Journal ArticleDOI
Quadratic regularization functionals for phase unwrapping
Jose L. Marroquin,Mariano Rivera +1 more
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TLDR
The Thikonov regularization theory is applied to find solutions that correspond to minimizers of positive-definite quadratic cost functionals and may be considered generalizations of the classical least-squares solution to the unwrapping problem.Abstract:
The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.read more
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Synthetic aperture radar interferometry
Paul A. Rosen,S. Hensley,Ian Joughin,F.K. Li,Soren N. Madsen,Ernesto Rodriguez,Richard M. Goldstein +6 more
TL;DR: In this paper, the authors present a review of the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering, including cartography, geodesy, land cover characterization, and natural hazards.
Journal ArticleDOI
Radar interferometry and its application to changes in the Earth's surface
Didier Massonnet,Kurt L. Feigl +1 more
TL;DR: In this paper, a review of the use of radar interferometry to measure changes in the Earth's surface has exploded in the early 1990s, and a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS2, JERS-1 and RADARSAT.
Journal ArticleDOI
Synthetic aperture radar interferometry
Richard Bamler,Philipp Hartl +1 more
TL;DR: In this article, a review of the technology and signal theoretical aspects of InSAR is presented, where the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times are exploited to measure several geophysical quantities, such as topography, deformations, glacier flows, ocean currents, vegetation properties, etc.
Journal ArticleDOI
Phase Unwrapping via Graph Cuts
TL;DR: A new energy minimization framework for phase unwrapping with considered objective functions are first-order Markov random fields and two algorithms, which solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques are named.
Journal ArticleDOI
Minimum Lp-norm two-dimensional phase unwrapping
TL;DR: In this paper, the minimum Lp-norm solution is obtained by embedding the transform-based methods for unweighted and weighted least squares within a simple iterative structure, and the data-dependent weights are generated within the algorithm and need not be supplied explicitly by the user.
References
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Journal ArticleDOI
Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods
TL;DR: In this article, a robust method for 2D phase principal values (in a least-squares sense) by using fast cosine transforms was developed, which can be used to isolate inconsistent regions (i.e., phase shear).
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Probabilistic Solution of Ill-Posed Problems in Computational Vision
TL;DR: This work derives efficient algorithms and describes parallel implementations on digital parallel SIMD architectures, as well as a new class of parallel hybrid computers that mix digital with analog components.
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Ill-posed problems in early vision
TL;DR: In this article, the authors reviewed mathematical results on ill-posed and ill-conditioned problems and formal aspects of regularization theory in the linear case are introduced, characterizing existence, uniqueness, and stability of solutions.
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Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements
TL;DR: In this article, the problem of fitting a wavefront distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem.
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Wave-front reconstruction for compensated imaging
TL;DR: In this paper, the authors analyzed the conversion from phase differences to phases and derived the optimal linear estimator in terms of least noise propagation for a compensated imaging (CI) system.