A Randomized Multivariate Matrix Pencil Method for Superresolution Microscopy
For superresolution microscopy, this work offers a computationally efficient reconstruction algorithm, though it is an incremental improvement over existing matrix pencil methods.
The paper presents a randomized multivariate matrix pencil method for superresolution microscopy, achieving parameter identification of sparse exponential sums via simultaneous diagonalization reduced to a single random matrix eigendecomposition. The algorithm is validated on synthetic and experimental fluorescence microscopy data.
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.