  The phase retrieval from multi-frequency intensity (power) observations is
considered. The object to be reconstructed is complex-valued. A novel algorithm
is presented that accomplishes both the object phase (absolute phase) retrieval
and denoising for Poissonian and Gaussian measurements. The algorithm is
derived from the maximum likelihood formulation with Block Matching 3D (BM3D)
sparsity priors. These priors result in two filtering: one is in the complex
domain for complex-valued multi-frequency object images and another one in the
real domain for the object phase. The algorithm is iterative with alternating
projections between the object and measurement variables. The simulation
experiments are produced for Fourier transform image formation and random phase
modulations of the object, then the observations are random object diffraction
patterns. The results demonstrate the success of the algorithm for
reconstruction of the complex phase objects with the high-accuracy performance
even for very noisy data.
