A randomized multivariate matrix pencil method for superresolution microscopy

[摘要] 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.

[学科分类] 数学（综合）

[关键词] frequency analysis;spectral analysis;exponential sum;moment problem;superresolution