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InSAR phase analysis: Phase unwrapping for noisy SAR interferograms

Interferometric Synthetic Aperture Radar (InSAR) exploits the phase difference between two complex radar signals for extracting information about the earth surface. Some significant application fields concerned by InSAR techniques are Digital ElevationModel (DEM) generation (Graham, 1974), geophysical hazard analysis (Massonet & Feigl, 1998), desertification (Bodart et al., 2009), deforestation (Balzter, 2001), glacier velocity measurements (Mattar et al., 1998) and land use classification (Wegmullerl & Werner, 1997). They exploit the interferometric phase, which is proportional to the difference of the path lengths between the radar positions and a target on the earth surface (Gabriel & Goldstein, 1988), and the interferometric correlation (Abdelfattah & Nicolas, 2006), which depends on target characteristics (Abdelfattah & Nicolas, 2002). The phase of complex InSAR pair, called the interferogram, may be used in the reconstructing of high resolution terrain digital elevation models (DEM), in measuring earth displacement and many other topographic applications. However, before the reconstruction applications, the interferometric phase have to be unwrapped. the phase that is measured (observed) is only modulo 2π, the so called principal phase value or wrapped phase. Moreover, it is well known that the speckle effects in the InSAR data generate noise in the InSAR phase, which is also noisy due to various decorrelation effects (thermal noise, temporal, geometrical, etc.) between the two images used in the interferogram generation. The phase unwrapping consists in estimating the true regular phase profile (multiples of 2π must be added or substracted) from the observed interferogram, which is noisy and wrapped, to make the phase image as smooth as possible. Formally, we have for each pixel (i, j):