We present eMAGPIE (extended Multilevel-Adaptive-Guided Ptychographic Iterative Engine), a stochastic multigrid method for blind ptychographic phase retrieval that jointly recovers the object and the probe. We recast the task as the iterative minimization of a quadratic surrogate that majorizes the exit-wave misfit. From this surrogate, we derive closed-form updates, combined in a geometric-mean, phase-aligned joint step, yielding a simultaneous update of the object and probe with guaranteed descent of the sampled surrogate. This formulation naturally admits a multigrid acceleration that speeds up convergence. In experiments, eMAGPIE attains lower data misfit and phase error at comparable compute budgets and produces smoother, artifact-reduced phase reconstructions.

翻译：本文提出eMAGPIE（扩展多级自适应引导叠层衍射迭代引擎），一种用于盲式叠层衍射相位恢复的随机多重网格方法，可联合重建样品与探针波函数。我们将该任务重新表述为对出射波失配函数进行二次代理函数迭代最小化，该代理函数始终主导原目标函数。基于此代理函数，我们推导出闭式更新公式，结合几何平均与相位对齐的联合步骤，实现了样品与探针的同步更新，并保证采样代理函数的严格下降。该公式天然支持多重网格加速机制以提升收敛速度。实验表明，在相同计算资源下，eMAGPIE能获得更低的数据失配度与相位误差，并生成更平滑、伪影更少的相位重建结果。