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

Hubig, Michael and Suchandt, Steffen and Adam, Nico (2004) A class of solution-invariant transformations of cost functions for minimum cost flow phase unwrapping. Journal of the Optical Society of America A, 21 (10), pp. 1975-1987.

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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.

Document Type:Article
Additional Information: LIDO-Berichtsjahr=2004,
Title:A class of solution-invariant transformations of cost functions for minimum cost flow phase unwrapping
Authors:
AuthorsInstitution or Email of Authors
Hubig, MichaelUNSPECIFIED
Suchandt, SteffenUNSPECIFIED
Adam, NicoUNSPECIFIED
Date:2004
Journal or Publication Title:Journal of the Optical Society of America A
Refereed publication:Yes
In ISI Web of Science:Yes
Volume:21
Page Range:pp. 1975-1987
Status:Published
Keywords:Cost Functions, Minimum Cost Flow, MCF, Phase Unwrapping, SAR Interferometry
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W EO - Erdbeobachtung
DLR - Research area:Space
DLR - Program:W EO - Erdbeobachtung
DLR - Research theme (Project):UNSPECIFIED
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute
Deposited By: elib DLR-Beauftragter
Deposited On:26 Jan 2006
Last Modified:06 Jan 2010 22:28

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