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Ptychography has risen as a reference X-ray imaging technique: it achievesresolutions of one billionth of a meter, macroscopic field of view, or thecapability to retrieve chemical or magnetic contrast, among other features. Aptychographyic reconstruction is normally formulated as a blind phase retrievalproblem, where both the image (sample) and the probe (illumination) have to berecovered from phaseless measured data. In this article we address a nonlinearleast squares model for the blind ptychography problem with constraints on theimage and the probe by maximum likelihood estimation of the Poisson noisemodel. We formulate a variant model that incorporates the information ofphaseless measurements of the probe to eliminate possible artifacts. Next, wepropose a generalized alternating direction method of multipliers designed forthe proposed nonconvex models with convergence guarantee under mild conditions,where their subproblems can be solved by fast element-wise operations.Numerically, the proposed algorithm outperforms state-of-the-art algorithms inboth speed and image quality.

Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers