Publication: Imaging with highly incomplete and corrupted data
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Métodos Numéricos y Aplicaciones | es |
dc.affiliation.instituto | UC3M. Instituto Universitario sobre Modelización y Simulación en Fluidodinámica, Nanociencia y Matemática Industrial Gregorio Millán Barbany | es |
dc.contributor.author | Moscoso, Miguel | |
dc.contributor.author | Novikov, Alexei | |
dc.contributor.author | Papanicolau, George | |
dc.contributor.author | Tsogka, Chrysoula | |
dc.contributor.funder | Ministerio de Economía y Competitividad (España) | es |
dc.date.accessioned | 2021-04-27T08:08:43Z | |
dc.date.available | 2021-04-27T08:08:43Z | |
dc.date.issued | 2020-03 | |
dc.description.abstract | We consider the problem of imaging sparse scenes from a few noisy data using an L1-minimization approach. This problem can be cast as a linear system of the form Ap = b, where A is an N x K measurement matrix. We assume that the dimension of the unknown sparse vector p E Ck is much larger than the dimension of the data vector b E Cn, i.e. K >>N. We provide a theoretical framework that allows us to examine under what conditions the L1-minimization problem admits a solution that is close to the exact one in the presence of noise. Our analysis shows that L1-minimization is not robust for imaging with noisy data when high resolution is required. To improve the performance of L1-minimization we propose to solve instead the augmented linear system [A|C]p = b, where the N = Σ matrix C is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data, a vector of dimension N, can be well approximated. Theoretically, the dimension Σ of the noise collector should be eN which would make its use not practical. However, our numerical results illustrate that robust results in the presence of noise can be obtained with a large enough number of columns Σ~10K. | en |
dc.description.sponsorship | Part of this material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the authors were in residence at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, during the Fall 2017 semester. The work of M Moscoso was partially supported by Spanish MICINN grant FIS2016-77892-R. The work of A Novikov was partially supported by NSF grants DMS-1515187, DMS-1813943. The work of C Tsogka was partially supported by AFOSR FA9550-17-1-0238. | en |
dc.format.extent | 21 | |
dc.identifier.bibliographicCitation | Moscoso, M., Novikov, A., Papanicolaou, G. & Tsogka, C. (2020). Imaging with highly incomplete and corrupted data. Inverse Problems, 36(3), 035010. | en |
dc.identifier.doi | https://doi.org/10.1088/1361-6420/ab5a21 | |
dc.identifier.issn | 0266-5611 | |
dc.identifier.publicationfirstpage | 1 | |
dc.identifier.publicationissue | 3(035010) | |
dc.identifier.publicationlastpage | 21 | |
dc.identifier.publicationtitle | Inverse Problems | en |
dc.identifier.publicationvolume | 36 | |
dc.identifier.uri | https://hdl.handle.net/10016/32486 | |
dc.identifier.uxxi | AR/0000026263 | |
dc.language.iso | eng | |
dc.publisher | IOP Publishing | en |
dc.relation.projectID | Gobierno de España. FIS2016-77892-R | es |
dc.rights | © 2020 IOP Publishing Ltd. | en |
dc.rights.accessRights | open access | en |
dc.subject.eciencia | Materiales | es |
dc.subject.eciencia | Química | es |
dc.subject.other | Array imaging | en |
dc.subject.other | L1-norm minimization | en |
dc.subject.other | Highly corrupted data | en |
dc.title | Imaging with highly incomplete and corrupted data | en |
dc.type | research article | * |
dc.type.hasVersion | AM | * |
dspace.entity.type | Publication |
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