Compressed Sensing with Binary Matrices: New Bounds on the Number of Measurements

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dc.contributor.VIAF27150194 (Vidyasagar, M)
dc.contributor.authorLotfi, Mahsa
dc.contributor.authorVidyasagar, Mathukumalli
dc.contributor.utdAuthorLotfi, Mahsa
dc.contributor.utdAuthorVidyasagar, Mathukumalli
dc.date.accessioned2020-03-24T15:57:27Z
dc.date.available2020-03-24T15:57:27Z
dc.date.issued2019-01-09
dc.descriptionDue to copyright restrictions and/or publisher's policy full text access from Treasures at UT Dallas is limited to current UTD affiliates (use the provided Link to Article).
dc.description.abstractIn this paper we study the problem of compressed sensing using binary measurement matrices. New bounds are derived for the number of measurements that suffice to achieve robust sparse recovery, and the number of measurements needed to achieve sparse recovery. In particular, by interpreting any binary measurement matrix as the biadjacency matrix of an unbalanced bipartite graph, we derive new lower bounds on the number of measurements required by any graph of girth six or larger, in order to satisfy a sufficient condition for sparse recovery. It is shown that the optimal choices for the girth of the graph associated with the measurement matrix are six and eight. Some interesting open problems that arise from our results are pointed out. The proofs of the results presented here are omitted. The reader is directed to (M. Lotfi and M. Vidyasagar, “Compressed sensing using binary matrices of nearly optimal dimensions,” arXiv:1808.03001, 2018) for stronger results than are presented here, as well as their proofs. © 2019 IEEE.
dc.description.departmentErik Jonsson School of Engineering and Computer Science
dc.identifier.bibliographicCitationLotfi, M., and M. Vidyasagar. 2019. "Compressed Sensing with Binary Matrices: New Bounds on the Number of Measurements." Indian Control Conference. 5th: 17-21, doi: 10.1109/INDIANCC.2019.8715630
dc.identifier.isbn9781538662465
dc.identifier.urihttp://dx.doi.org/10.1109/INDIANCC.2019.8715630
dc.identifier.urihttps://hdl.handle.net/10735.1/7454
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers Inc.
dc.relation.isPartOfIndian Control Conference, 5th
dc.rights©2019 IEEE
dc.subjectCompressed sensing (Telecommunication)
dc.subjectGraph theory
dc.subjectBinary matrices
dc.subjectMeasurements (Binary)
dc.subjectBipartite graphs
dc.subjectMatrices
dc.titleCompressed Sensing with Binary Matrices: New Bounds on the Number of Measurements
dc.type.genrearticle

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