  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.
