Detection and estimation with compressive measurements
Author
Baraniuk, Richard G.; Davenport, Mark A.; Wakin, Michael B.
Date
2006-11-01Abstract
The recently introduced theory of compressed sensing enables the reconstruction 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 satisfactory measurement scheme.
This has inspired the design of physical systems that directly implement similar measurement
schemes. However, despite the intense focus on the reconstruction of signals, many (if not most)
signal processing problems do not require a full reconstruction of the signal { we are often
interested only in solving some sort of detection problem or in the estimation of some function
of the data. In this report, we show that the compressed sensing framework is useful for a
wide range of statistical inference tasks. In particular, we demonstrate how to solve a variety of
signal detection and estimation problems given the measurements without ever reconstructing
the signals themselves. We provide theoretical bounds along with experimental results.
Citation
Keyword
compressive sensing; detection; estimation
Type
Report
Related Work(s)
Rice University ECE Technical Report;TREE 0610Citable link to this page
https://hdl.handle.net/1911/21677Metadata
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