Merging Point Data for InSAR Deformation Processing

TL;DR

This paper introduces a method for merging overlapping point datasets representing smooth functions, demonstrated on InSAR deformation measurements, involving offset correction and Dirichlet problem solving.

Contribution

The paper presents a novel two-step approach combining least-squares offset correction and Dirichlet problems for merging point data in InSAR applications.

Findings

Effective offset correction via least-squares.

Successful resolution of remaining differences with Dirichlet problems.

Demonstrated on InSAR deformation data.

Abstract

Given a collection of points $S \subset \mathbb{R}^N$, 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 $f:\mathbb{R}^N \rightarrow \mathbb{R}$ 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).