Sobolev duals of random frames

C. Sinan Gunturk, Mark Lammers, Alex Powell, Rayan Saab, Özgür Yilmaz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Sobolev dual frames have recently been proposed as optimal alternative reconstruction operators that are specifically tailored for Sigma-Delta (ΣΔ) quantization of frame coefficients. While the canonical dual frame of a given analysis (sampling) frame is optimal for the white-noise type quantization error of Pulse Code Modulation (PCM), the Sobolev dual offers significant reduction of the reconstruction error for the colored-noise of ΣΔ quantization. However, initial quantitative results concerning the use of Sobolev dual frames required certain regularity assumptions on the given analysis frame in order to deduce improvements of performance on reconstruction that are similar to those achieved in the standard setting of bandlimited functions. In this paper, we show that these regularity assumptions can be lifted for (Gaussian) random frames with high probability on the choice of the analysis frame. Our results are immediately applicable in the traditional oversampled (coarse) quantization scenario, but also extend to compressive sampling of sparse signals.

Original languageEnglish (US)
Title of host publication2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
DOIs
StatePublished - 2010
Event44th Annual Conference on Information Sciences and Systems, CISS 2010 - Princeton, NJ, United States
Duration: Mar 17 2010Mar 19 2010

Other

Other44th Annual Conference on Information Sciences and Systems, CISS 2010
CountryUnited States
CityPrinceton, NJ
Period3/17/103/19/10

Fingerprint

Sampling
Pulse code modulation
White noise
Quantization
Regularity

ASJC Scopus subject areas

  • Information Systems
  • Information Systems and Management

Cite this

Gunturk, C. S., Lammers, M., Powell, A., Saab, R., & Yilmaz, Ö. (2010). Sobolev duals of random frames. In 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010 [5464811] https://doi.org/10.1109/CISS.2010.5464811

Sobolev duals of random frames. / Gunturk, C. Sinan; Lammers, Mark; Powell, Alex; Saab, Rayan; Yilmaz, Özgür.

2010 44th Annual Conference on Information Sciences and Systems, CISS 2010. 2010. 5464811.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gunturk, CS, Lammers, M, Powell, A, Saab, R & Yilmaz, Ö 2010, Sobolev duals of random frames. in 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010., 5464811, 44th Annual Conference on Information Sciences and Systems, CISS 2010, Princeton, NJ, United States, 3/17/10. https://doi.org/10.1109/CISS.2010.5464811
Gunturk CS, Lammers M, Powell A, Saab R, Yilmaz Ö. Sobolev duals of random frames. In 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010. 2010. 5464811 https://doi.org/10.1109/CISS.2010.5464811
Gunturk, C. Sinan ; Lammers, Mark ; Powell, Alex ; Saab, Rayan ; Yilmaz, Özgür. / Sobolev duals of random frames. 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010. 2010.
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