Merging Point Data for InSAR Deformation Processing

Given a collection of points S ⊂ℝ^N, which is partitioned into M overlapping subsets {S_i}_i=1^M, and approximate data {D_i}_i=1^M associated with the subsets, one may seek a consistent merged dataset D that is derived from {S_i}_i=1^M and {D_i}_i=1^M. This note presents a method for constructing D under the assumption that D represents discrete samples of a suitably smooth function f:ℝ^N →ℝ evaluated at the points in S. The method has two steps. The first step uses a least-squares solve to approximate the constant offsets for each D_i. The second step uses a sequence of discrete Dirichlet problems to resolve any remaining differences. We include a two dimensional example of this method applied to deformation measurements derived from Interferometric Synthetic Aperture Radar (InSAR).