TY - GEN
T1 - Random filters for compressive sampling and reconstruction
AU - Tropp, Joel A.
AU - Wakin, Michael B.
AU - Duarte, Marco F.
AU - Baron, Dror
AU - Baraniuk, Richard G.
PY - 2006
Y1 - 2006
N2 - We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a non-linear Orthogonal Matching Pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like Compressed Sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes.
AB - We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a non-linear Orthogonal Matching Pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like Compressed Sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes.
UR - http://www.scopus.com/inward/record.url?scp=33947632909&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33947632909&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:33947632909
SN - 142440469X
SN - 9781424404698
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - III872-III875
BT - 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
T2 - 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
Y2 - 14 May 2006 through 19 May 2006
ER -