Polynomial Procrustes Solution for Randomly Perturbed Near-Paraunitary Systems

We want to recover paraunitary matrices under small random perturbations. The polynomial Procrustes method, based on the analytic singular value decomposition of the perturbed system, in principle solves this. For small random perturbations, where the analytic singular values are close to unity, we propose a simplified polynomial Procrustes method that exploits this property, but show that the support of the solution is generally increased compared to the perturbed matrix. We therefore embed the simplified Procrustes method into an iterative truncation scheme, which can reduce the support while ensuring that a paraunitary approximation remains within a perimeter that is equivalent to the level of perturbation.