On high-order denoising models and fast algorithms for vector-valued images

Authors:
Carlos Brito-Loeza;Ke Chen
Affiliations:
Centre for Mathematical Imaging Techniques, Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK;Centre for Mathematical Imaging Techniques, Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK
Venue:
IEEE Transactions on Image Processing
Year:
2010

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Abstract

Variational techniques for gray-scale image denoising have been deeply investigated for many years; however, little research has been done for the vector-valued denoising case and the very few existent works are all based on total-variation regularization. It is known that total-variation models for denoising gray-scaled images suffer from staircasing effect and there is no reason to suggest this effect is not transported into the vector-valued models. High-order models, on the contrary, do not present staircasing. In this paper, we introduce three high-order and curvature-based denoising models for vector-valued images. Their properties are analyzed and a fast multigrid algorithm for the numerical solution is provided. AMS subject classifications: 68U10, 65F10, 65K10.