In this work we analyze and compare two recent variational models for image denoising and improve their reconstructions by applying a Bregman iteration strategy. One of the standard techniques in image denoising, the ROF-model (cf. [ROF92]), is well known for recovering sharp edges of a signal or image, but also for producing staircase-like artifacts. In order to overcome these model-dependent deficiencies, total variation modifications that incorporate higher-order derivatives have been proposed (cf. [CL97,BKP10]). These models reduce staircasing for reasonable parameter choices. However, the combination of derivatives of different order leads to other undesired side effects, which we shall also highlight in several examples. The goal of this paper is to analyze capabilities and limitations of the different models and to improve their reconstructions in quality by introducing Bregman iterations. Besides general modelling and analysis we discuss efficient numerical realizations of Bregman iterations and modified versions thereof.

@TechReport{BBBM11,
  author       = {Benning, M. and Brune, C. and Burger, M. and Mueller, J.},
  title        = {Higher-Order TV Methods - Enhancement via Bregman Iteration},
  institution  = {submitted J. Sci. Comp. special issue in honor of S. Oshers 70th Birthday},
  month        = {december},
  year         = {2011},
  url          = \{/2011/BBBM11},
}