A new algorithmic framework is developed for holographic coherent diffraction imaging (HCDI) based on maximum likelihood estimation (MLE). This method provides superior image reconstruction results for various practical HCDI settings, such as when data is highly corrupted by Poisson shot noise and when low-frequency data is missing due to occlusion from a beamstop apparatus. This method is also highly robust in that it can be implemented using a variety of standard numerical optimization algorithms, and requires fewer constraints on the physical HCDI setup compared to current algorithms. The mathematical framework developed using MLE is also applicable beyond HCDI to any holographic imaging setup where data is corrupted by Poisson shot noise.
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