The Split-Band Interferometry Approach to Determine the Phase Unwrapping Offset

Ludivine Libert1, Dominique Derauw1, Nicolas d’Oreye2,3, François Kervyn4, Anne Orban1 and Christian Barbier1

1Centre Spatial de Liège (CSL), Université de Liège, Avenue du Pré-Aily, 4031 Angleur, Belgium 2European Center for Geodynamics and Seismology, Rue Josy Welter 19, L-7256 Walferdange, Grand-Duchy of Luxembourg

3National Museum of Natural History, Rue de Munster 25, L-2160 Luxembourg, Grand-Duchy of Luxembourg 4Royal Museum of Central Africa, Leuvensesteenweg 13, 3080 Tervuren, Belgium

Contact email : llibert@ulg.ac.be

Split-BandInterferometry

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sensors to split it into subbands and produce several subrange images of a same scene, with lower resolution and shifted frequencies. In a first time, the same spectral decomposition is applied to both master and slave images of a given pair. Then interferometry is applied to the subrange images of the pair, yielding a stack of subrange interferograms. Finally, the linear phase trend is explored through the stack of interferograms in order to provide absolute phase measurements. The issued phase is called the split-band phase (Figure 1).

PhaseAmbigui:esConventional phase unwrapping algorithms for InSAR processing perform a relative measurement of the phase, i.e. the phase is reconstructed for each pixel with respect its neighbours. In practice, this causes distinct phase unwrapping of regions separated by noncoherent patches and it introduces unknown phase-offsets that prevent from comparing the phase from one region to another (Figure 2). Since SBInSAR is supposed to provide absolute phase measurements, it can potentially solve the phase ambiguities and reconnect the phase of separately unwrapped regions. In this study, we propose to use SBInSAR to assist the phase unwrapping and reconnect separately unwrapped areas. We consider the general case where the phase ambiguity is an unknown number of cycles 2πn, with nbeing an integer. This phase ambiguity has the same value for all the points through a given region of continuously unwrapped phase.

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Frequency-PersistentSca>erersTargets with a stable response across the spectral domain are called frequency-persistent scatterers (PSf). The spectral stability of a PSf ensures the linear behaviour of the phase with the frequency and therefore the accuracy of the split-band phase. Consequently, absolute and spatially independent measurements are possible using SBInSAR at these points only. We propose two criteria to select PSf assuming a one-cycle accuracy of the split-band phase: first, the standard deviation of the slope of the linear regression; second, the stability of the phase variance throughout the subrange interferograms.

In a first time, the SBInSAR-assisted phase unwrapping selects the PSf of a given region based on one criterion or the other. Then it computes the difference in cycles between the split-band phase and the unwrapped phase for each selected PSf. The value of the phase offset with the highest number of occurrences, i.e. the mode of the distribution, is assumed to be the correction that must be applied to the unwrapped area.

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SBInSAR-assisted phase unwrapping was tested on a pair of Spotlight images acquired by TerraSAR-X over Copahue Volcano on December 15 and 26, 2014. A spectral decomposition into 5 nonoverlapping subbands of 60 MHz was applied. In order to validate our results, we artificially disconnected regions of the unwrapped phase (Figure 3). This approach enables a validation based on the relative values of the phase-offsets.

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When applied to the test case, the method provides the expected phase ambiguities for the artificially disconnected areas, whatever the selection criterion. However, the distribution shows less dispersion when the phase variance stability is used (Figure 4). Moreover, the procedure has been tested on both artificially and naturally disconnected areas and we observed that the percentage of PSf contributing to the mode of the distribution stabilizes around 25-35% when the region contains more than 30 PSf. This amount is considered to be the minimum number of PSf to have a statisticallly significant population (Figure 5).

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This work was carried out in the framework of the MUZUBI project financed by Belgian Science Policy Contract NR SR/00/324. This work was carried out in the framework of the MUZUBI project financed by Belgian Science Policy Contract NR SR/00/324.

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