Volume 51, pp. 63-74, 2019.

A randomized multivariate matrix pencil method for superresolution microscopy

Martin Ehler, Stefan Kunis, Thomas Peter, and Christian Richter


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.

Full Text (PDF) [2.2 MB], BibTeX

Key words

frequency analysis, spectral analysis, exponential sum, moment problem, superresolution

AMS subject classifications

65T40, 42C15, 30E05, 65F30

Links to the cited ETNA articles

[19]Vol. 40 (2013), pp. 204-224 Daniel Potts and Manfred Tasche: Parameter estimation for multivariate exponential sums

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