On Optimal Multi-Resolution Scalar Quantization

Any scalar quantizer of $2^{h}$ bins, where $h$ is a positive integer, can be structured by a balanced binary quantizer tree $T$ of $h$ levels. Any pruned subtree $\tau$ of $T$ corresponds to an operational rate $R(\tau)$ and distortion $D(\tau)$ pair. Denote by $S_{n}$ the set of all pruned subtrees of n leaf nodes, $1\leq n\leq 2^{h}$. We consider the problem of designing a $2^{h}$-bin scalar quantizer that minimizes the weighted average …