[22]  Jean-Michel Morel,et al.  A Nonlocal Bayesian Image Denoising Algorithm , 2013, SIAM J. Imaging Sci..

[23]  Gilles Aubert,et al.  A Variational Approach to Removing Multiplicative Noise , 2008, SIAM J. Appl. Math..

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

[25]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

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

[27]  Giacomo Boracchi,et al.  Foveated self-similarity in nonlocal image filtering , 2012, Electronic Imaging.

[28]  Mila Nikolova,et al.  Regularizing Flows for Constrained Matrix-Valued Images , 2004, Journal of Mathematical Imaging and Vision.

[29]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[30]  Leonid P. Yaroslavsky,et al.  Local adaptive image restoration and enhancement with the use of DFT and DCT in a running window , 1996, Optics & Photonics.

[31]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[32]  Joachim Weickert,et al.  Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Generalised Nonlocal Image Smoothing Generalised Nonlocal Image Smoothing , 2022 .

[33]  Michael Elad,et al.  Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.

[34]  Jean-Michel Morel,et al.  Non-Local Means Denoising , 2011, Image Process. Line.

[35]  Joachim Weickert,et al.  Rotationally invariant similarity measures for nonlocal image denoising , 2011, J. Vis. Commun. Image Represent..

[36]  Guillermo Sapiro,et al.  A Variational Framework for Exemplar-Based Image Inpainting , 2011, International Journal of Computer Vision.

[37]  Peyman Milanfar,et al.  A General Framework for Regularized, Similarity-Based Image Restoration , 2014, IEEE Transactions on Image Processing.

[38]  Yu Liu,et al.  Rotation invariant similarity measure for non-local self-similarity based image denoising , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

[39]  J. Weickert,et al.  A ROTATIONALLY INVARIANT BLOCK MATCHING STRATEGY IMPROVING IMAGE DENOISING WITH NON-LOCAL MEANS , 2008 .

[40]  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).

[41]  Jean-Michel Morel,et al.  Secrets of image denoising cuisine* , 2012, Acta Numerica.

[42]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..