Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
15 January 2020 |
30 January 2020 |
10 March 2020 |
Abstract: We present a state-of-the-art of recent nonlocal models applied in image denoising. In [1], Gilboa and Osher defined a nonlocal gradient, divergence and Laplacian operatos, and proposed different applications in image processing. Different definitions have been proposed by Jin, Jost, and Wang [2]. Based on nonlocal operators, many applications have been proposed. A nonlocal H1 has been proposed in [5] which improves on the model of Gilboa-Osher. In [2], the authors proposed a new variant of the total variation model, based on Rudin-Osher's nonlocal operators. Experiments show that the new model is capable of producing good denoising results. In [3], the authors defined an approximation of the nonlocal Meyer's model. In [4], a variable exponent nonlocal p(x)-Laplacian model has been proposed to reduce the execution time and to represent textures and small details. The aim of this presentation is to give an overview of some important nonlocal methods, using two different definitions of nonlocal gradient, and to compare their theoretical properties and experimental results. [1] Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005-1028 (2008). [2] Jin, Y., Jost, J., Wang, G.: A New Nonlocal variational setting for image processing. American Institute of Mathematical Sciences .(2015), 415-430. [3] Jin, Y., Jost, J., Wang, G.: A Nonlocal Version of the Osher-Solé-Vese Model. Springer (2012). [4] Karami, F., Meskine, D., Sadik, K.: Variable Exponent Nonlocal Model with Weaker Norm in the Fidelity Term for Image Restoration. Springer (2018), 397-406. [5] Jin, Y., Jost, J., Wang, G.: A New Nonlocal H 1 Model for Image Denoising. Springer (2012).
