Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability

Yunho Kim; Luminita A. Vese

doi:10.3934/ipi.2009.3.43

Article Contents

2009, Volume 3, Issue 1: 43-68. Doi: 10.3934/ipi.2009.3.43

This issue Previous Article A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination Next Article A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data

Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability

Yunho Kim^1, and
Luminita A. Vese^1,

1.
Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555

Received: September 2008

Revised: November 2008

Published: February 2009

Abstract / Introduction Related Papers Cited by

Abstract

In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form $u + v$, where $u$ is a function of bounded variation (cartoon component), while $v$ is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. We give several results of existence and characterization of minimizers of the proposed optimization problem. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.

Keywords:

Mathematics Subject Classification: Primary: 35J85, 49J40, 65M06; Secondary: 65M32.

Citation:

Article Metrics

HTML views() PDF downloads(153) Cited by(0)

Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content