Solving ptychography with a convex relaxation
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.
© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Received 9 January 2015; Revised 7 April 2015; Accepted For Publication 27 April 2015; Published 27 May 2015. We thank Stephen Becker for useful suggestions regarding TFOCS, as well as Laura Waller, Lei Tian, Salman Asif and John Bruer for helpful discussions and feedback. RH, XO and CY acknowledge funding support from the National Institutes of Health (grant no. 1DP2OD007307-01) and The Caltech Innovation Initiative (CI2) internal grant program (grant no. 13520135). JAT gratefully acknowledges support from ONR award N00014-11-1002 and a Sloan Research Fellowship. Thanks are also due to the Moore Foundation.
Published - 1367-2630_17_5_053044.pdf
Submitted - 1412.1209v1.pdf
Supplemental Material - njp053044_suppdata.pdf