Total variation denoising (an MM algorithm)

Total variation denoising (TVD) is an approach for noise reduction developed so as to preserve sharp edges in the underlying signal. Unlike a conventional low-pass lter, TV denoising is de ned in terms of an optimization problem. This module describes an algorithm for TV denoising derived using the majorization-minimization (MM) approach, developed by Figueiredo et al. [ICIP 2006]. To keep it simple, this module addresses TV denoising of 1-D signals only. For computational e ciency, the algorithm may use a solver for sparse banded systems.

[1]  M. Nikolova An Algorithm for Total Variation Minimization and Applications , 2004 .

[2]  Jean-Jacques Fuchs,et al.  On sparse representations in arbitrary redundant bases , 2004, IEEE Transactions on Information Theory.

[3]  Laurent Condat,et al.  A Direct Algorithm for 1-D Total Variation Denoising , 2013, IEEE Signal Processing Letters.

[4]  Robert D. Nowak,et al.  On Total Variation Denoising: A New Majorization-Minimization Algorithm and an Experimental Comparisonwith Wavalet Denoising , 2006, 2006 International Conference on Image Processing.

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

[6]  Brendt Wohlberg,et al.  Efficient Minimization Method for a Generalized Total Variation Functional , 2009, IEEE Transactions on Image Processing.

[7]  Robert D. Nowak,et al.  Majorization–Minimization Algorithms for Wavelet-Based Image Restoration , 2007, IEEE Transactions on Image Processing.

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

[9]  Stephen J. Wright,et al.  Duality-based algorithms for total-variation-regularized image restoration , 2010, Comput. Optim. Appl..

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

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

[12]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[13]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[14]  Ivan W. Selesnick,et al.  Total variation filtering , 2009 .

[15]  Antonin Chambolle,et al.  A l1-Unified Variational Framework for Image Restoration , 2004, ECCV.

[16]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[17]  Mathews Jacob,et al.  Higher Degree Total Variation (HDTV) Regularization for Image Recovery , 2012, IEEE Transactions on Image Processing.

[18]  Victor Solo Selection of regularisation parameters for total variation denoising , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[19]  Jack Dongarra,et al.  LAPACK's user's guide , 1992 .