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Statistical compressive sensing of Gaussian mixture models

Publication ,  Journal Article
Yu, G; Sapiro, G
Published in: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
August 18, 2011

A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is introduced. For signals following a Gaussian distribution, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS, where N is the signal dimension, and with an optimal decoder implemented with linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the best k-term approximation with probability one, and the bound constant can be efficiently calculated. For signals following Gaussian mixture models, SCS with a piecewise linear decoder is introduced and shown to produce for real images better results than conventional CS based on sparse models. © 2011 IEEE.

Duke Scholars

Published In

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

DOI

ISSN

1520-6149

Publication Date

August 18, 2011

Start / End Page

3728 / 3731
 

Citation

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Yu, G., & Sapiro, G. (2011). Statistical compressive sensing of Gaussian mixture models. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 3728–3731. https://doi.org/10.1109/ICASSP.2011.5947161
Yu, G., and G. Sapiro. “Statistical compressive sensing of Gaussian mixture models.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, August 18, 2011, 3728–31. https://doi.org/10.1109/ICASSP.2011.5947161.
Yu G, Sapiro G. Statistical compressive sensing of Gaussian mixture models. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2011 Aug 18;3728–31.
Yu, G., and G. Sapiro. “Statistical compressive sensing of Gaussian mixture models.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Aug. 2011, pp. 3728–31. Scopus, doi:10.1109/ICASSP.2011.5947161.
Yu G, Sapiro G. Statistical compressive sensing of Gaussian mixture models. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2011 Aug 18;3728–3731.

Published In

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

DOI

ISSN

1520-6149

Publication Date

August 18, 2011

Start / End Page

3728 / 3731