Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields

Villa, Jesús; Rodrı́guez-Vera, Ramón; Quiroga, Juan Antonio; Vargas, José Ismael De la Rosa; González, Efrén

doi:10.1016/j.optlaseng.2010.02.002

Cited by 33 publications

(7 citation statements)

References 20 publications

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“…1) Put the set of data window sizes with increasing order h(1) < h(2) < · · · < h(n) 2) For every point (i, j) 3) For every data window size h(t) 4) estimate the denoised phaseφ h (i, j)| u=0,v=0 by the (7) and (9). calculate the variance of it by (10).…”

Section: Window Size Select Criteriamentioning

confidence: 99%

PUMA-SPA: A Phase Unwrapping Method Based on PUMA and Second-Order Polynomial Approximation

Hao

2014

IEEE Geosci. Remote Sensing Lett.

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This letter focuses on the phase unwrapping algorithm. A state-of-the-art phase unwrapping method called PUMA which is based on the max-flow/min-cut was proposed recently. The proposed method in this letter postprocesses the results of PUMA to improve the unwrapping results. A pointwise local second-order polynomial approximation method is considered to suppress the noise. We estimate the parameters of the polynomial by solving the overdetermined equations and get the solution with the Least Squares Error Fitting. The proposed algorithm synthesizes the unwrapping with the denoising method and is abbreviated as PUMA-SPA. In the denoising step, adaptive local window sizes are selected to compromise the fitting error and the suppression of noise. Experiments show that the proposed method can achieve better results than the method Congruence Operation and Least Squares Fitting (CO-LSF) proposed recently.Index Terms-Adaptive window size selection, local polynomial approximation (LPA), phase estimation, phase unwrapping.

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Section: Window Size Select Criteriamentioning

confidence: 99%

PUMA-SPA: A Phase Unwrapping Method Based on PUMA and Second-Order Polynomial Approximation

Hao

2014

IEEE Geosci. Remote Sensing Lett.

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“…Some of the first contributions in this field were mainly based on convolution filters using different kinds of anisotropic filtering masks [8][9][10][11][12]. Other set of the main contributions in the last years is based on the variational calculus approach by solving partial differential equations [13][14][15][16][17][18], and by means of the regularization theory [19,20]. The use of the Fourier transform for fringe or phase map denoising has also been proposed in [21,22] (Localized Fourier transform filter and windowed Fourier transform, respectively).…”

Section: Introductionmentioning

confidence: 99%

The 2D Continuous Wavelet Transform: Applications in Fringe Pattern Processing for Optical Measurement Techniques

Hernández¹,

Rosa²,

GustavoRodríguez³

et al. 2018

Wavelet Theory and Its Applications

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Optical metrology and interferometry are widely known disciplines that study and develop techniques to measure physical quantities such as dimensions, force, temperature, stress, etc. A key part of these disciplines is the processing of interferograms, also called fringe patterns. Owing that this kind of images contains the information of interest in a codified form, processing them is of main relevance and has been a widely studied topic for many years. Several mathematical tools have been used to analyze fringe patterns, from the classic Fourier analysis to regularization methods. Some methods based on wavelet theory have been proposed for this purpose in the last years and have evidenced virtues to consider them as a good alternative for fringe pattern analysis. In this chapter, we resume the theoretical basis of fringe pattern image formation and processing, and some of the most relevant applications of the 2D continuous wavelet transform (CWT) in fringe pattern analysis.

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“…The main aim of any fringe filtering technique being to remove the speckle noise effectively while preserving the details of the fringe pattern pertaining to the true interference phase, a number of noise filtering techniques of the phase fringe pattern have been proposed, such as the anisotropic sine/cosine average filter [1], the local histogram-data-orientated filter [2], the tangent least-squares fitting filter [3], the adaptive filter [4], etc. The fringe filtering techniques based on the use of regularized cost function with the complex-valued Markov random fields [5], windowed Fourier transform [6], local polynomial approximation of phase [7], localized Fourier transform [8] and 2D continuous wavelet tranform [9] have also been reported. The comparisons of few of the fringe filtering techniques can be found in [10,11].…”

Section: Introductionmentioning

confidence: 99%

Patch-wise denoising of phase fringe patterns based on matrix enhancement

Kulkarni

Rastogi

2016

Optics and Lasers in Engineering

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We propose a new approach for the denoising of a phase fringe pattern recorded in an optical interferometric setup. The phase fringe pattern which is generally corrupted by high amount of speckle noise is first converted into an exponential phase field. This phase field is divided into number of overlapping patches. Owing to the small size of each patch, the presence of a simple structure of the interference phase is assumed in it. Accordingly, the singular value decomposition (SVD) of the patch allows to separate the signal and noise components effectively. The patch is reconstructed only with the signal component. In order to further improve the robustness of the proposed method, an enhanced data matrix is generated using the patch and the SVD of this enhanced matrix is computed. The matrix enhancement results in an increased dimension of the noise subspace which thus accommodates more amount of noise component. Reassignment of the filtered pixels of the preceding patch in the current patch improves the noise filtering accuracy. The fringe denoising capability in function of the noise level and the patch size is studied. Simulation and experimental results are provided to demonstrate the practical applicability of the proposed method.

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Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields

Cited by 33 publications

References 20 publications

PUMA-SPA: A Phase Unwrapping Method Based on PUMA and Second-Order Polynomial Approximation

PUMA-SPA: A Phase Unwrapping Method Based on PUMA and Second-Order Polynomial Approximation

The 2D Continuous Wavelet Transform: Applications in Fringe Pattern Processing for Optical Measurement Techniques

Patch-wise denoising of phase fringe patterns based on matrix enhancement

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