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Marc Honikel
measurements served as an approximation of the mean terrain shape, while details from the interferometric DEM were
added. In the other case, weights have been introduced to the fusion process, which indicated the local height error. In
both cases, the height error decreased significantly after the fusion.
The Wiener-based method, which is proposed in this paper, unifies these approaches, for the processing of
interferometric phase measurements. The data are fused by taking advantage from having a general approximation from
an independent data source and knowledge of the expected error of each measurement. With the great deal of
information available through the introduction of the simulated interferogram, the filter is realized by modeling the ideal
phase course and then fitting the model to the observation. It is intended to improve the interferometric height
determination process by restoration of the noise-corrupted interferometric phase measurements, thus easing the noise-
sensitive phase unwrapping process and taking full advantage of the InSAR height accuracy, which is theoretically
limited by the SAR wavelength (cm-scale!).
2 WIENER PHASE ESTIMATION
The-reduction of the phase noise is crucial for the correct determination of the multiple 2x, which has to be added to
each phase value during the unwrapping process. In presence of noise, phase jumps (residuals) can occur, which spoil
the implicit unwrapping assumption of a smooth terrain, with phase changes not higher than x between two adjacent
values. The unwrapping is bound to fail, if these measurements are not excluded from the procedure. Common
automated phase unwrapping techniques, e.g. using ghost-lines (Goldstein, 1988), are able to deal with this problem
only to a certain extent. Large regions of low SNR still lead either to failure of the DEM generation process, or, worse,
add a global error also to uncorrupted phase measurements, if unwrapped erroneously. Zebker (1994) gives an
evaluation of InSAR errors and topographic map accuracy for ERS-1.
Common approaches of noise reduction include multi-look image processing, averaging or interferogram filtering. All
these techniques have in common that they are hardly noise adaptive, thus affecting also valid measurements while
dealing with the noise. The phase reconstruction in regions, where the interferometric measurement fails (e.g. due to
layover) is generally not possible with these methods. The proposed method aims therefore at a restoration process,
which not only removes or reduces the noise, but also restores these regions, where the phase measurement previously
failed.
2.1 Interferometric phase restoration model
The following considerations relate to the general degradation and restoration model, given in Fig. 1, in which the
image vector f is subject to some unspecified type of degradation, which affects the image both spatially
(multiplicatively), resulting in a blurred image g, and pointwise (additively), resulting in an observation g.
Applied to the interferometric phase, degradation causes both, a local blurring of the fringe lines and adds to the local
noise. Especially blurring of the fringe lines endangers correct phase unwrapping, as the border between the phase
cycles is not determinable, resulting possibly in coarse unwrapping errors. Fig. 6 and 8 illustrate these effects, occurring
due to layover and temporal decorrelation.
Restoration
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Figure 1. Wiener estimation for spatial image restoration. Explanations are given in the text.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 149
