Bayesian approaches to phase unwrapping: theoretical study

Nico, Giovanni; Palubinskas, Gintautas; Datcu, Mihai

doi:10.1109/78.863057

Cited by 95 publications

(62 citation statements)

References 54 publications

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“…The same objective has been pursued in papers [8], [9], [10], [11] by adopting a Bayesian viewpoint. Papers [8], [9] apply a nonlinear recursive filtering technique to determine the absolute phase.…”

Section: Introductionmentioning

confidence: 93%

“…The unwrapping step (14) finds the maximum of the posterior density p φ|x (φ|x) on a mesh obtained by discretizing each coordinate φ ij according to (11). The first estimate k (1) delivered by the unwrapping step is based on the maximum likelihood estimate η ≡ {η ij | (i, j) ∈ Z}.…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…Paper [10] considers an InSAR (interferometric synthetic aperture radar) observation model taking into account not only the image absolute phase, but also the backscattering coefficient and the correlation factor images, which are jointly recovered from InSAR image pairs. Paper [11] proposes a fractal based prior and the simulated annealing scheme to compute the absolute phase image.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Discrete/Continuous Minimization Method in Interferometric Image Processing

Dias

Leitao

2001

Lecture Notes in Computer Science

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Abstract. The 2D absolute phase estimation problem, in interferometric applications, is to infer absolute phase (not simply modulo-2π) from incomplete, noisy, and modulo-2π image observations. This is known to be a hard problem as the observation mechanism is nonlinear. In this paper we adopt the Bayesian approach. The observation density is 2π-periodic and accounts for the observation noise; the a priori probability of the absolute phase is modeled by a first order noncausal Gauss Markov random field (GMRF) tailored to smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques, and an iterative conditional modes (ICM) step (π-step). Accordingly, we name the algorithm ZπM, where letter M stands for maximization. A set of experimental results, comparing the proposed algorithm with other techniques, illustrates the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 93%

Section: Estimation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Discrete/Continuous Minimization Method in Interferometric Image Processing

Dias

Leitao

2001

Lecture Notes in Computer Science

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“…Phase unwrapping approaches belong mainly to one of the following classes: path following [17], [22], [23], minimum L p norm [24], [25], [19], [20], [26], [7], Bayesian/regularization [18], [27], [28], [29], [30], [7], [31], [32], and parametric modelling [33], [34].…”

Section: Introductionmentioning

confidence: 99%

Phase Unwrapping via Graph Cuts

Bioucas-Dias

Valadão

2007

IEEE Trans. on Image Process.

474

220

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Abstract-Phase unwrapping is the inference of absolute phase from modulo-2π phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical L p norm, with p ≥ 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2π units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems, by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrapping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms.

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“…Existing phase unwrapping methods (some of which are 3D) can be classified into four different categories: pathfollowing (5-10), cost function optimization (11)(12)(13)(14), Bayesian (15), and parametric modeling methods (16). Since the presented method belongs to the first category, a brief introduction of path-following methods follows.…”

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confidence: 99%

Reliable two‐dimensional phase unwrapping method using region growing and local linear estimation

Zhou

Zaitsev

Bao

2009

Magnetic Resonance in Med

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In MRI, phase maps can provide useful information about parameters such as field inhomogeneity, velocity of blood flow, and the chemical shift between water and fat. As phase is defined in the (؊,] range, however, phase wraps often occur, which complicates image analysis and interpretation. This work presents a two-dimensional phase unwrapping algorithm that uses quality-guided region growing and local linear estimation. The quality map employs the variance of the second-order partial derivatives of the phase as the quality criterion. Phase information from unwrapped neighboring pixels is used to predict the correct phase of the current pixel using a linear regression method. The algorithm was tested on both simulated and real data, and is shown to successfully unwrap phase images that are corrupted by noise and have rapidly changing phase. Magn Reson Med 62:1085-1090, 2009.

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Bayesian approaches to phase unwrapping: theoretical study

Cited by 95 publications

References 54 publications

A Discrete/Continuous Minimization Method in Interferometric Image Processing

A Discrete/Continuous Minimization Method in Interferometric Image Processing

Phase Unwrapping via Graph Cuts

Reliable two‐dimensional phase unwrapping method using region growing and local linear estimation

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