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 filter, TV denoising is defined in terms of an optimization problem. The output of the TV denoising 'filter' is obtained by minimizing a particular cost function.

This tutorial 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 tutorial addresses TV denoising of 1-D signals only.

Tutorial
TVDmm.pdf

Matlab software
TVD_software.zip
TVD_software (link)

TV denoising example (link)

This tutorial is also a CNX module (link)

Ivan W. Selesnick
Polytechnic Institute of New York University
Electrical and Computer Engineering
Brooklyn, New York, United States