<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.</p></abstract>

We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.

A well-posed multiscale regularization scheme for digital image denoising

Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal

International Journal of Applied Mathematics and Computer Science

{"article-title":"A well-posed multiscale regularization scheme for digital image denoising"}

We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an...

A well-posed multiscale regularization scheme for digital image denoising

Published Online: Dec 21, 2011

Page range: 769 - 777

DOI: https://doi.org/10.2478/v10006-011-0061-7

Keywords
image restoration, edge-preserving, regularization, normalized local variance, adaptive parameter

This content is open access.

A well-posed multiscale regularization scheme for digital image denoising

Published Online: Dec 21, 2011

Page range: 769 - 777

DOI: https://doi.org/10.2478/v10006-011-0061-7

Keywordsimage restoration, edge-preserving, regularization, normalized local variance, adaptive parameter

This content is open access.

Keywords
image restoration, edge-preserving, regularization, normalized local variance, adaptive parameter