DC Element | Wert | Sprache |
dc.contributor.author | Boufounos, Petros | |
dc.contributor.author | Kutyniok, Gitta | |
dc.contributor.author | Rauhut, Holger | |
dc.date.accessioned | 2021-12-23T16:14:02Z | - |
dc.date.available | 2021-12-23T16:14:02Z | - |
dc.date.issued | 2011 | |
dc.identifier.issn | 00189448 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/10870 | - |
dc.description.abstract | Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as compressed sensing (CS). Fusion frames are very rich new signal representation methods that use collections of subspaces instead of vectors to represent signals. This work combines these exciting fields to introduce a new sparsity model for fusion frames. Signals that are sparse under the new model can be compressively sampled and uniquely reconstructed in ways similar to sparse signals using standard CS. The combination provides a promising new set of mathematical tools and signal models useful in a variety of applications. With the new model, a sparse signal has energy in very few of the subspaces of the fusion frame, although it does not need to be sparse within each of the subspaces it occupies. This sparsity model is captured using a mixed l(1)/l(2) norm for fusion frames. A signal sparse in a fusion frame can be sampled using very few random projections and exactly reconstructed using a convex optimization that minimizes this mixed l(1)/l(2) norm. The provided sampling conditions generalize coherence and RIP conditions used in standard CS theory. It is demonstrated that they are sufficient to guarantee sparse recovery of any signal sparse in our model. Moreover, a probabilistic analysis is provided using a stochastic model on the sparse signal that shows that under very mild conditions the probability of recovery failure decays exponentially with increasing dimension of the subspaces. | |
dc.description.sponsorship | NSFNational Science Foundation (NSF) [CCF-0431150, CCF-0728867, CNS-0435425, CNS-0520280]; DARPA/ONRUnited States Department of DefenseDefense Advanced Research Projects Agency (DARPA)Office of Naval Research [N66001-08-1-2065, ONR N00014-07-1-0936, N00014-08-1-1067, N00014-08-1-1112, N00014-08-1-1066]; AFOSRUnited States Department of DefenseAir Force Office of Scientific Research (AFOSR) [FA9550-07-1-0301]; ARO MURIMURI [W311NF-07-1-0185]; Texas Instruments Leadership University; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [KU 1446/8, SPP-1324, KU 1446/13, KU 1446/14]; Hausdorff Center for Mathematics; WWTF [MA 07-004]; Mitsubishi Electric Research Laboratories (MERL); Department of Statistics at Stanford University; Department of Mathematics at Yale University; P. Boufounos was supported in part by NSF Grants CCF-0431150, CCF-0728867, CNS-0435425, and CNS-0520280, DARPA/ONR N66001-08-1-2065, ONR N00014-07-1-0936, N00014-08-1-1067, N00014-08-1-1112, and N00014-08-1-1066, AFOSR FA9550-07-1-0301, ARO MURI W311NF-07-1-0185, and in part by the Texas Instruments Leadership University Program. G. Kutyniok was supported in part by the Deutsche Forschungsgemeinschaft (DFG) Heisenberg Fellowship KU 1446/8, DFG Grant SPP-1324, KU 1446/13, and DFG Grant KU 1446/14. H. Rauhut was supported in part by the Hausdorff Center for Mathematics and by the WWTF project SPORTS (MA 07-004). This work was supported in part by Mitsubishi Electric Research Laboratories (MERL).; G. Kutyniok would like to thank Peter Casazza, David Donoho, and Ali Pezeshki for inspiring discussions on l<INF>1</INF> minimization and fusion frames. G. Kutyniok would also like to thank the Department of Statistics at Stanford University and the Department of Mathematics at Yale University for their hospitality and support during her visits. | |
dc.language.iso | en | |
dc.publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | |
dc.relation.ispartof | IEEE TRANSACTIONS ON INFORMATION THEORY | |
dc.subject | ALGORITHMS | |
dc.subject | AVERAGE-CASE ANALYSIS | |
dc.subject | Compressed sensing (CS) | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Information Systems | |
dc.subject | Engineering | |
dc.subject | Engineering, Electrical & Electronic | |
dc.subject | fusion frames | |
dc.subject | l(1)-minimization | |
dc.subject | l(1,2)-minimization | |
dc.subject | mutual coherence | |
dc.subject | random matrices | |
dc.subject | RECONSTRUCTION | |
dc.subject | REPRESENTATIONS | |
dc.subject | SIGNAL RECOVERY | |
dc.subject | sparse recovery | |
dc.title | Sparse Recovery From Combined Fusion Frame Measurements | |
dc.type | journal article | |
dc.identifier.doi | 10.1109/TIT.2011.2143890 | |
dc.identifier.isi | ISI:000291003900052 | |
dc.description.volume | 57 | |
dc.description.issue | 6 | |
dc.description.startpage | 3864 | |
dc.description.endpage | 3876 | |
dc.contributor.orcid | 0000-0003-4750-5092 | |
dc.contributor.orcid | 0000-0003-1369-0947 | |
dc.contributor.researcherid | A-6913-2018 | |
dc.contributor.researcherid | C-3602-2013 | |
dc.identifier.eissn | 15579654 | |
dc.publisher.place | 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA | |
dcterms.isPartOf.abbreviation | IEEE Trans. Inf. Theory | |
dcterms.oaStatus | Green Submitted | |