Merging Point Data for InSAR Deformation Processing
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929339615936512 |
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| author | Calef, Matthew T. Olsen, Kelly M. Agram, Piyush S. |
| author_facet | Calef, Matthew T. Olsen, Kelly M. Agram, Piyush S. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Merging Point Data for InSAR Deformation Processing Calef, Matthew T. Olsen, Kelly M. Agram, Piyush S. Image and Video Processing 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). |
| title | Merging Point Data for InSAR Deformation Processing |
| topic | Image and Video Processing |
| url | https://arxiv.org/abs/2405.06838 |