Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising

Published

Journal Article

Inspired by papers of Vese-Osher [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and Osher-Solé-Vese [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002] we present a wavelet-based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an appropriate 'noise' component. In the setting of [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002], the cartoon component of an image is modeled by a BV function; the corresponding incorporation of BV penalty terms in the variational functional leads to PDE schemes that are numerically intensive. By replacing the BV penalty term by a B11(L1) term (which amounts to a slightly stronger constraint on the minimizer), and writing the problem in a wavelet framework, we obtain elegant and numerically efficient schemes with results very similar to those obtained in [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002]. This approach allows us, moreover, to incorporate general bounded linear blur operators into the problem so that the minimization leads to a simultaneous decomposition, deblurring and denoising. © 2004 Elsevier Inc. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Teschke, G

Published Date

  • July 1, 2005

Published In

Volume / Issue

  • 19 / 1

Start / End Page

  • 1 - 16

International Standard Serial Number (ISSN)

  • 1063-5203

Digital Object Identifier (DOI)

  • 10.1016/j.acha.2004.12.004

Citation Source

  • Scopus