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.

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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-Modified = {2019-09-06 15:51:10 +0200},
	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}},
	Url = {http://rdcu.be/mDVd},
	Volume = {34},
	Year = {2007},
	Bdsk-Url-1 = {http://rdcu.be/mDVd},
	Bdsk-Url-2 = {https://doi.org/10.1007/s10915-007-9160-x}}