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Nonlocal Mumford-Shah Regularizers for Color Image Restoration

Jung, Miyoun; Bresson, Xavier; Chan, Tony F.; Vese, Luminita A. (2011), Nonlocal Mumford-Shah Regularizers for Color Image Restoration, IEEE Transactions on Image Processing, 20, 6, p. 1583-1598. http://dx.doi.org/10.1109/TIP.2010.2092433

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
IEEE Transactions on Image Processing
Volume
20
Number
6
Publisher
IEEE
Pages
1583-1598
Publication identifier
http://dx.doi.org/10.1109/TIP.2010.2092433
Metadata
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Author(s)
Jung, Miyoun
Bresson, Xavier
Chan, Tony F.
Vese, Luminita A.
Abstract (EN)
We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.
Subjects / Keywords
Ambrosio-Tortorelli elliptic approximations; Mumford-Shah (MS) regularizer; deblurring; demosaicing; denoising; impulse noise; inpainting; nonlocal operators; super-resolution

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