Databases Reference
In-Depth Information
F I GU R E 9 . 15
Sena image quantized to 3.25 bits per pixel using forward adaptive
quantization.
9.5.2 Backward Adaptive Quantization
In backward adaptive quantization, only the past quantized samples are available for use in
adapting the quantizer. The values of the input are only known to the encoder; therefore,
this information cannot be used to adapt the quantizer. How can we get information about
mismatch simply by examining the output of the quantizer without knowing what the input
was? If we studied the output of the quantizer for a long period of time, we could get some
idea about mismatch from the distribution of output values. If the quantizer step size
is well
matched to the input, the probability that an input to the quantizer would land in a particular
interval would be consistent with the
pdf
assumed for the input. However, if the actual
pdf
differs from the assumed
pdf
, the number of times the input falls in the different quantization
intervals will be inconsistent with the assumed
pdf
.If
is smaller than what it should be, the
input will fall in the outer levels of the quantizer an excessive number of times. On the other
hand, if
is larger than it should be for a particular source, the input will fall in the inner
levels an excessive number of times. Therefore, it seems that we should observe the output of
the quantizer for a long period of time, then expand the quantizer step size if the input falls in
the outer levels an excessive number of times, and contract the step size if the input falls in the
inner levels an excessive number of times.
Nuggehally S. Jayant at Bell Labs showed that we did not need to observe the quantizer
output over a long period of time [
124
]. In fact, we could adjust the quantizer step size after
observing a single output. Jayant named this quantization approach “quantization with one
word memory.” The quantizer is better known as the
Jayant quantizer
. The idea behind the
Jayant quantizer is very simple. If the input falls in the outer levels, the step size needs to be
expanded, and if the input falls in the inner quantizer levels, the step size needs to be reduced.
The expansions and contractions should be done in such a way that once the quantizer is
matched to the input, the product of the expansions and contractions is unity.
