Adaptive numerical regularization for variational denoising model with complementary approach | [VFAST Transactions on Mathematics • 2023]

Author(s):

1. Mohsin Ali Amur: Department of General Faculity, Shaheed Benazir Bhutto University, Shaheed Benazir Abad, Nawabshah, Pakistan

2. khuda bux Amur: Department of Mathematics and Statistics, QUEST, Nawabshah, Pakistan

3. Azam Ali Amur: Department of BSRS, Mehran University of Engineering and Technology Jamshoro,,Pakistan

4. Izhar Ali Amur: Department of General Faculity, Shaheed Benazir Bhutto University, Shaheed Benazir Abad, Nawabshah, Pakistan

5. K. N. Memon: Department of Mathematics and Statistics, QUEST, Nawabshah, Pakistan

Abstract:

Denoising is a process to suppress the noise and preserve the important information in the image. In this paper, a complementary approach is proposed for variational denoising problem. A FEM (Finite Element Method) based post optimization method (mesh refinement strategy) is designed which is based on a priori estimate called mean square error. The post optimization algorithm is adaptive and intelligent in nature which allows the adaptive choice of the regularization parameters. The manual choice of the smoothing parameters is taken uniformly on spatial domain and testing of the automatic selection of these parameters in adaptive way. This is an interesting idea of computation. The intelligent and automatic choice of the values for the smoothing function is smaller in the less regular regions of the image, to refine the grid and keep constant in the other complementary regions is one of the main interests, which produces the better and enhanced version of the noisy image.

Page(s): 77-92

DOI: DOI not available

Published: Journal: VFAST Transactions on Mathematics, Volume: 11, Issue: 2, Year: 2023

Keywords:

numerical modeling , Subject Classification , Image Denoising , Regularization , Adaptive Algorithm , Variational Models , Modeling for nonlinear partial diferential equation , Adaptive Finite Element Method

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