Hierarchical Distributed Scalar Quantization

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. Recent theoretical work has provided some insights on improving this trade-off, using nonmonotonic quantization functions. This paper builds upon this work to provide a practical hierarchical quantization scheme that enables efficient reconstruction through a hierarchy of convex optimization problems. Our approach generalizes the bit hierarchy—most to least significant bit—of classical multi-bit scalar quantization. We demonstrate experimental results both for dense and sparse signals that demonstrate significant gains and confirm our theoretical analysis. Keywords— scalar quantization, randomization, oversampling, robustness