A mesh-free algorithm for ROF model

• Published in: EURASIP journal on advances in signal processing Vol. 2017; no. 1; pp. 1 - 16
• Main Authors: Khan, Mushtaq Ahmad, Chen, Wen, Ullah, Asmat, Fu, Zhuojia
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 18.07.2017; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analysis; Collocation; Differential equations; Engineering; Finite element method; Image denoising; Mathematical analysis; Mathematical models; Mesh-based methods; Mesh-free method; Meshless methods; Neural networks; Noise; Noise control; Noise reduction; Partial differential equations; Quantum Information Technology; Radial basis function; Radial basis functions (RBF); Ramps; Regularization; Restoration equation; Robustness (mathematics); Signal to noise ratio; Signal,Image and Speech Processing; Spintronics; Total variation (TV) filter; Visual signals; Mesh-based methods; Mesh-free method; Restoration equation; Total variation (TV) filter; Radial basis functions (RBF); Image denoising
• ISSN: 1687-6180; 1687-6172; 1687-6180
• DOI: 10.1186/s13634-017-0488-6

The total variation (TV) denoising method is a PDE-based technique that preserves the edges well but has undesirable staircase effect in some cases, namely, the translation of smooth regions (ramps) into piecewise constant regions (stairs). This paper introduces a novel mesh-free approach using TV (ROF model) regularization and radial basis function (RBF) for the numerical approximation of TV-based model to remove the additive noise from the measurements. This approach is structured on local collocation and multiquadric radial basis function. These features enable this strategy not only to eliminate noise from images and preserve the edges but also has the advantage to minimize the staircase effect substantially from real and artificial images which cause the image to look blocky. Experimental results demonstrate that the proposed mesh-free approach is robust and performs well in visual improvement as well as peak signal-to-noise ratio compared with the recent partial differential equation (PDE)-based traditional methods.