Variational denoising of partly textured images by spatially varying constraints

Guy Gilboa*, Nir Sochen, Yehoshua Y. Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

176 Scopus citations


Denoising algorithms based on gradient dependent regularizers, such as nonlinear diffusion processes and total variation denoising, modify images towards piecewise constant functions. Although edge sharpness and location is well preserved, important information, encoded in image features like textures or certain details, is often compromised in the process of denoising. We propose a mechanism that better preserves fine scale features in such denoising processes. A basic pyramidal structure-texture decomposition of images is presented and analyzed. A first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures. A variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions. Our results show visual improvement as well as an increase in the signal-to-noise ratio over scalar fidelity term processes. This type of processing can be used for a variety of tasks in partial differential equation-based image processing and computer vision, and is stable and meaningful from a mathematical viewpoint.

Original languageEnglish
Pages (from-to)2281-2289
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - Aug 2006


FundersFunder number
Adams Center
EC 6th Framework IST Programme
Israeli Ministry of Science
Ollendorf Minerva Center
Tel-Aviv University fund
National Science FoundationDMS-0312222, ITR ACI-0321917
National Institutes of Health
National Institute of Mental HealthP20MH065166
European Commission
Israel Science Foundation
Technion-Israel Institute of TechnologyHPRN-CT-2002-00285


    • Image denoising
    • Nonlinear diffusion
    • Spatially varying fidelity term
    • Texture processing
    • Variational image processing


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