title: Undersampled Phase Retrieval with Outliers.
abstract: This paper proposes a general framework for reconstructing sparse images from undersampled (squared)-magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1D Monte Carlo tests and 2D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.
authors.affiliation: Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904 USA.
authors.forename: Daniel S
authors.initials: DS
authors.lastname: Weller
authors.affiliation: Electrical Engineering Department, Technion, Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Ayelet
authors.initials: A
authors.lastname: Pnueli
authors.affiliation: Electrical Engineering Department, Technion, Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Gilad
authors.initials: G
authors.lastname: Divon
authors.affiliation: Electrical Engineering Department, Technion, Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Ori
authors.initials: O
authors.lastname: Radzyner
authors.affiliation: Electrical Engineering Department, Technion, Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Yonina C
authors.initials: YC
authors.lastname: Eldar
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler
keywords: alternating direction method of multipliers; majorize-minimize; phase retrieval; sparsity