Image denoising using the Gaussian curvature of the image surface



Brito-Loeza, Carlos, Chen, Ke ORCID: 0000-0002-6093-6623 and Uc-Cetina, Victor
(2016) Image denoising using the Gaussian curvature of the image surface. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 32 (3). pp. 1066-1089.

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Abstract

A number of high-order variational models for image denoising have been proposed within the last few years. The main motivation behind these models is to fix problems such as the staircase effect and the loss of image contrast that the classical Rudin-Osher-Fatemi model [Leonid I. Rudin, Stanley Osher and Emad Fatemi, Nonlinear total variation based noise removal algorithms, Physica D 60 (1992), pp. 259-268] and others also based on the gradient of the image do have. In this work, we propose a new variational model for image denoising based on the Gaussian curvature of the image surface of a given image. We analytically study the proposed model to show why it preserves image contrast, recovers sharp edges, does not transform piecewise smooth functions into piecewise constant functions and is also able to preserve corners. In addition, we also provide two fast solvers for its numerical realization. Numerical experiments are shown to illustrate the good performance of the algorithms and test results.

Item Type: Article
Uncontrolled Keywords: denoising, variational models, regularization, augmented Lagrangian method
Depositing User: Symplectic Admin
Date Deposited: 01 Jul 2016 10:35
Last Modified: 19 Jan 2023 07:35
DOI: 10.1002/num.22042
Open Access URL: http://ftp.liv.ac.uk/pub/maths_chen/chen/GC_nv3.pd...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001975