A TV Based Restoration Model with Local Constraints

Almansa, A.; Ballester, C.; Caselles, V.; Haro, G.

doi:10.1007/s10915-007-9160-x

by A. Almansa, C. Ballester, V. Caselles, G. Haro

Abstract:

Abstract We propose in this paper a total variation based restoration model which incorporates the image acquisition model z=h U+n (where z represents the observed sampled image, U is the ideal undistorted image, h denotes the blurring kernel and n is a white Gaussian noise) as a set of local constraints. These constraints, one for each pixel of the image, express the fact that the variance of the noise can be estimated from the residuals zh U if we use a neighborhood of each pixel. This is motivated by the fact that the usual inclusion of the image acquisition model as a single constraint expressing a bound for the variance of the noise does not give satisfactory results if we wish to simultaneously recover textured regions and obtain a good denoising of the image. We use Uzawas algorithm to minimize the total variation subject to the proposed family of local constraints and we display some experiments using this model.

Reference:

A TV Based Restoration Model with Local Constraints (A. Almansa, C. Ballester, V. Caselles, G. Haro), In Journal of Scientific Computing, Springer Netherlands, volume 34, 2007.

Bibtex Entry:

@article{Almansa2007a,
	Abstract = {Abstract We propose in this paper a total variation based restoration model which incorporates the image acquisition model z=h U+n (where z represents the observed sampled image, U is the ideal undistorted image, h denotes the blurring kernel and n is a white Gaussian noise) as a set of local constraints. These constraints, one for each pixel of the image, express the fact that the variance of the noise can be estimated from the residuals zh U if we use a neighborhood of each pixel. This is motivated by the fact that the usual inclusion of the image acquisition model as a single constraint expressing a bound for the variance of the noise does not give satisfactory results if we wish to simultaneously recover textured regions and obtain a good denoising of the image. We use Uzawas algorithm to minimize the total variation subject to the proposed family of local constraints and we display some experiments using this model.},
	Author = {Almansa, A. and Ballester, C. and Caselles, V. and Haro, G.},
	Date-Added = {2015-02-18 17:00:16 +0000},
	Date-Modified = {2015-02-18 17:01:30 +0000},
	Doi = {10.1007/s10915-007-9160-x},
	Issn = {08857474},
	Journal = {Journal of Scientific Computing},
	Keywords = {image restoration,satellite images,total variation,variational methods},
	Month = oct,
	Number = {3},
	Pages = {209--236},
	Publisher = {Springer Netherlands},
	Title = {{A TV Based Restoration Model with Local Constraints}},
	Volume = {34},
	Year = {2007},
	Bdsk-Url-1 = {http://www.springerlink.com/index/10.1007/s10915-007-9160-x%20http://link.springer.com/10.1007/s10915-007-9160-x},
	Bdsk-Url-2 = {http://dx.doi.org/10.1007/s10915-007-9160-x}}