Team for Research in
Ubiquitous Secure Technology

Citation
Galen Reeves, Michael Gastpar. "Differences between Observation and Sampling Error in Sparse Signal Reconstruction". IEEE 2007 Statistical ignal Processing Workshop, August, 2007.

Abstract
The field of Compressed Sensing has shown that a relatively small number of random projections provide sufficient information to accurately reconstruct sparse signals. Inspired by applications in sensor networks in which each sensor is likely to observe a noisy version of a sparse signal and subsequently add sampling error through computation and communication, we investigate how the distortion differs depending on whether noise is introduced before sampling (observation error) or after sampling (sampling error). We analyze the optimal linear estimator (for known support) and an $\ell_1$ constrained linear inverse (for unknown support). In both cases, observation noise is shown to be less detrimental than sampling noise and low sampling rates. We also provide sampling bounds for a non-stochastic $\ell_\infty$ bounded noise model.

Electronic downloads

• ssp07-final.pdf · application/pdf · 143 kbytes

• HTML

  Galen Reeves, Michael Gastpar. <a
  href="http://www.truststc.org/pubs/278.html"
  >Differences between Observation and Sampling Error in
  Sparse Signal Reconstruction</a>, IEEE 2007
  Statistical ignal Processing Workshop, August, 2007.

• Plain text

  Galen Reeves, Michael Gastpar. "Differences between
  Observation and Sampling Error in Sparse Signal
  Reconstruction". IEEE 2007 Statistical ignal Processing
  Workshop, August, 2007.

• BibTeX

  @inproceedings{ReevesGastpar07_DifferencesBetweenObservationSamplingErrorInSparseSignal,
      author = {Galen Reeves and Michael Gastpar},
      title = {Differences between Observation and Sampling Error
                in Sparse Signal Reconstruction},
      booktitle = {IEEE 2007 Statistical ignal Processing Workshop},
      month = {August},
      year = {2007},
      abstract = {The field of Compressed Sensing has shown that a
                relatively small number of random projections
                provide sufficient information to accurately
                reconstruct sparse signals. Inspired by
                applications in sensor networks in which each
                sensor is likely to observe a noisy version of a
                sparse signal and subsequently add sampling error
                through computation and communication, we
                investigate how the distortion differs depending
                on whether noise is introduced before sampling
                (observation error) or after sampling (sampling
                error). We analyze the optimal linear estimator
                (for known support) and an $\ell_1$ constrained
                linear inverse (for unknown support). In both
                cases, observation noise is shown to be less
                detrimental than sampling noise and low sampling
                rates. We also provide sampling bounds for a
                non-stochastic $\ell_\infty$ bounded noise model.},
      URL = {http://www.truststc.org/pubs/278.html}
  }
  

Posted by Galen Reeves on 2 Aug 2007.
For additional information, see the Publications FAQ or contact webmaster at www truststc org.