CPRL: An Extension of Compressive Sensing to the Phase Retrieval Problem
2012 (English)In: Proceedings of the 26th Conference on Advances in Neural Information Processing Systems / [ed] P. Bartlett and F.C.N. Pereira and C.J.C. Burges and L. Bottou and K.Q. Weinberger, 2012, 1376-1384 p.Conference paper (Refereed)
While compressive sensing (CS) has been one of the most vibrant research fields in the past few years, most development only applies to linear models. This limits its application in many areas where CS could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique – CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation.
Place, publisher, year, edition, pages
2012. 1376-1384 p.
Phase retrieval, Compressive sensing, Compressive phase retrieval, X-ray crystallography, X-ray diffraction, Lifting, Sparse, Semidefinite programming
IdentifiersURN: urn:nbn:se:liu:diva-88925ISBN: 9781627480031OAI: oai:DiVA.org:liu-88925DiVA: diva2:606301
16th Conference on Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA, 3-6 December, 2012
FunderLinnaeus research environment CADICSEU, European Research Council, 267381