TY - GEN

T1 - Reconstructing sparse signals from their zero crossings

AU - Boufounos, Petros T.

AU - Baraniuk, Richard G.

PY - 2008

Y1 - 2008

N2 - Classical sampling records the signal level at pre-determined time instances, usually uniformly spaced. An alternative implicit sampling model is to record the timing of pre-determined level crossings. Thus the signal dictates the sampling times but not the sampling levels. Logan's theorem provides sufficient conditions for a signal to be recoverable, within a scaling factor, from only the timing of its zero crossings. Unfortunately, recovery from noisy observations of the timings is not robust and usually fails to reproduce the original signal. To make the reconstruction robust this paper introduces the additional assumption that the signal is sparse in some basis. We reformulate the reconstruction problem as a minimization of a sparsity inducing cost function on the unit sphere and provide an algorithm to compute the solution. While the problem is not convex, simulation studies indicate that the algorithm converges in typical cases and produces the correct solution with very high probability.

AB - Classical sampling records the signal level at pre-determined time instances, usually uniformly spaced. An alternative implicit sampling model is to record the timing of pre-determined level crossings. Thus the signal dictates the sampling times but not the sampling levels. Logan's theorem provides sufficient conditions for a signal to be recoverable, within a scaling factor, from only the timing of its zero crossings. Unfortunately, recovery from noisy observations of the timings is not robust and usually fails to reproduce the original signal. To make the reconstruction robust this paper introduces the additional assumption that the signal is sparse in some basis. We reformulate the reconstruction problem as a minimization of a sparsity inducing cost function on the unit sphere and provide an algorithm to compute the solution. While the problem is not convex, simulation studies indicate that the algorithm converges in typical cases and produces the correct solution with very high probability.

KW - Implicit sampling

KW - Level-crossing problems

KW - Sparse reconstruction

UR - http://www.scopus.com/inward/record.url?scp=51449090819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51449090819&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2008.4518371

DO - 10.1109/ICASSP.2008.4518371

M3 - Conference contribution

AN - SCOPUS:51449090819

SN - 1424414849

SN - 9781424414840

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 3361

EP - 3364

BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP

T2 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP

Y2 - 31 March 2008 through 4 April 2008

ER -