Reconstructing Analytic Dinosaurs: Polynomial Eigenvalue Decomposition for Eigenvalues with Unmajorised Ground Truth

This paper proposes a novel method for accurately estimating the ground truth analytic eigenvalues from estimated space-time covariance matrices, where the estimation process obscures any intersection of eigenvalues with probability one. The approach involves grouping sufficiently separated, bin-wise eigenvalues into segments that belong to analytic functions and then solves a permutation problem to align these segments. By leveraging an inverse partial discrete Fourier transform and a linear assignment algorithm, the proposed EigenBone method retrieves analytic eigenvalues efficiently and accurately. Experimental results demonstrate the effectiveness of this approach in accurately reconstructing eigenvalues from noisy estimates. Overall, the proposed method offers a robust solution for approximating analytic eigenvalues in scenarios where state-of-the-art methods may fail.