Luke, Russell

[["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.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"]]

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[["dc.bibliographiccitation.firstpage","1501"],["dc.bibliographiccitation.issue","13"],["dc.bibliographiccitation.journal","Mathematical Methods in the Applied Sciences"],["dc.bibliographiccitation.lastpage","1521"],["dc.bibliographiccitation.volume","29"],["dc.contributor.author","Luke, Russell"],["dc.contributor.author","Potthast, Roland"],["dc.date.accessioned","2017-09-07T11:50:10Z"],["dc.date.available","2017-09-07T11:50:10Z"],["dc.date.issued","2006"],["dc.description.abstract","Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time‐harmonic scattering, or nearly time‐harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non‐time‐harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time‐dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi‐frequency data."],["dc.identifier.doi","10.1002/mma.738"],["dc.identifier.gro","3147600"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5080"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0170-4214"],["dc.title","The point source method for inverse scattering in the time domain"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]