2019/11/29 by Eitan Levin, Levin, Eitan, Tamir Bendory +1 · 1 citation
Engineering · #FOS: Computer and information sciences #FOS: Electrical engineering #Hydrocarbon exploration and reservoir analysis #Information Theory (cs.IT) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.13179
openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can be interpreted as variants of Douglas-Rachford splitting. In this work, we establish a connection between Douglas-Rachford and gradient algorithms. Specifically, we show that in some cases a generalization of Douglas-Rachford, called relaxed-reflect-reflect (RRR), can be viewed as gradient descent on a certain objective function. The solutions coincide with the critical points of that objective, which---in contrast to standard gradient techniques---are not its minimizers. Using the objective function, we give simple proofs of some basic properties of the RRR algorithm. Specifically, we describe its set of solutions, show a local convexity around any solution, and derive stability guarantees. Nevertheless, in its present state, the analysis does not elucidate the remarkable empirical performance of RRR and its global properties.