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

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...

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Bibliographic Details
Published in:IEEE transactions on image processing 2010-06, Vol.19 (6), p.1518-1527
Main Authors: Brito-Loeza, Carlos, Chen, Ke
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Case depth
Classifications
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Fourth-order partial differential equations (PDEs)
Gray-scale
Image color analysis
Image denoising
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Information, signal and communications theory
Mathematical models
Miscellaneous
multilevel methods
Noise reduction
Partial differential equations
Regularization
Reproducibility of Results
Sensitivity and Specificity
Signal and communications theory
Signal processing
Signal Processing, Computer-Assisted
Signal, noise
Telecommunications and information theory
variational models
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Summary: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.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2010.2042655