TY - JOUR
T1 - Signal processing with compressive measurements
AU - Davenport, Mark A.
AU - Boufounos, Petros T.
AU - Wakin, Michael B.
AU - Baraniuk, Richard G.
N1 - Funding Information:
Manuscript received February 28, 2009; revised November 12, 2009. Current version published March 17, 2010. The work of M. A. Davenport and R. G. Baraniuk was supported by the Grants NSF 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, ARO MURI W911NF-09-1-0383, and by the Texas Instruments Leadership University Program. The work of M. B. Wakin was supported by NSF Grants DMS-0603606 and CCF-0830320, and DARPA Grant HR0011-08-1-0078. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Rick Chartrand.
PY - 2010/4
Y1 - 2010/4
N2 - 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 problemssuch as detection, classification, or estimationand filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.
AB - 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 problemssuch as detection, classification, or estimationand filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.
KW - Compressive sensing (CS)
KW - Compressive signal processing
KW - Estimation
KW - Filtering
KW - Pattern classification
KW - Random projections
KW - Signal detection
KW - Universal measurements
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U2 - 10.1109/JSTSP.2009.2039178
DO - 10.1109/JSTSP.2009.2039178
M3 - Article
AN - SCOPUS:77949735239
SN - 1932-4553
VL - 4
SP - 445
EP - 460
JO - IEEE Journal on Selected Topics in Signal Processing
JF - IEEE Journal on Selected Topics in Signal Processing
IS - 2
M1 - 5419058
ER -