Covariance Fitting Interferometric Phase Linking: Modular Framework and Optimization Algorithms
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910365979246592 |
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| author | Vu, Phan Viet Hoa Breloy, Arnaud Brigui, Frédéric Yan, Yajing Ginolhac, Guillaume |
| author_facet | Vu, Phan Viet Hoa Breloy, Arnaud Brigui, Frédéric Yan, Yajing Ginolhac, Guillaume |
| contents | Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scaterrers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all pairs of SAR images in a time series from the sample covariance matrix of pixel patches on a sliding window. This paper reformulates this task as a covariance fitting problem: in this setup, IPL appears as a form of projection of an input covariance matrix so that it satisfies the phase closure property. Given this modular formulation, we propose an overview of covariance matrix estimates, regularization options, and matrix distances, that can be of interest when processing multi-temporal SAR data. In particular, we will observe that most of the existing IPL algorithms appear as special instances of this framework. We then present tools to efficiently solve related optimization problems on the torus of phase-only complex vectors: majorization-minimization and Riemannian optimization. We conclude by illustrating the merits of different options on a real-world case study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Covariance Fitting Interferometric Phase Linking: Modular Framework and Optimization Algorithms Vu, Phan Viet Hoa Breloy, Arnaud Brigui, Frédéric Yan, Yajing Ginolhac, Guillaume Applications Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scaterrers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all pairs of SAR images in a time series from the sample covariance matrix of pixel patches on a sliding window. This paper reformulates this task as a covariance fitting problem: in this setup, IPL appears as a form of projection of an input covariance matrix so that it satisfies the phase closure property. Given this modular formulation, we propose an overview of covariance matrix estimates, regularization options, and matrix distances, that can be of interest when processing multi-temporal SAR data. In particular, we will observe that most of the existing IPL algorithms appear as special instances of this framework. We then present tools to efficiently solve related optimization problems on the torus of phase-only complex vectors: majorization-minimization and Riemannian optimization. We conclude by illustrating the merits of different options on a real-world case study. |
| title | Covariance Fitting Interferometric Phase Linking: Modular Framework and Optimization Algorithms |
| topic | Applications |
| url | https://arxiv.org/abs/2403.08646 |