Multiwavelength Absolute Phase Retrieval from Noisy Diffractive Patterns: Wavelength Multiplexing Algorithm

We study the problem of multiwavelength absolute phase retrieval from noisy diffraction patterns. The system is lensless with multiwavelength coherent input light beams and random phase masks applied for wavefront modulation. The light beams are formed by light sources radiating all wavelengths simultaneously. A sensor equipped by a Color Filter Array (CFA) is used for spectral measurement registration. The developed algorithm targeted on optimal phase retrieval from noisy observations is based on maximum likelihood technique. The algorithm is specified for Poissonian and Gaussian noise distributions. One of the key elements of the algorithm is an original sparse modeling of the multiwavelength complex-valued wavefronts based on the complex-domain block-matching 3D filtering. Presented numerical experiments are restricted to noisy Poissonian observations. They demonstrate that the developed algorithm leads to effective solutions explicitly using the sparsity for noise suppression and enabling accurate reconstruction of absolute phase of high-dynamic range