Variational Decomposition Model in Besov Spaces and Negative Hilbert-Sobolev Spaces

Authors:
Min Li;Xiangchu Feng
Affiliations:
School of Science, Xidian University, Xi'an 710071, China;School of Science, Xidian University, Xi'an 710071, China
Venue:
Computational Intelligence and Security
Year:
2007

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Abstract

In this paper, we propose a new variational decomposition model which splits an image into two components: a first one containing the structure and a second one the texture or noise. Our decomposition model relies on the use of two semi-norms: the Besov semi-norm for the geometrical component, the negative Hilbert-Sobolev norms for the texture or noise. And the proposed model can be understood as generalizations of Daubechies-Teschke's model and have been motivated also by Lorenz's idea. And we illustrate our study with numerical examples for image decomposition and denoising.