通用速率高效标量Quantization
Universal Rate-Efficient Scalar Quantization
摘要：
纯量量化是最实用、最直接的信号量化方法。然而，已经表明，过采样或压缩感知信号的标量量化在速率-失真权衡方面可能是低效的，特别是当信号的过采样率或稀疏度增加时。在本文中，我们修改标量量化器有不连续的量化区域。我们证明，通过这种修改，可以实现指数衰减的量化误差作为过采样率的函数，而不是目前的方法所表现出的二次衰减。我们的方法是通用的，在这个意义上说，先验知识的信号模型是不必要的量化器的设计，只有在重建。因此，我们证明，它是可能的，以减少量化误差，通过将边信息的采集信号，如稀疏信号模型或信号相似性与已知信号。在这样做时，我们建立了量化性能和信号模型的Kolmogorov熵之间的关系。
英文摘要：
Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the rate-distortion trade-off, especially as the oversampling rate or the sparsity of the signal increases. In this paper, we modify the scalar quantizer to have discontinuous quantization regions. We demonstrate that with this modification it is possible to achieve exponential decay of the quantization error as a function of the oversampling rate instead of the quadratic decay exhibited by current approaches. Our approach is universal in the sense that prior knowledge of the signal model is not necessary in the quantizer design, only in the reconstruction. Thus, we demonstrate that it is possible to reduce the quantization error by incorporating side information on the acquired signal, such as sparse signal models or signal similarity with known signals. In doing so, we establish a relationship between quantization performance and the Kolmogorov entropy of the signal model.
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