Luke, Russell

[["dc.bibliographiccitation.firstpage","11552"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","Optics Express"],["dc.bibliographiccitation.lastpage","11569"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Hagemann, Johannes"],["dc.contributor.author","Robisch, Anna-Lena"],["dc.contributor.author","Luke, D. R."],["dc.contributor.author","Homann, C."],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Cloetens, Peter"],["dc.contributor.author","Suhonen, H."],["dc.contributor.author","Salditt, Tim"],["dc.date.accessioned","2017-09-07T11:46:15Z"],["dc.date.available","2017-09-07T11:46:15Z"],["dc.date.issued","2014"],["dc.description.abstract","We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF). (C) 2014 Optical Society of America"],["dc.identifier.doi","10.1364/OE.22.011552"],["dc.identifier.fs","604845"],["dc.identifier.gro","3142122"],["dc.identifier.isi","000336957700017"],["dc.identifier.pmid","24921276"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/12635"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4789"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10 / Funder: [SFB 755]"],["dc.notes.intern","Merged from goescholar"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.issn","1094-4087"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.orgunit","Fakultät für Physik"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.relation.orgunit","Institut für Röntgenphysik"],["dc.relation.workinggroup","RG Salditt (Structure of Biomolecular Assemblies and X-Ray Physics)"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.subject.gro","x-ray imaging"],["dc.title","Reconstruction of wave front and object for inline holography from a set of detection planes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original_ja"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","576"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","SIAM Journal on Control and Optimization"],["dc.bibliographiccitation.lastpage","595"],["dc.bibliographiccitation.volume","42"],["dc.contributor.author","Burke, James V."],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:50:30Z"],["dc.date.available","2017-09-07T11:50:30Z"],["dc.date.issued","2003"],["dc.description.abstract","We apply nonsmooth analysis to a well-known optical inverse problem, phase retrieval. The phase retrieval problem arises in many different modalities of electromagnetic imaging and has been studied in the optics literature for over forty years. The state of the art for this problem in two dimensions involves iterated projections for solving a nonconvex feasibility problem. Despite widespread use of these algorithms, current mathematical theory cannot explain their success. At the heart of projection algorithms is a nonconvex, nonsmooth optimization problem. We obtain some insight into these algorithms by applying techniques from nonsmooth analysis. In particular, we show that the weak closure of the set of directions toward the projection generate the subdifferential of the corresponding squared set distance function. Following a pattern of proof described in [F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998], this result is generalized to provide conditions under which the subdifferential of an integral function equals the integral of the subdifferential."],["dc.identifier.doi","10.1137/s0363012902406436"],["dc.identifier.gro","3147608"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5084"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0363-0129"],["dc.title","Variational Analysis Applied to the Problem of Optical Phase Retrieval"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","701"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Set-Valued and Variational Analysis"],["dc.bibliographiccitation.lastpage","729"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Kruger, Alexander Y."],["dc.contributor.author","Luke, D. Russell"],["dc.contributor.author","Thao, Nguyen H."],["dc.date.accessioned","2020-12-10T14:11:55Z"],["dc.date.available","2020-12-10T14:11:55Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1007/s11228-017-0436-5"],["dc.identifier.eissn","1877-0541"],["dc.identifier.issn","1877-0533"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/71250"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.intern","DOI-Import GROB-394"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.title","About Subtransversality of Collections of Sets"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","PII S0036144501390754"],["dc.bibliographiccitation.firstpage","169"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","SIAM Review"],["dc.bibliographiccitation.lastpage","224"],["dc.bibliographiccitation.volume","44"],["dc.contributor.author","Luke, D. Russell"],["dc.contributor.author","Burke, James V."],["dc.contributor.author","Lyon, Richard G."],["dc.date.accessioned","2018-11-07T10:29:41Z"],["dc.date.available","2018-11-07T10:29:41Z"],["dc.date.issued","2002"],["dc.description.abstract","Optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in NASA's Hubble Space Telescope (HST). NASA's success with reconstruction algorithms on the HST has led to an effort to develop software that can aid and in some cases replace complicated, expensive, and error-prone hardware. Among the many applications is HST's replacement, the Next Generation Space Telescope (NGST). This work details the theory of optical wavefront reconstruction, reviews some numerical methods for this problem, and presents a novel numerical technique that we call extended least squares. We compare the performance of these numerical methods for potential inclusion in prototype NGST optical wavefront reconstruction software. We begin with a tutorial on Rayleigh-Sommerfeld diffraction theory."],["dc.identifier.doi","10.1137/S003614450139075"],["dc.identifier.gro","3146916"],["dc.identifier.isi","000175914100002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/43691"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Society for Industrial & Applied Mathematics (SIAM)"],["dc.relation.issn","0036-1445"],["dc.title","Optical wavefront reconstruction: Theory and numerical