Moving ahead with phase

Patil, Abhijit; Rastogi, Pramod K.

doi:10.1016/j.optlaseng.2006.04.001

Cited by 30 publications

(14 citation statements)

References 86 publications

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“…For instance, in synthetic aperture radar interferometry (InSAR), the phase values are proportional to the terrain elevation height; in magnetic resonance imaging, the phase is used to measure temperature, to map the main magnetic field inhomogeneities, to identify veins in the tissues, and to segment water from fat. Other examples can be found in adaptive optics, diffraction tomography, nondestructive testing of components, and deformation and vibration measurements (see, e.g., [1][2][3][4][5][6]). …”

Section: Introductionmentioning

confidence: 99%

“…In particular, it has been demonstrated in [17] that a fringe pattern processed locally or block by block using the windowed Fourier transform method removes artifacts in phase measurements better than the simple carrier based Fourier transform methods such as the windowed Fourier ridges, the wavelet transform, and the regularized phase tracking. Presently, the windowed Fourier transform method is considered to be a promising tool among the spatial techniques in use for phase measurement [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Absolute phase estimation: adaptive local denoising and global unwrapping

Bioucas-Dias¹,

Katkovnik

Astola

et al. 2008

Appl. Opt.

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The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2π noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2π phase obtained in the first step. The adaptive local modulo-2π phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the firstorder approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process. 16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Absolute phase estimation: adaptive local denoising and global unwrapping

Bioucas-Dias¹,

Katkovnik

Astola

et al. 2008

Appl. Opt.

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“…For instance, in synthetic aperture radar interferometry (InSAR), the phase is proportional to the terrain elevation height; in magnetic resonance imaging, the phase is used to measure temperature, to map the main magnetic field inhomogeneity, to identify veins in the tissues, and to segment water from fat. Other examples can be found in adaptive optics, diffraction tomography, nondestructive testing of components, and deformation and vibration measurements (see, e.g., [2], [4], [3], [5]). In all these applications, the observation mechanism is a 2π-periodic function of the true phase, hereafter termed absolute phase.…”

Section: Introductionmentioning

confidence: 99%

Multi-frequency Phase Unwrapping from Noisy Data: Adaptive Local Maximum Likelihood Approach

et al. 2009

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Abstract. The paper introduces a new approach to absolute phase estimation from frequency diverse wrapped observations. We adopt a discontinuity preserving nonparametric regression technique, where the phase is reconstructed based on a local maximum likelihood criterion. It is shown that this criterion, applied to the multifrequency data, besides filtering the noise, yields a 2πQ-periodic solution, where Q > 1 is an integer. The filtering algorithm is based on local polynomial (LPA) approximation for the design of nonlinear filters (estimators) and the adaptation of these filters to the unknown spatially smoothness of the absolute phase. Depending on the value of Q and of the original phase range, we may obtain complete or partial phase unwrapping. In the latter case, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed method yields state-of-the-art performance, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.

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“…For instance, in synthetic aperture radar interferometry, the phase value is proportional to a terrain elevation height; in magnetic resonance imaging, the phase is used to measure a magnetic field inhomogeneity. Other examples are in adaptive optics, diffraction tomography, nondestructive testing, deformation, and vibration measurements (e.g., [1]- [3]). …”

Section: Introductionmentioning

confidence: 99%

“…Proposition 1 [4]: Assume that the absolute phase satisfy to the conditions (2) then (3) According to Proposition 1, the phase can be restored by a two stage algorithm. First, the differences (derivatives) and are calculated according to the formula (3). Second, the phase is reconstructed by summation (integration) of these differences.…”

Section: Introductionmentioning

confidence: 99%

Phase Local Approximation (PhaseLa) Technique for Phase Unwrap From Noisy Data

Katkovnik

Astola

Егиазарян

2008

IEEE Trans. on Image Process.

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Abstract-The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (ICI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval [ ) and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the ICI adaptation algorithm.Index Terms-Adaptive window size, interferometric imaging, local polynomial approximation (LPA), phase image reconstruction, phase unwrapping.

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Moving ahead with phase

Cited by 30 publications

References 86 publications

Absolute phase estimation: adaptive local denoising and global unwrapping

Absolute phase estimation: adaptive local denoising and global unwrapping

Multi-frequency Phase Unwrapping from Noisy Data: Adaptive Local Maximum Likelihood Approach

Phase Local Approximation (PhaseLa) Technique for Phase Unwrap From Noisy Data

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