2016
DOI: 10.1007/s00365-016-9344-4
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Distributed Noise-Shaping Quantization: I. Beta Duals of Finite Frames and Near-Optimal Quantization of Random Measurements

Abstract: This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements. The main contributions include the development of a general quantization framework called distributed noise-shaping, and in particular, beta duals of frames, as well as the performance analysis of beta duals in both deterministic and probabilistic settings. It is shown that for random frames, using beta duals result… Show more

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Cited by 26 publications
(45 citation statements)
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“…Moreover, if the frame satisfies certain smoothness conditions, the decay rate can be super-linear for first order Σ∆ quantization. Noise shaping schemes for finite frames have also been investigated, some of which yield exponential error decay rate [8,7,9]. In this section, we shall provide necessary information on quantization for finite frames before stating our results in Section 3.…”
Section: Preliminaries On Finite Frame Quantizationmentioning
confidence: 99%
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“…Moreover, if the frame satisfies certain smoothness conditions, the decay rate can be super-linear for first order Σ∆ quantization. Noise shaping schemes for finite frames have also been investigated, some of which yield exponential error decay rate [8,7,9]. In this section, we shall provide necessary information on quantization for finite frames before stating our results in Section 3.…”
Section: Preliminaries On Finite Frame Quantizationmentioning
confidence: 99%
“…Σ∆ quantization is a subclass of the more general noise shaping quantization, where the quantization scheme is designed such that the reconstruction error is easily separated from the true signal in the frequency domain. For instance, it is pointed out in [9] that the reconstruction error of Σ∆ quantization for bandlimited functions is concentrated in high frequency ranges. Since audio signals have finite bandwidth, it is then possible to separate the signal from the error using low-pass filters.…”
Section: 2mentioning
confidence: 99%
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