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A randomized multivariate matrix pencil method for superresolution microscopy. (English) Zbl 1436.65219

Summary: 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.

MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
15A22 Matrix pencils
42C15 General harmonic expansions, frames
65Z05 Applications to the sciences
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