ADMM and spectral proximity operators in hyperspectral broadband phase retrieval for quantitative phase imaging

The hyperspectral broadband phase retrieval is developed for a scenario where both object and modulation phase masks are spectrally varying. The proposed iterative algorithm is based on a complex domain version of the alternating direction method of multipliers (ADMM) and the novel Spectral Proximity Operators derived for Gaussian and Poissonian multiple intensity observations. These proximity operators solve two problems. First, the complex-domain spectral components of the object are extracted from the total intensity observations calculated as the sums of the spectral intensities of diffractive patterns. Second, noisy observations are filtered, compromising noisy intensity observations and their predicted counterparts. The simulation and physical tests confirm that the broadband hyperspectral phase retrieval in the proposed formulation can be successfully resolved.