Lensless hyperspectral phase retrieval via alternating direction method of multipliers and spectral proximity operators.

We propose a hyperspectral broadband phase retrieval technique with spectrally varying object and modulation phase masks. The technique is based on a complex domain version of the alternating direction method of multipliers (ADMM) and the Spectral Proximity Operators derived for Gaussian and Poisson intensity observations, which are considered as a sum of separate spectral diffractive patterns. The proximity operators filter noisy observations compromising between noisy intensity observations and their predicted counterparts and retrieve the complex-domain spectral components of the object from these filtered observations. The simulation and physical tests confirm that the broadband hyperspectral phase retrieval in the proposed formulation is resolved.