Convergent Alternating Minimization for Multislice Ptychographic Phase Retrieval and Its Acceleration via Forwad Correction and Extrapolation

Multislice ptychography (msPtycho) extends conventional two-dimensional ptychographic phase retrieval to thick or strongly scattering specimens by modeling the object as a stack of slices and accounting for multiple scattering. While this improves physical fidelity, existing reconstruction algorithms lack rigorous theoretical guarantees and often suffer from either slow convergence or high computational complexity. In this work, we propose a fast and theoretically grounded framework for msPtycho. We formulate a constrained optimization model that exploits the successive dependence of adjacent exit waves, reducing the multilinear coupling into a chain of bilinear relations. Building on this structure, we develop an alternating minimization of msPtycho (AM[Formula: see text]SP), which admits closed-form updates for all subproblems and is proven to converge globally to stationary points. To further enhance the performance for reconstructing deeply layered specimens, we introduce a forward-propagating correction to suppress error accumulation across slices and an extrapolation strategy to accelerate convergence. Together, these yield the accelerated AM[Formula: see text]SP-FX algorithm. Extensive numerical experiments demonstrate that the proposed methods achieve faster convergence and better reconstructions. Notably, AM[Formula: see text]SP-FX achieves superior reconstruction quality and consistently faster per-iteration runtimes than both layer-wise optimization and 3D Ptychographical Iterative Engine (3PIE); in particular, it requires an order of magnitude less time per iteration than 3PIE. Overall, the proposed framework offers a practical and theoretically sound solution for high-fidelity multislice ptychographic imaging.