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On High-Order Denoising Models and Fast Algorithms for Vector-Valued Images

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2 Author(s)
Carlos Brito-Loeza ; Centre for Mathematical Imaging Techniques (CMIT), Department of Mathematical Sciences, The University of Liverpool, Liverpool, United Kingdom ; Ke Chen

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.

Published in:

IEEE Transactions on Image Processing  (Volume:19 ,  Issue: 6 )