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

机译:两种定向偏微分方程滤波模型在劣质散斑条纹及其数值快速算法中的应用

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摘要

In this paper, we are concerned with denoising in experimentally obtained electronic speckle pattern interferometry (ESPI) speckle fringe patterns with poor quality. We extend the application of two existing oriented partial differential equation (PDE) filters, including the second-order single oriented PDE filter and the double oriented PDE filter, to two experimentally obtained ESPI speckle fringe patterns with very poor quality, and compare them with other efficient filtering methods, including the adaptive weighted filter, the improved nonlinear complex diffusion PDE, and the windowed Fourier transform method. All of the five filters have been illustrated to be efficient denoising methods through previous comparative analyses in published papers. The experimental results have demonstrated that the two oriented PDE models are applicable to low-quality ESPI speckle fringe patterns. Then for solving the main shortcoming of the two oriented PDE models, we develop the numerically fast algorithms based on Gauss-Seidel strategy for the two oriented PDE models. The proposed numerical algorithms are capable of accelerating the convergence greatly, and perform significantly better in terms of computational efficiency. Our numerically fast algorithms are extended automatically to some other PDE filtering models.
机译:在本文中,我们关注通过实验获得的质量较差的电子散斑干涉图(ESPI)散斑条纹的去噪。我们将两个现有的定向偏微分方程(PDE)滤波器(包括二阶单方向PDE滤波器和双向PDE滤波器)的应用扩展到两个通过实验获得的质量非常差的ESPI散斑条纹图案,并将它们与其他高效的滤波方法,包括自适应加权滤波器,改进的非线性复扩散PDE和开窗傅立叶变换方法。通过先前发表论文中的比较分析,已将所有五个滤波器都说明为有效的降噪方法。实验结果表明,两种定向的PDE模型均适用于低质量的ESPI散斑条纹图案。为了解决两个定向PDE模型的主要缺点,我们针对两个定向PDE模型开发了基于高斯-塞德尔策略的数值快速算法。所提出的数值算法能够大大加快收敛速度​​,并且在计算效率方面具有明显更好的性能。我们的数值快速算法自动扩展到其他一些PDE过滤模型。

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