Multigrid optimization for large-scale ptychographic phase retrieval.

*(English)*Zbl 07196102Summary: Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. In this work, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.

Reviewer: Reviewer (Berlin)

##### MSC:

65J22 | Numerical solution to inverse problems in abstract spaces |

90C06 | Large-scale problems in mathematical programming |

68U10 | Computing methodologies for image processing |

##### Keywords:

phase retrieval; multigrid optimization; inverse problems; ptychography; coherent diffraction imaging
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\textit{S. W. Fung} and \textit{Z. Di}, SIAM J. Imaging Sci. 13, No. 1, 214--233 (2020; Zbl 07196102)

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