Sparse approximations of phase and amplitude for wave field reconstruction from noisy data

摘要

The topic of sparse representations (SR) of images has attracted tremendous interest from the research community in the last ten years. This interest stems from the fundamental role that the low dimensional models play in many signal and image processing areas, i.e., real world images can be well approximated by a linear combination of a small number of atoms (i.e., patches of images) taken from a large frame, often termed dictionary. The principal point is that these large dictionaries as well as the elements of these dictionaries taken for approximation are not known in advance and should be taken from given noisy observations. The sparse phase and amplitude reconstruction (SPAR) algorithm has been developed for monochromatic coherent wave field reconstruction, for phase-shifting interferometry and holography. In this paper the SPAR technique is extended to off-axis holography. Pragmatically, SPAR representations are result in design of efficient data-adaptive filters. We develop and study the algorithm where these filters are applied for denoising of phase and amplitude in object and sensor planes. This algorithm is iterative and developed as a maximum likelihood optimal solution provided that the noise in intensity measurements is Gaussian. The multiple simulation and real data experiments demonstrate the advance performance of the new technique.