title: Solving ptychography with a convex relaxation.
abstract: Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.
authors.affiliation: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Roarke
authors.initials: R
authors.lastname: Horstmeyer
authors.affiliation: Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Richard Y
authors.initials: RY
authors.lastname: Chen
authors.affiliation: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Xiaoze
authors.initials: X
authors.lastname: Ou
authors.affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA.
authors.forename: Brendan
authors.initials: B
authors.lastname: Ames
authors.affiliation: Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Joel A
authors.initials: JA
authors.lastname: Tropp
authors.affiliation: Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Changhuei
authors.initials: C
authors.lastname: Yang