The 8 th Undergraduate in Applied Mathematics Conference (UAMC 2019) Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang Total variation-based image restoration model for color images Noppadol Chumchob *, Phacharaporn Khwanmueang and Manchupa Jindawong Abstract This work proposes a mathematical model for removing noise from color images. In the proposed model, we apply the total variation regularization for gray-scale images and solve the associated variational problem by the so-called split Bregman method. Our experimental results on real and synthetic images show that 1) the quality of restored color images by the proposed model is reliable; and 2) the performance of the proposed numerical method is significantly better than the explicit time marching method. Keywords : Finite difference, time marching, split bregman, variational model 2010 Mathematics Subject Classification: 46N23 1. Introduction Xxxxxxxxx xxxxxxxx xxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxx
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The 8th Undergraduate in Applied Mathematics Conference (UAMC 2019)
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang
Total variation-based image restoration model for color images
Noppadol Chumchob*, Phacharaporn Khwanmueang and Manchupa Jindawong
Abstract
This work proposes a mathematical model for removing noise from color images. In the proposed model, we apply the total variation regularization for gray-scale images and solve the associated variational problem by the so-called split Bregman method. Our experimental results on real and synthetic images show that 1) the quality of restored color images by the proposed model is reliable; and 2) the performance of the proposed numerical method is significantly better than the explicit time marching method.
Keywords : Finite difference, time marching, split bregman, variational model
2010 Mathematics Subject Classification: 46N23
1.IntroductionXxxxxxxxx xxxxxxxx xxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxx
* Corresponding authorNoppadol Chumchob Department of Mathematics Faculty of Science, Silpakorn University, Nakhon
Pathom, 73000 (email: [email protected])Phacharaporn Khwanmueang Department of Mathematics Faculty of Science, Silpakorn University,
Nakhon Pathom, 73000 (email: [email protected])Manchupa Jindawong Department of Mathematics Faculty of Science, Silpakorn University, Nakhon
Pathom, 73000 (email: [email protected])Acknowledgement: ………………………..
Proceedings of UAMC2019
2.Main resultXxxxxxxxx xxxxxxxx xxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxx
3.ConclusionXxxxxxxxx xxxxxxxx xxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxx
References[1] L. Rudin, S. Osher and E. Fatemi. Nonlinear total variation based noise removal
algorithms. Physica D Vol. 60 (1992), pp. 259-268.[2] T. Goldstein and S. Osher. The split bregman method for l1-regularized problems. SIAM
Journal on Sciences 2009, 2(2), pp. 323-343.[3] W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Lim and L. Bai. Implementation of high-order
variational models made easy for image processing. Mathematical Methods in the Applied Sciences. 39 (2016), pp. 4208-4233.
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