A randomized multivariate matrix pencil method for superresolution microscopy. ETNA - Electronic Transactions on Numerical Analysis
Richter, Christian, Martin Ehler, Stefan Kunis, Thomas Peter · Oesterreichisches Musiklexikon online (Institut für kunst- und musikhistorische Forschungen der Österreichischen Akademie der Wissenschaften) · 2019
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.