MULTISCALE TOTAL VARIATION AND MULTISCALE ANISOTROPIC DIFFUSION ALGORITHMS FOR IMAGE DENOISING

As digital photography rapidly replacing the traditional film photography as the photography of choice for all but a few devoted professionals, post processing to enhance images such as denoising becomes increasingly an integral part of digital photography. In this paper we propose the multiscale total variation (MTV) and the multiscale anisotropic diffusion (MAD) algorithms for denoising. Both methods offers more flexibility than the classical TV method and the related anisotropic diffusion method. We shall discuss the algorithms as well as their implementation in details. An advantage of the MTV and the MAD methods is that an automatic stopping criterion can easilt be implemented to prevent over-processing of an image. We also raise several mathematical questions.

[1]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[2]  Pavel Mrázek,et al.  Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering , 2001, International Journal of Computer Vision.

[3]  Antonin Chambolle,et al.  Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage , 1998, IEEE Trans. Image Process..

[4]  Jacques Froment,et al.  Artifact free signal denoising with wavelets , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[5]  Y. Meyer,et al.  Wavelets and Filter Banks , 1991 .

[6]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[7]  Murray Eden,et al.  Fundamentals of Digital Optics , 1996 .

[8]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[9]  Tony F. Chan,et al.  Total Variation Wavelet Thresholding , 2007, J. Sci. Comput..

[10]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

[11]  Tsachy Weissman,et al.  A discrete universal denoiser and its application to binary images , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[12]  Yang Wang,et al.  Total Variation Wavelet-Based Medical Image Denoising , 2006, Int. J. Biomed. Imaging.

[13]  Joachim Weickert,et al.  Coherence-enhancing diffusion of colour images , 1999, Image Vis. Comput..

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

[15]  S. Osher,et al.  IMAGE DECOMPOSITION AND RESTORATION USING TOTAL VARIATION MINIMIZATION AND THE H−1 NORM∗ , 2002 .

[16]  Ge Wang,et al.  Evolution-Operator-Based Single-Step Method for Image Processing , 2006, Int. J. Biomed. Imaging.

[17]  P. Lions,et al.  Image recovery via total variation minimization and related problems , 1997 .

[18]  F. Malgouyres,et al.  Mathematical analysis of a model which combines total variation and wavelet for image restoration 1 , 2002 .

[19]  Pavel Mrázek Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering , 2001, Scale-Space.

[20]  D. Dobson,et al.  Convergence of an Iterative Method for Total Variation Denoising , 1997 .

[21]  R. Chan,et al.  Tight frame: an efficient way for high-resolution image reconstruction , 2004 .

[22]  Tony F. Chan,et al.  The digital TV filter and nonlinear denoising , 2001, IEEE Trans. Image Process..

[23]  Yehoshua Y. Zeevi,et al.  Estimation of optimal PDE-based denoising in the SNR sense , 2006, IEEE Transactions on Image Processing.

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

[25]  L. P. I︠A︡roslavskiĭ Digital picture processing : an introduction , 1985 .

[26]  Tony F. Chan,et al.  Euler's Elastica and Curvature-Based Inpainting , 2003, SIAM J. Appl. Math..

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

[28]  Raymond H. Chan,et al.  Wavelet Algorithms for High-Resolution Image Reconstruction , 2002, SIAM J. Sci. Comput..