MAGPIE: Multilevel-Adaptive-Guided Solver for Ptychographic Phase Retrieval

We introduce MAGPIE (Multilevel-Adaptive-Guided Ptychographic Iterative Engine), a stochastic multigrid solver for the ptychographic phase-retrieval problem. The ptychographic phase-retrieval problem is inherently nonconvex and ill-posed. To address these challenges, we reformulate the original nonlinear and nonconvex inverse problem as the iterative minimization of a quadratic surrogate model that majorizes the original objective. This surrogate not only ensures favorable convergence properties but also generalizes the Ptychographic Iterative Engine (PIE) family of algorithms. By solving the surrogate model using a multigrid method, MAGPIE achieves substantial gains in convergence speed and reconstruction quality over traditional approaches.