Title: Alternating projections with applications to Gerchberg-Saxton error reduction

Speaker: Dominikus Noll (Institut de Mathématiques de Toulouse)

Date and Time: Wed Oct 6, 17:00 AEST (Register here for remote connection via Zoom)

Abstract:

We discuss alternating projections between closed non-convex sets A, B in R^n and obtain criteria for convergence when A, B do not intersect transversally. The infeasible case, A∩B=∅, is also addressed, and here we expect convergence toward a gap between A, B. For sub-analytic sets A, B sub-linear convergence rates depending on the Lojasiewicz exponent of the distance function can be computed. We then present applications to the Gerchberg-Saxton error reduction algorithm, to Cadzow’s denoising algorithm, and to instances of the Gaussian EM-algorithm.