BROWSE

Related Researcher

Author's Photo

Kim, Yunho
Mathematical Imaging Lab
Research Interests
  • Optimization, inverse problems, convex analysis, calculus of variations, partial differential equations, computational mathematics, medical/biomedical imaging

ITEM VIEW & DOWNLOAD

Image Restoration Using One-Dimensional Sobolev Norm Profiles of Noise and Texture

Cited 0 times inthomson ciCited 0 times inthomson ci
Title
Image Restoration Using One-Dimensional Sobolev Norm Profiles of Noise and Texture
Author
Kim, YunhoGarnett, John BVese, Luminita A.
Keywords
Convex optimization; Image decomposition; Image restoration; Sobolev spaces
Issue Date
2014-02
Publisher
SIAM PUBLICATIONS
Citation
SIAM JOURNAL ON IMAGING SCIENCES, v.7, no.1, pp.366 - 390
Abstract
This work is devoted to image restoration (denoising and deblurring) by variational models. As in our prior work [Inverse Probl. Imaging, 3 (2009), pp. 43-68], the image (f) over tilde to be restored is assumed to be the sum of a cartoon component u (a function of bounded variation) and a texture component v (an oscillatory function in a Sobolev space with negative degree of differentiability). In order to separate noise from texture in a blurred noisy textured image, we need to collect some information that helps distinguish noise, especially Gaussian noise, from texture. We know that homogeneous Sobolev spaces of negative differentiability help capture oscillations in images very well; however, these spaces do not directly provide clear distinction between texture and noise, which is also highly oscillatory, especially when the blurring effect is noticeable. Here, we propose a new method for distinguishing noise from texture by considering a family of Sobolev norms corresponding to noise and texture. It turns out that the two Sobolev norm profiles for texture and noise are different, and this enables us to better separate noise from texture during the deblurring process.
URI
Go to Link
DOI
10.1137/130911275
ISSN
1936-4954
Appears in Collections:
PHY_Journal Papers
Files in This Item:
000333762900013.pdf Download

find_unist can give you direct access to the published full text of this article. (UNISTARs only)

Show full item record

qrcode

  • mendeley

    citeulike

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

MENU