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.

本研究通过修改标量量化器来实现分段量化，进而实现量化误差的指数衰减，并且证明了在量化器设计时无需先了解已知信号的模型，但是在重建时考虑已知信号的相似度，例如稀疏信号模型，这一融合方法可以显著降低量化误差，并且与信号模型的 Kolmogorov 熵之间存在一定的关联。