Linearization-based direct reconstruction for EIT using triangular Zernike decompositions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918341444108288 |
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| author | Autio, Antti Garde, Henrik Hirvensalo, Markus Hyvönen, Nuutti |
| author_facet | Autio, Antti Garde, Henrik Hirvensalo, Markus Hyvönen, Nuutti |
| contents | This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was originally designed for a linearized setting, we numerically demonstrate its functionality when the input data is the corresponding change in the current-to-voltage boundary operator. Both idealized continuum model and practical complete electrode model measurements are considered in the numerical studies, with the examined domain being either the unit disk or a convex polygon. Special attention is paid to regularizing the algorithm and its connections to the singular value decomposition of a truncated linearized forward map, as well as to the explicit triangular structures originating from the properties of the employed Zernike polynomial basis for the conductivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linearization-based direct reconstruction for EIT using triangular Zernike decompositions Autio, Antti Garde, Henrik Hirvensalo, Markus Hyvönen, Nuutti Numerical Analysis 65N21, 65N20, 35R30, 35R25 This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was originally designed for a linearized setting, we numerically demonstrate its functionality when the input data is the corresponding change in the current-to-voltage boundary operator. Both idealized continuum model and practical complete electrode model measurements are considered in the numerical studies, with the examined domain being either the unit disk or a convex polygon. Special attention is paid to regularizing the algorithm and its connections to the singular value decomposition of a truncated linearized forward map, as well as to the explicit triangular structures originating from the properties of the employed Zernike polynomial basis for the conductivity. |
| title | Linearization-based direct reconstruction for EIT using triangular Zernike decompositions |
| topic | Numerical Analysis 65N21, 65N20, 35R30, 35R25 |
| url | https://arxiv.org/abs/2403.03320 |