  Sparse modeling is one of the efficient techniques for imaging that allows
recovering lost information. In this paper, we present a novel iterative
phase-retrieval algorithm using a sparse representation of the object amplitude
and phase. The algorithm is derived in terms of a constrained maximum
likelihood, where the wave field reconstruction is performed using a number of
noisy intensity-only observations with a zero-mean additive Gaussian noise. The
developed algorithm enables the optimal solution for the object wave field
reconstruction. Our goal is an improvement of the reconstruction quality with
respect to the conventional algorithms. Sparse regularization results in
advanced reconstruction accuracy, and numerical simulations demonstrate
significant enhancement of imaging.
