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Total Variation Based Parameter-Free Model for Impulse Noise Removal

Part of: Existence theories Numerical methods in calculus of variations and optimal control Communication, information General convexity

Published online by Cambridge University Press:  20 February 2017

Federica Sciacchitano ,
Yiqiu Dong  and
Martin S. Andersen
Federica Sciacchitano*
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
Yiqiu Dong*
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
Martin S. Andersen*
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
*
*Corresponding author. Email addresses:feds@dtu.dk (F. Sciacchitano), yido@dtu.dk (Y. Dong), mskan@dtu.dk (M. S. Andersen)
*Corresponding author. Email addresses:feds@dtu.dk (F. Sciacchitano), yido@dtu.dk (Y. Dong), mskan@dtu.dk (M. S. Andersen)
*Corresponding author. Email addresses:feds@dtu.dk (F. Sciacchitano), yido@dtu.dk (Y. Dong), mskan@dtu.dk (M. S. Andersen)
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Abstract

We propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semismooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.

Keywords

Image deblurringimage denoisingimpulse noisenoise detectorprimal-dual first-order algorithmsemismooth Newton methodtotal variation regularization

MSC classification

Secondary: 68U10: Image processing 94A08: Image processing (compression, reconstruction, etc.) 49J40: Variational methods including variational inequalities 52A41: Convex functions and convex programs 65K10: Optimization and variational techniques 90C47: Minimax problems 49M15: Newton-type methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017 , pp. 186 - 204
Copyright
Copyright © Global-Science Press 2017 

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