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Inverse Problems and Imaging (IPI)
 

A wavelet frame approach for removal of mixed gaussian and impulse noise on surfaces

Pages: 783 - 798, Volume 11, Issue 5, October 2017      doi:10.3934/ipi.2017037

 
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Jianbin Yang - College of Science, Hohai University, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu Province, China (email)
Cong Wang - College of Science, Hohai University, No.8 Focheng West Road, Jiangning, Nanjing, Jiangsu Province, 211100, China (email)

Abstract: Surface denoising is a fundamental problem in geometry processing and computer graphics. In this paper, we propose a wavelet frame based variational model to restore surfaces which are corrupted by mixed Gaussian and impulse noise, under the assumption that the region corrupted by impulse noise is unknown. The model contains a universal $\ell_1 + \ell_2$ fidelity term and an $\ell_1$-regularized term which makes additional use of the wavelet frame transform on surfaces in order to preserve key features such as sharp edges and corners. We then apply the augmented Lagrangian and accelerated proximal gradient methods to solve this model. In the end, we demonstrate the efficacy of our approach with numerical experiments both on surfaces and functions defined on surfaces. The experimental results show that our method is competitive relative to some existing denoising methods.

Keywords:  Wavelet frame, surface denoising, mixed Gaussian and impulse noise, ALM-APG algorithm, variational model.
Mathematics Subject Classification:  Primary: 68U10, 47A52, 65T60; Secondary: 65K10.

Received: August 2016;      Revised: May 2017;      Available Online: June 2017.

 References