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arXiv · 2405.06838

Merging Point Data for InSAR Deformation Processing

Matthew T. Calef·Kelly M. Olsen·Piyush S. Agram
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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).

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Matthew T. Calef, Kelly M. Olsen, Piyush S. Agram. 2024-05-10. Merging Point Data for InSAR Deformation Processing. https://arxiv.org/abs/2405.06838

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