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Proceedings Paper

Image denoising based on Kolmogorov structure function for a class of hierarchical image models
Author(s): Bogdan Barliga; Ioan Tabus; Jorma Rissanen; Jaakko Astola
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Paper Abstract

Kolmogorov's structure function (KSF) is used in the algorithmic theory of complexity for describing the structure of a string by use of models (programs) of increasing complexity. Recently, inspired by the structure function, an extension of the minimum description length theory was introduced for achieving a decomposition of the total description of the data into a noise part and a model part, where the models are parametric distributions instead of programs, the code length necessary for the model part being restricted by a parameter. In this way a new "rate-distortion" type of curve is obtained, which may be further used as a general model of the data, quantifying the amount of noise left "unexplained" by models of increasing complexity. In this paper we present a complexity-noise function for a class of hierarchical image models in the wavelet transform domain, in the spirit of the Kolmogorov structure function. The minimization of the model description can be shown to have a form similar to one resulting from the minimization in the rate-distortion sense, and thus it will be achieved as in lossy image compression. As an application of the complexity-noise function introduced we study the image denoising problem and analyze the conditions under which the best reconstruction along the complexity-noise function is obtained.

Paper Details

Date Published: 30 August 2005
PDF: 10 pages
Proc. SPIE 5916, Mathematical Methods in Pattern and Image Analysis, 591607 (30 August 2005); doi: 10.1117/12.622240
Show Author Affiliations
Bogdan Barliga, Tampere Univ. of Technology (Finland)
Ioan Tabus, Tampere Univ. of Technology (Finland)
Jorma Rissanen, Tampere Univ. of Technology (Finland)
Jaakko Astola, Tampere Univ. of Technology (Finland)

Published in SPIE Proceedings Vol. 5916:
Mathematical Methods in Pattern and Image Analysis
Jaakko T. Astola; Ioan Tabus; Junior Barrera, Editor(s)

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