Image denoising via a new hybrid TGV model based on Shannon interpolation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 26 دی 1400  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.71857.1052

نویسندگان

Elaheh Tavakkol¹؛ Seyed Mohammad Hosseini ¹؛ Alireza Hosseini²

¹Department of Applied Mathematics, Tarbiat Modares University, P. O. Box 14115-175, Tehran, Iran.

²School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, P. O. Box 14155-6455, Tehran, Iran

چکیده

A new hybrid variational model is presented for image denoising, which incorporates the merits of Shannon interpolation, total generalized variation (TGV) regularization, and a symmetrized derivative regularization term  based on $l^1$-norm. In this model, the regularization term is a combination of a TGV functional and the symmetrized derivative regularization term, while the data fidelity term is characterized by the $l^2$-norm. Unlike most variational models that are discretized using a finite-differences scheme, our approach in structure is based on Shannon interpolation. Quantitative and qualitative assessments of the new model indicate its effectiveness in restoration accuracy and staircasing effect suppression. Numerical experiments are carried out using the primal-dual algorithm, and numerous real-world examples are conducted to confirm that the new proposed method outperforms several current state-of-the-art numerical methods in terms of the peak signal to noise ratio (PSNR) and the structural similarity (SSIM) index.

کلیدواژه‌ها

Variational model؛ Total generalized variation regularization؛ Staircasing effect؛ Primal-dual algorithm