A Factor-Two Approximation Algorithm for Two-Dimensional Phase-Unwrapping
Reuven Bar-Yehuda,Irad Yavneh +1 more
TL;DR: A novel approach to two-dimensional phase unwrapping is presented, based on the local-ratio principle, which guarantees a solution whose cost is at most twice the minimum sought.
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Abstract: Two-dimensional phase unwrapping is the problem of deducing unambiguous “phase” from values known only modulo 2�. Many authors agree that the objective of phase unwrapping should be to find a (weighted) minimum of the number of places where adjacent discretized phase values differ by more than �. This problem, which is known to be NP-hard, is of considerable practical interest, largely due to its importance in interpreting data acquired with synthetic aperture radar (SAR) interferometry. Consequently, many heuristic algorithms for its approximate solution have been proposed. Here we present a novel approach to this problem, based on the local-ratio principle, which guarantees a solution whose cost is at most twice the minimum sought.
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Citations
•Journal Article
Minimum L~2-norm two dimensional phase unwrapping
TL;DR: In this article, a formula of minimum L 2 -norm two-dimensional phase unwrapping was derived based on relationship between wrapping and unwrapping phase. But, the results of the formula were not compared with that by traditional Goldstain's method.
42
A multilevel graph algorithm for two dimensional phase unwrapping
Iddit Shalem,Irad Yavneh +1 more
TL;DR: An efficient multi-level graph algorithm is presented for the approximate solution of an equivalent problem—minimal residue cut in the dual graph of two-dimensional phase unwrapping.
3
References
Satellite radar interferometry: Two-dimensional phase unwrapping
TL;DR: In this paper, an approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented, where it is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image.
2.5K
•Book
Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software
Dennis C. Ghiglia,Mark D. Pritt +1 more
- 28 Apr 1998
TL;DR: Methods for Phase Unwrapping, Phase Data, Quality Maps, Masks, and Filters, and Minimum-Norm Methods.
2K
A General Approximation Technique for Constrained Forest Problems
TL;DR: The first approximation algorithms for many NP-complete problems, including the non-fixed point-to-point connection problem, the exact path partitioning problem and complex location-design problems are derived.
•Proceedings Article
A general approximation technique for constrained forest problems
Michel X. Goemans,David P. Williamson +1 more
- 01 Sep 1992
TL;DR: A 2-approximation algorithm for the Steiner tree problem was given in this paper with running time of O(n 2 log n) for the shortest path problem, where n is the number of vertices in a graph.
Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms.
Curtis W. Chen,Howard A. Zebker +1 more
TL;DR: In this paper, the authors use network constructions to show that the minimum L0-norm problem is NP-hard, or one that complexity theory suggests is impossible for efficient algorithms to solve exactly.
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