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

Katkovnik, Vladimir; Astola, Jaakko; Егиазарян, Карен

doi:10.1109/tip.2008.916046

Cited by 40 publications

(31 citation statements)

References 29 publications

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“…PUMA is able to preserve discontinuities by using graph cut based methods to solve the integer optimization problem associated with phase unwrapping. The reconstructed error is comparable to or better than state-of-the-art algorithms developed for noisy phase unwrapping, of which the ZπM [15] and the PhaseLa [27] are two examples.…”

Section: A Proposed Approachmentioning

confidence: 88%

“…The material herein presented is an elaboration of [26] and a development of the phase-tracking unwrap proposed in [27], where the ICI adaptive varying windows are used for the phase estimates calculated by recursive local minimization of the least square criterion. In this paper we are mainly focused on filtering the wrapped phase as the prefiltering procedure for the forthcoming unwrapping.…”

Section: A Proposed Approachmentioning

confidence: 99%

“…The details of the observation models relating the noisy wrapped phase with the true phase depend on the coherent imaging system under consideration (see, e.g., [8,15,27] for an account of observation models in different coherent imaging systems). Nevertheless, the essential of all these observation mechanisms is captured by the relation…”

Section: Local Polynomial Phase Approximationsmentioning

confidence: 99%

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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: A Proposed Approachmentioning

confidence: 88%

Section: A Proposed Approachmentioning

confidence: 99%

Section: Local Polynomial Phase Approximationsmentioning

confidence: 99%

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Absolute phase estimation: adaptive local denoising and global unwrapping

Bioucas-Dias¹,

Katkovnik

Astola

et al. 2008

Appl. Opt.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nevertheless, these approaches may either be too computationally intensive or not robust enough at high noise levels. Another direction is to directly denoise the estimated wrapped phase image [11][12][13][14]. However, the errors in the estimated wrapped phase image can hardly be modeled by a random process with known distribution.…”

Section: Introductionmentioning

confidence: 99%

Efficient fringe image enhancement based on dual-tree complex wavelet transform

Hsung

Lun

2011

Appl. Opt.

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In optical phase shift profilometry (PSP), parallel fringe patterns are projected onto an object and the deformed fringes are captured using a digital camera. It is of particular interest in real time threedimensional (3D) modeling applications because it enables 3D reconstruction using just a few image captures. When using this approach in a real life environment, however, the noise in the captured images can greatly affect the quality of the reconstructed 3D model. In this paper, a new image enhancement algorithm based on the oriented two-dimenional dual-tree complex wavelet transform (DT-CWT) is proposed for denoising the captured fringe images. The proposed algorithm makes use of the special analytic property of DT-CWT to obtain a sparse representation of the fringe image. Based on the sparse representation, a new iterative regularization procedure is applied for enhancing the noisy fringe image. The new approach introduces an additional preprocessing step to improve the initial guess of the iterative algorithm. Compared with the traditional image enhancement techniques, the proposed algorithm achieves a further improvement of 7:2 dB on average in the signal-to-noise ratio (SNR). When applying the proposed algorithm to optical PSP, the new approach enables the reconstruction of 3D models with improved accuracy from 6 to 20 dB in the SNR over the traditional approaches if the fringe images are noisy.

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“…The structure of the observation models relating the noisy wrapped phase with the true phase depends on the system under consideration (see, e.g., [12][13][14] for an account of observation models in different coherent imaging systems). The essence of most of these observation mechanisms is, however, captured by the relation…”

Section: Introductionmentioning

confidence: 99%

CAPE: combinatorial absolute phase estimation

Valadão

Bioucas-Dias

2009

J. Opt. Soc. Am. A

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An absolute phase estimation algorithm for interferometric applications is introduced. The approach is Bayesian. Besides coping with the 2-periodic sinusoidal nonlinearity in the observations, the proposed methodology assumes a first-order Markov random field prior and a maximum a posteriori probability (MAP) viewpoint. For computing the MAP solution, we provide a combinatorial suboptimal algorithm that involves a multiprecision sequence. In the coarser precision, it unwraps the phase by using, essentially, the previously introduced PUMA algorithm [IEEE Trans. Image Proc. 16, 698 (2007)], which blindly detects discontinuities and yields a piecewise smooth unwrapped phase. In the subsequent increasing precision iterations, the proposed algorithm denoises each piecewise smooth region, thanks to the previously detected location of the discontinuities. For each precision, we map the problem into a sequence of binary optimizations, which we tackle by computing min-cuts on appropriate graphs. This unified rationale for both phase unwrapping and denoising inherits the fast performance of the graph min-cuts algorithms. In a set of experimental results, we illustrate the effectiveness of the proposed approach.

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

Cited by 40 publications

References 29 publications

Absolute phase estimation: adaptive local denoising and global unwrapping

Absolute phase estimation: adaptive local denoising and global unwrapping

Efficient fringe image enhancement based on dual-tree complex wavelet transform

CAPE: combinatorial absolute phase estimation

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