A RANDOMIZED MULTIVARIATE MATRIX PENCIL METHOD FOR SUPERRESOLUTION MICROSCOPY
| Autor(en): | Ehler, Martin Kunis, Stefan Peter, Thomas Richter, Christian |
Stichwörter: | exponential sum; EXPONENTIAL-SUMS; frequency analysis; Mathematics; Mathematics, Applied; moment problem; PARAMETER-ESTIMATION; PRONYS METHOD; spectral analysis; superresolution | Erscheinungsdatum: | 2019 | Herausgeber: | KENT STATE UNIVERSITY | Enthalten in: | ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | Band: | 51 | Startseite: | 63 | Seitenende: | 74 | Zusammenfassung: | The matrix pencil method is an eigenvalue-based approach for the parameter identification of sparse exponential sums. We derive a reconstruction algorithm for multivariate exponential sums that is based on simultaneous diagonalization. Randomization is used and quantified to reduce the simultaneous diagonalization to the eigendecomposition of a single random matrix. To verify feasibility, the algorithm is applied to synthetic and experimental fluorescence microscopy data. |
ISSN: | 10689613 | DOI: | 10.1553/etna_vol51s63 |
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