A nonconvex regularized approach for phase retrieval

Audrey Repetti (1) , Emilie Chouzenoux (1) , Jean-Christophe Pesquet (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

With the development of new imaging systems delivering large-size data sets, phase retrieval has become recently the focus of much attention. The problem is especially challenging due to its intrinsically nonconvex formulation. In addition, the applicability of many existing solutions may be limited either by their estimation performance or by their computational cost, especially in the case of non-Fourier measurements. In this paper, we propose a novel phase retrieval approach, which is based on a smooth nonconvex approximation of the standard data fidelity term. In addition, the proposed method allows us to employ a wide range of convex separable regularization functions. The optimization process is performed by a block coordinate proximal algorithm which is amenable to solving large-scale problems. An application of this algorithm to an image reconstruction problem shows that it may be very competitive with respect to state-of-the-art methods.

Keywords: Nonsmooth optimization; Proximal methods; Phase retrieval problem; Nonconvex optimization

Domains: Signal and Image processing

Audrey Repetti, Emilie Chouzenoux, Jean-Christophe Pesquet. A nonconvex regularized approach for phase retrieval. 21st IEEE International Conference on Image Processing (ICIP 2014), Oct 2014, Paris, France. ⟨hal-01094452⟩