  A novel formulation of the hyperspectral broadband phase retrieval is
developed for the scenario where both object and modulation phase masks are
spectrally varying. The proposed algorithm is based on a complex domain version
of the alternating direction method of multipliers (ADMM) and Spectral
Proximity Operators (SPO) derived for Gaussian and Poissonian observations.
Computations for these operators are reduced to the solution of sets of cubic
(for Gaussian) and quadratic (for Poissonian) algebraic equations. These
proximity operators resolve two problems. Firstly, the complex domain spectral
components of signals are extracted from the total intensity observations
calculated as sums of the signal spectral intensities. In this way, the
spectral analysis of the total intensities is achieved. Secondly, the noisy
observations are filtered, compromising noisy intensity observations and their
predicted counterparts. The ability to resolve the hyperspectral broadband
phase retrieval problem and to find the spectrum varying object are essentially
defined by the spectral properties of object and image formation operators. The
simulation tests demonstrate that the phase retrieval in this formulation can
be successfully resolved.
