Overview of anisotropic filtering methods based on partial differential equations for electronic speckle pattern interferometry

Abstract

In this paper, we first present the general description for partial differential equations (PDEs) based image processing methods, including the basic idea, the main advantages and disadvantages, a few representative PDE models, and the derivation of PDE models. Then we review our contributions on PDE-based anisotropic filtering methods for electronic speckle pattern interferometry, including the second-order, fourth-order, and coupled nonoriented PDE filtering models and the second-order and coupled nonlinear oriented PDE filtering models. We have summarized the features of each model.

©2012 Optical Society of America

Application of two oriented partial differential equation filtering models on speckle fringes with poor quality and their numerically fast algorithms

Xinjun Zhu, Zhanqing Chen, Chen Tang, Qinghua Mi, and Xiusheng Yan
Appl. Opt. 52(9) 1814-1823 (2013)

Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the δ-mollification phase map method

Chen Tang, Fang Zhang, Botao Li, and Haiqing Yan
Appl. Opt. 45(28) 7392-7400 (2006)

The oriented-couple partial differential equations for filtering in wrapped phase patterns

Chen Tang, Lin Han, Hongwei Ren, Tao Gao, Zhifang Wang, and Ke Tang
Opt. Express 17(7) 5606-5617 (2009)

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns

Wenjun Xu, Chen Tang, Fan Gu, and Jiajia Cheng
Appl. Opt. 56(10) 2843-2850 (2017)

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry

Chen Tang, Wenjing Lu, Song Chen, Zhen Zhang, Botao Li, Wenping Wang, and Lin Han
Appl. Opt. 46(30) 7475-7484 (2007)