TY - GEN
T1 - Sobolev duals of random frames
AU - Güntürk, C. Sinan
AU - Lammers, Mark
AU - Powell, Alex
AU - Saab, Rayan
AU - Yilmaz, Özgür
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1109/CISS.2010.5464811
DO - 10.1109/CISS.2010.5464811
M3 - Conference contribution
AN - SCOPUS:77953714893
SN - 9781424474172
T3 - 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
BT - 2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
T2 - 44th Annual Conference on Information Sciences and Systems, CISS 2010
Y2 - 17 March 2010 through 19 March 2010
ER -