Abstract
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.
Original language | English (US) |
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Title of host publication | 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings |
Volume | 3 |
State | Published - Dec 1 2006 |
Event | 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France Duration: May 14 2006 → May 19 2006 |
Other
Other | 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 |
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Country/Territory | France |
City | Toulouse |
Period | 5/14/06 → 5/19/06 |
ASJC Scopus subject areas
- Software
- Signal Processing
- Electrical and Electronic Engineering