Technical Program

Paper Detail

Paper:	SPTM-P14.12
Session:	Sampling, Extrapolation and Interpolation II
Time:	Friday, May 19, 16:30 - 18:30
Presentation:	Poster
Topic:	Signal Processing Theory and Methods: Sampling, Extrapolation, and Interpolation
Title:	Random Filters for Compressive Sampling and Reconstruction
Authors:	Joel Tropp, University of Michigan, Ann Arbor, United States; Michael Wakin, Marco Duarte, Dror Baron, Richard Baraniuk, Rice University, United States
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 nonlinear 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.