New regularization scheme for phase unwrapping

Guerriero, L.; Nico, Giovanni; Pasquariello, G.; Stramaglia, Sebastiano

doi:10.1364/ao.37.003053

Cited by 34 publications

(13 citation statements)

References 16 publications

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“…Lemma 1: Let and be two wrap-counts images such that (21) Then there exists a binary image such that (22) Proof: See Appendix A. According to Lemma 1, we can iteratively compute , where minimizes , until the the minimum energy is reached.…”

Section: A -Stepmentioning

confidence: 99%

The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS

Dias

Leitao

2002

IEEE Trans. on Image Process.

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Abstract-This paper presents an effective algorithm for absolute phase (not simply modulo-2 ) estimation from incomplete, noisy and modulo-2 observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2 -periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step ( -step), implemented by network programming techniques and an iterative conditional modes (ICM) step ( -step). Accordingly, the algorithm is termed , where the letter stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2 -multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.

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Section: A -Stepmentioning

confidence: 99%

The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS

Dias

Leitao

2002

IEEE Trans. on Image Process.

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“…In a quite different vein, and recognizing that the absolute phase estimation is an ill-posed problem, papers [4], [5], [6], [7] have adopted the regularization framework to impose smoothness on the solution. The same objective has been pursued in papers [8], [9], [10], [11] by adopting a Bayesian viewpoint.…”

Section: Introductionmentioning

confidence: 99%

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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“…In a couple of recent papers, the phase unwrapping problem was handled by methods of Statistical Mechanics. Simulated annealing was applied in [14]. In [15] the problem is solved by the Mean-Field Annealing (MFA) technique; PU is formulated as a constrained optimization problem for the field of integer corrections to be added to the wrapped phase gradient in order to recover the true phase gradient, with the cost function consisting of second order differences, and measuring the smoothness of the reconstructed phase field.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics approach to the phase unwrapping problem

Stramaglia

Refice

Guerriero

2000

Physica A: Statistical Mechanics and its Applications

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The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem is formulated as that of finding the ground state of a locally constrained, finite size, spin-L Ising model under a non-uniform magnetic field. The optimization problem is solved by the Mean-Field Annealing technique. Synthetic experiments show the effectiveness of the proposed algorithm

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New regularization scheme for phase unwrapping

Cited by 34 publications

References 16 publications

The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS

The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS

A Discrete/Continuous Minimization Method in Interferometric Image Processing

Statistical mechanics approach to the phase unwrapping problem

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