Total variation, adaptive total variation and nonconvex smoothly clipped absolute deviation penalty for denoising blocky images

  • Authors:
  • Aditya Chopra;Heng Lian

  • Affiliations:
  • School of Computing Sciences, VIT University, Vellore, TN, India;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore

  • Venue:
  • Pattern Recognition
  • Year:
  • 2010

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Abstract

The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical literature on high-dimensional variable selection. Using a particular instantiation of the majorization-minimization algorithm, the optimization problem can be efficiently solved and the computational procedure realized is similar to the spatially adaptive total variation model. Our two-pixel image model shows theoretically that the new penalty function solves the bias problem inherent in the total variation model. The superior performance of the new penalty function is demonstrated through several experiments. Our investigation is limited to ''blocky'' images which have small total variation.