Image denoising based on Kolmogorov structure function for a class of hierarchical image models

Bogdan Barliga; Ioan Tabus; Jorma Rissanen; Jaakko Astola

doi:10.1117/12.622240

30 August 2005 Image denoising based on Kolmogorov structure function for a class of hierarchical image models

Bogdan Barliga, Ioan Tabus, Jorma Rissanen, Jaakko Astola

Proceedings Volume 5916, Mathematical Methods in Pattern and Image Analysis; 591607 (2005) https://doi.org/10.1117/12.622240
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

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.

Citation Download Citation

Bogdan Barliga, Ioan Tabus, Jorma Rissanen, and Jaakko Astola "Image denoising based on Kolmogorov structure function for a class of hierarchical image models", Proc. SPIE 5916, Mathematical Methods in Pattern and Image Analysis, 591607 (30 August 2005); https://doi.org/10.1117/12.622240

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available