Alternating projections with applications to Gerchberg-Saxton error reduction

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, $A \cap B = \emptyset$, 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.

optimization and control

Audience: researchers in the topic

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