## A class of solution-invariant transformations of cost functions for minimum cost flow phase unwrapping

JOSA A, Vol. 21, Issue 10, pp. 1975-1987 (2004)

http://dx.doi.org/10.1364/JOSAA.21.001975

Acrobat PDF (254 KB)

### Abstract

Phase unwrapping (PU) represents an important step in synthetic aperture radar interferometry (InSAR) and other interferometric applications. Among the different PU methods, the so called branch-cut approaches play an important role. In 1996 M. Costantini [*Proceedings of the Fringe ’96 Workshop ERS SAR Interferometry* (European Space Agency, Munich, 1996), pp. 261–272] proposed to transform the problem of correctly placing branch cuts into a minimum cost flow (MCF) problem. The crucial point of this new approach is to generate cost functions that represent the *a priori* knowledge necessary for PU. Since cost functions are derived from measured data, they are random variables. This leads to the question of MCF solution stability: How much can the cost functions be varied without changing the cheapest flow that represents the correct branch cuts? This question is partially answered: The existence of a whole linear subspace in the space of cost functions is shown; this subspace contains all cost differences by which a cost function can be changed without changing the cost difference between any two flows that are discharging any residue configuration. These cost differences are called strictly stable cost differences. For quadrangular nonclosed networks (the most important type of MCF networks for interferometric purposes) a complete classification of strictly stable cost differences is presented. Further, the role of the well-known class of node potentials in the framework of strictly stable cost differences is investigated, and information on the vector-space structure representing the MCF environment is provided.

© 2004 Optical Society of America

**OCIS Codes**

(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(280.6730) Remote sensing and sensors : Synthetic aperture radar

**Citation**

Michael Hubig, Steffen Suchandt, and Nico Adam, "A class of solution-invariant transformations of cost functions for minimum cost flow phase unwrapping," J. Opt. Soc. Am. A **21**, 1975-1987 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-10-1975

Sort: Year | Journal | Reset

### References

- R. Bamler and P. Hartl, “Synthetic aperture radar interferometry,” Inverse Probl. 14, R1–R54 (1998).
- D. Ghilia and M. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, New York, 1998).
- R. Bamler, N. Adam, G. Davidson, and D. Just, “Noise-induced slope distortion in 2-D phase unwrapping by linear estimators with application to SAR interferometry,” IEEE Trans. Geosci. Remote Sens. 36, 913–921 (1998).
- M. Costantini, “A phase unwrapping method based on network programming,” Proceedings of the Fringe ’96 Workshop ERS SAR Interferometry (European Space Agency, Munich, 1996), pp. 261–272.
- M. Costantini, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998).
- R. Ahuja, T. Magnanti, and J. Orlin, Network Flows: Theory, Algorithms and Applications (Prentice Hall, Englewood Cliffs, N.J., 1993).
- M. Eineder, M. Hubig, and B. Milcke, “Unwrapping large interferograms using the minimum cost flow algorithm,” in Proceedings of the International Geoscience and Remote Sensing Society, T. Stein, ed. (IEEE Press, Piscataway, N.J., 1998), pp. 83–87.
- G. F. Carballo and P. W. Fieguth, “Probabilistic cost functions for network flow phase unwrapping,” in Proceedings of the International Geoscience and Remote Sensing Society, T. Stein, ed. (IEEE Press, Piscataway, N.J., 1999), Vol. III, pp. 1531–1533.
- C. Chen and H. Zebker, “Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms,” J. Opt. Soc. Am. A 17, 401–414 (2000).
- A. Refice, G. Satalino, S. Stramaglia, M. T. Chiaradia, and N. Veneziani, “Weights determination for minimum cost flow InSAR phase unwrapping,” in Proceedings of the International Geoscience and Remote Sensing Society, T. Stein, ed. (IEEE Press, Piscataway, N.J., 1999), Vol. II, pp. 1342–1344.
- M. Hubig, S. Suchandt, and N. Adam, “Equivalence of cost generators for minimum cost flow phase unwrapping,” J. Opt. Soc. Am. A 19, 64–70 (2002).
- N. Jacobson, Lectures in Abstract Algebra I: Basic Concepts (Van Nostrand Reinhold, New York, 1953).
- N. Jacobson, Lectures in Abstract Algebra II: Linear Algebra (Van Nostrand Reinhold, New York, 1953).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.