Phase retrieval from incomplete data via weighted nuclear norm minimization

Recovering an unknown object from the magnitude of its Fourier transform is a phase retrieval problem. Here, we consider much difficult case, where those observed intensity values are incomplete and contaminated by both salt-and-pepper random-valued impulse noise. To take advantage low-rank property within image object, use regularization term which penalizes high weighted nuclear norm patch groups. For outliers (impulse noise) in observation, ?1?2 metric adopted as data fidelity term. Then break down resulting optimization problem into smaller ones, for example, proximal mapping minimization, because nonconvex nonsmooth subproblems have available closed-form solutions. The convergence results also presented, numerical experiments provided to demonstrate superior reconstruction quality proposed method.