methods"],["dc.type","review"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","130"],["dc.bibliographiccitation.lastpage","150"],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:48:01Z"],["dc.date.available","2017-09-07T11:48:01Z"],["dc.date.issued","2000"],["dc.identifier.gro","3146836"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4641"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.eventend","2000-05-12"],["dc.relation.eventlocation","NASA/Goddard Space Flight Center"],["dc.relation.eventstart","2000-05-10"],["dc.relation.ispartof","'', in Proceedings of the Workshop on Computational Optics and Imaging for Space Applications"],["dc.title","Fast Algorithms for Phase Retrieval and Deconvolution"],["dc.type","conference_paper"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1283"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","SIAM Journal on Applied Mathematics"],["dc.bibliographiccitation.lastpage","1304"],["dc.bibliographiccitation.volume","70"],["dc.contributor.author","Arens, Tilo"],["dc.contributor.author","Lechleiter, Armin"],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:50:28Z"],["dc.date.available","2017-09-07T11:50:28Z"],["dc.date.issued","2009"],["dc.identifier.doi","10.1137/080737836"],["dc.identifier.gro","3147595"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/5999"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5076"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Society for Industrial & Applied Mathematics (SIAM)"],["dc.relation.issn","0036-1399"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","MUSIC for Extended Scatterers as an Instance of the Factorization Method"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","PII S0036139902406887"],["dc.bibliographiccitation.firstpage","1292"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","SIAM Journal on Applied Mathematics"],["dc.bibliographiccitation.lastpage","1312"],["dc.bibliographiccitation.volume","63"],["dc.contributor.author","Luke, D. Russell"],["dc.contributor.author","Potthast, Roland"],["dc.date.accessioned","2018-11-07T10:42:59Z"],["dc.date.available","2018-11-07T10:42:59Z"],["dc.date.issued","2003"],["dc.description.abstract","We describe a novel technique, which we call the no response test, to locate the support of a scatterer from knowledge of a far field pattern of a scattered acoustic wave. The method uses a set of sampling surfaces and a special test response to detect the support of a scatterer without a priori knowledge of the physical properties of the scatterer. Specifically, the method does not depend on information about whether the scatterer is penetrable or impenetrable nor does it depend on any knowledge of the nature of the scatterer (absorbing, reflecting, etc.). In contrast to previous sampling algorithms, the techniques described here enable one to locate obstacles or inhomogeneities from the far field pattern of only one incident field-the no response test is a one-wave method. We investigate the theoretical basis for the no response test and derive a one-wave uniqueness proof for a region containing the scatterer. We show how to find the object within this region. We demonstrate the applicability of the method by reconstructing sound-soft, sound-hard, impedance, and inhomogeneous medium scatterers in two dimensions from one wave with full and limited aperture far-field data."],["dc.identifier.doi","10.1137/S0036139902406887"],["dc.identifier.gro","3147610"],["dc.identifier.isi","000183528000009"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/46937"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Siam Publications"],["dc.relation.issn","0036-1399"],["dc.title","The no response test - A sampling method for inverse scattering problems"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","SIAG/OPT Views and News"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:48:01Z"],["dc.date.available","2017-09-07T11:48:01Z"],["dc.date.issued","2017"],["dc.identifier.gro","3146837"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4642"],["dc.notes.intern","Not valid abstract: Ask an engineer to solve a problem and she will come back in a day or so with something that seems to work well enough most of the time. Ask a mathematician to solve the same problem and he will return many months later with an exact but unimplementable solution to a di\\\\.erent problem. I'm sure most readers of this newsletter have heard some variation of that joke. But a true story lies somewhere in there, a story that is writ large with the phase retrieval problem."],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.title","Phase Retrieval, What's New?"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","485"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Foundations of Computational Mathematics"],["dc.bibliographiccitation.lastpage","513"],["dc.bibliographiccitation.volume","9"],["dc.contributor.author","Lewis, A. S."],["dc.contributor.author","Luke, Russell"],["dc.contributor.author","Malick, J."],["dc.date.accessioned","2017-09-07T11:48:35Z"],["dc.date.available","2017-09-07T11:48:35Z"],["dc.date.issued","2008"],["dc.identifier.doi","10.1007/s10208-008-9036-y"],["dc.identifier.gro","3146900"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4697"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Springer Nature"],["dc.relation.issn","1615-3375"],["dc.title","Local Linear Convergence for Alternating and Averaged Nonconvex Projections"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","426"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","SIAM Journal on Imaging Sciences"],["dc.bibliographiccitation.lastpage","457"],["dc.bibliographiccitation.volume","8"],["dc.contributor.author","Hesse, Robert"],["dc.contributor.author","Luke, Russell"],["dc.contributor.author","Sabach, Shoham"],["dc.contributor.author","Tam, Matthew K."],["dc.date.accessioned","2017-09-07T11:48:31Z"],["dc.date.available","2017-09-07T11:48:31Z"],["dc.date.issued","2015"],["dc.identifier.doi","10.1137/14098168x"],["dc.identifier.gro","3146887"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4692"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1936-4954"],["dc.title","Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]