An Iteratively Reweighted Norm Algorithm for Minimization of Total Variation Functionals

Abstract

Total variation (TV) regularization has become a popular method for a wide variety of image restoration problems, including denoising and deconvolution. A number of authors have recently noted the advantages of replacing the standard lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> data fidelity term with an lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> norm. We propose a simple but very flexible method for solving a generalized TV functional that includes both the lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -TV and lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -TV problems as special cases. This method offers competitive computational performance for lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -TV and is comparable to or faster than any other lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -TV algorithms of which we are aware.