Two-Dimensional Phase Unwrapping using Mixed Mathematical Arts (MMA)

Abstract:

The 2D phase unwrapping problem is long standing in interferometric SAR. Solutions fall in two broad classes: local (region growing) and global (eg. network methods) which attempt to unwrap the whole scene as one problem.

Large scenes are often split into tiles with overlap. Each tile is unwrapped by itself and the overlap is used to create a solution for the whole scene. Challenging topography, complex coastline, and vegetated or snow covered landscapes can cause problems with disconnected regions in a tiled approach, both for local and global methods. We have implemented a local/global method for unwrapping large interferograms on a sparse domain. The fundamental idea is to

1. use a local, quality-driven method to identify well-connected segments;
2. use global methods (e.g. MCF) to unwrap each segment in isolation;
3. use a global method to balance the segments to arrive at the global solution.

The first two stages have been described previously. The number of segments in a scene varies with scene size and quality, but there will typically be several thousand pixels in the larger segments. Segment size is limited to 20-50 thousand to keep segment unwrapping tractable. The crucial final stage is performed using segment balancing with a novel method which does not rely on direct pixel-neighbour contact.

Since each segment is itself unwrapped, the remaining problem is to determine a small integer (the difference in absolute wrapping number) for every relevant pair of segments. Each segment tends to have less than ten neighbours, so the number of neighbour relations to be determined is in the low thousands for typical scenes. Good guesses can be made for each of these small integers using boundary or vicinity pixels. Balancing segments for the entire scene is therefore computationally tractable.

The quality-guided segmentation always leaves some pixels unsegmented. After balancing, a novel wrapping interval interpolation method is used to extend the solution to the remainder of the scene. This gives a smooth and pleasing impression, while preserving the property that the unwrapped scene will wrap back to the original phase field.