Journal
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
Volume 4, Issue 2, Pages 445-460Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JSTSP.2009.2039178
Keywords
Compressive sensing (CS); compressive signal processing; estimation; filtering; pattern classification; random projections; signal detection; universal measurements
Categories
Funding
- NSF [CCF-0431150, CCF-0728867, CNS-0435425, CNS-0520280, HR0011-08-1-0078]
- DARPA/ONR [N66001-08-1-2065]
- ONR [N00014-07-1-0936, N00014-08-1-1067, N00014-08-1-1112, N00014-08-1-1066]
- AFOSR [FA9550-07-1-0301]
- ARO MURI [W311NF-07-10185, W911NF-09-1-0383]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [0830320] Funding Source: National Science Foundation
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The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.
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