On the edge detection of an image by numerical differentiations for gray function

On the edge detection of an image by numerical differentiations for gray function The detection of image edges is of great importance in image processing. One of the efficient implementations for this image recovery problem is based on the identification of sharp jumps of the gray function of the image. Mathematically, this problem can be modeled by the numerical differentiation of the gray function with 2 variables. For this ill‐posed problem with nonsmooth solution, we investigate the regularization schemes with total variation and L1 penalty term, respectively. We prove that the regularizing parameter under the Tikhonov regularization framework can be uniquely chosen in terms of the Morozov's discrepancy principle and then establish the convergence rate of the regularizing solutions in terms of the Bregman distance. The discrete schemes are performed by the lagged diffusivity fixed point iteration, with numerical implementations showing the validity of the proposed scheme. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods in the Applied Sciences Wiley

On the edge detection of an image by numerical differentiations for gray function

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0170-4214
eISSN
1099-1476
D.O.I.
10.1002/mma.4752
Publisher site
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Abstract

The detection of image edges is of great importance in image processing. One of the efficient implementations for this image recovery problem is based on the identification of sharp jumps of the gray function of the image. Mathematically, this problem can be modeled by the numerical differentiation of the gray function with 2 variables. For this ill‐posed problem with nonsmooth solution, we investigate the regularization schemes with total variation and L1 penalty term, respectively. We prove that the regularizing parameter under the Tikhonov regularization framework can be uniquely chosen in terms of the Morozov's discrepancy principle and then establish the convergence rate of the regularizing solutions in terms of the Bregman distance. The discrete schemes are performed by the lagged diffusivity fixed point iteration, with numerical implementations showing the validity of the proposed scheme.

Journal

Mathematical Methods in the Applied SciencesWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ;

References

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