SAR interferometry: a novel method for enhancing elevation maps by combining interferometry with shape-from-shading

The classical method for computing a digital elevation map from a pair of synthetic aperture radar (SAR) images is well known. Height estimates based on theoretical considerations have been compared to empirical height estimates and although the estimates are often consistent, it happens on occasion that they differ by a wide margin. The reasons for this discrepancy are often either temporal decorrelation or spatial decorrelation. Spatial decorrelation occurs when the two SAR collects are not properly aligned in space to ensure that the Nyquist criterion is satisfied. That is, the baseline between the two collects is too large. If the baseline is indeed too long, then standard SAR interferometry will not be useful in generation of a digital elevation map. The second major source of elevation error is temporal decorrelation. This occurs when the terrain being imaged has changed between the collection of the first SAR image and the collection of the second SAR image. Temporal decorrelation can happen if, for instance, snow falls on the day of the second collection. Clearly in this case all phase information is destroyed. In shape-from-shading (SFS) the goal is to reconstruct height information from its two-dimensional intensity image. This paper presents a method for computing a digital elevation map by combining the principles of interferometric processing with the procedure of SFS. A novel improvement to the SFS algorithm is presented, and it is shown that SFS provides a valid estimate for the phase gradient in those areas of the image where the phase has been destroyed by temporal decorrelation. An outline of the algorithm is presented, as well as, simulation results showing the improvement in elevation accuracy that is possible with the new algorithm.