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.

Adaptive anisotropic diffusion for noise reduction of phase images in Fourier domain Doppler optical coherence tomography

“…It is worthy to note that many diffusion models adopt the constant step size [25][26][27][28] for each iteration or whole iterative process of the image. Here a better iteration step is propsoed in the Eq.…”

Contribution study of monogenic wavelets transform to reduce speckle noise in digital speckle pattern interferometry

“…Several different denoising methods have been reported so far to reduce speckle noise in DSPI. [10][11][12][13][14][15][16][17][18][19][20][21][22] Various approaches for speckle noise reduction including gray-scale modification, frame averaging, low-pass filtering, and short space spectral subtraction image restoration technique have been suggested by Lim and Nawab. 10 Another considerable work by Varman and Wykes 11 presents a demonstration of curve fitting and fast Fourier transform techniques to reduce residual speckle noise.…”

“…10 Another considerable work by Varman and Wykes 11 presents a demonstration of curve fitting and fast Fourier transform techniques to reduce residual speckle noise. Tang et al 12 gave an overview about the exploitation of partial differential equations (PDEs) and the anisotropic filter-based method for DSPI fringes denoising. Bernini et al 13 exploited bidimensional empirical mode decomposition to reduce speckle in DSPI, which gives high-and low-frequency mode called intrinsic mode functions (IMFs): the technique recommends to remove the first IMF that contain speckle noise and then reconstruct others IMFs to obtain despeckled fringe patterns.…”

Windowed fourier transform based fringe pattern analysis techniques

“…Noise is an inevitable problem in fringe pattern analysis, and fringe patterns with noises must be denoised before further analysis. Current denoising techniques can be generally classified into two groups, spatial domain techniques [15,[59][60][61][62][63][64][65][66][67] and transform domain techniques [19,42,[68][69][70]. The spatial domain techniques reduce noises by a smoothing process.…”

“…The mean and median filtering methods [15], oriented partial differential equations (OPDE) [59][60][61][62], coherence enhancing diffusion (CED) [63,64] and spin filters [65][66][67] are examples of those spatial domain techniques. A comparison study of the spatial domain techniques can be found in Ref.…”