A Randomized Multivariate Matrix Pencil Method for Superresolution Microscopy

TL;DR

This paper introduces a randomized multivariate matrix pencil method that enhances superresolution microscopy by efficiently reconstructing sparse exponential sums from microscopy data.

Contribution

It develops a novel randomized algorithm for multivariate exponential sum reconstruction using simultaneous diagonalization, reducing computational complexity.

Findings

Successfully applied to synthetic microscopy data

Effective in experimental fluorescence microscopy data

Reduces computational complexity of multivariate exponential sum reconstruction

Abstract

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.