- Adaptive scalar quantization without side
- A. Ortega and M. Vetterli
- IEEE Transactions on Image Processing, to appear, 1997
In this paper we introduce a novel technique for adaptive
scalar quantization. Adaptivity is useful in applications, including
image compression, where the statistics of the source are either not
known a priori or will change over time.
Our algorithm uses previously quantized
samples to estimate the distribution of the source and does
not require that side information be sent in order to adapt
to changing source statistics. Our quantization scheme is
thus backward adaptive. We propose that an adaptive
quantizer can be separated into two building blocks, namely,
model estimation and quantizer design. The model estimation
produces an estimate of the changing source probability
density function, which is then used to re-design the
quantizer using standard techniques.
We introduce non-parametric estimation techniques
that only assume smoothness of the input distribution.
We discuss the various sources of error in our estimation
and argue that for a wide class of sources with a smooth
pdf we provide a good approximation to a ``universal''
quantizer, with the approximation becoming better as
the rate increases.
We study the performance of our scheme and show how the
loss due to adaptivity is minimal in typical scenarios.
In particular, we provide examples and
show how our technique can achieve
SNRs within 0.05 dB of the optimal Lloyd-Max quantizer
for a memoryless source, while achieving over 1.5 dB gain
over a fixed quantizer for a bi-modal source.