Multi-Frequency Phase Retrieval from Noisy Data

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 in the complex domain for complex-valued multi-frequency object images and another one in the real domain for the object absolute 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 observations are random object diffraction patterns. The simulation results demonstrate the success of the algorithm for reconstruction of the complex phase objects with the high-accuracy performance even for a high dynamic range of the absolute phase and very noisy data.