A well-posed multiscale regularization scheme for digital image denoising

V.B. Surya Prasath

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 4, page 769-777
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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V.B. Surya Prasath. "A well-posed multiscale regularization scheme for digital image denoising." International Journal of Applied Mathematics and Computer Science 21.4 (2011): 769-777. <http://eudml.org/doc/208087>.

@article{V2011,
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.},
author = {V.B. Surya Prasath},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {image restoration; edge-preserving; regularization; normalized local variance; adaptive parameter},
language = {eng},
number = {4},
pages = {769-777},
title = {A well-posed multiscale regularization scheme for digital image denoising},
url = {http://eudml.org/doc/208087},
volume = {21},
year = {2011},
}

TY - JOUR
AU - V.B. Surya Prasath
TI - A well-posed multiscale regularization scheme for digital image denoising
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 4
SP - 769
EP - 777
AB - 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.
LA - eng
KW - image restoration; edge-preserving; regularization; normalized local variance; adaptive parameter
UR - http://eudml.org/doc/208087
ER -

References

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