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5.1 Quantization
5.1.1 Dead-Zone Quantization
Each subband's coefficients are quantised by Dirac using so-called uniform dead-
zone quantisers. A simple uniform quantiser is a division of the real line into
equal-width bins, of size equal to the quantization factor Q
f
:
The bins are numbered and a reconstruction value is selected for each bin. So
the bins consist of the intervals.
1
2
,
1
2
The labels for the bin are integer N, that is subsequently encoded. The
reconstruction value used in the decoder (and for local decoding in the encoder)
can be any value in each of the bins. The obvious, but not necessarily the best,
reconstruction value is the midpoint NQ
f
.
A uniform dead-zone quantizer is slightly different. Bins in that quantizer
containing zeros is twice as wide. So the bins consist of [-Qf ,Qf] , with a
reconstruction value of 0, together with other bins of the form.
,
for N>0 &
1
,
for N<0 with reconstruction points
somewhere in the intervals.
5.1.1.1 Advantages of Dead Zone Quantiser
The advantage of the dead-zone quantiser is two-fold. It applies more severe
quantisation of the smallest values, which acts as a simple but effective de-noising
operation. Secondly, it admits a very simple and efficient implementation: simply
divide by the quantisation factor and round towards zero. In Dirac, this process is
approximated by a multiplication and a bit shift.
A value of X=0.5, giving the mid-point of the interval might be the obvious
reconstruction point, as it gives the mid-point of the bin. This is indeed what we
use for intra pictures. For inter pictures (motion compensated prediction residues),
the values of transformed coefficients in a wavelet subband have a distribution
with mean very near zero and which decays pretty rapidly and uniformly for larger
values. Values are therefore more likely to occur in the first half of a bin than in
the second half and the smaller value of X=0.375 reflects this bias, and gives
better performance in practice [8].
5.1.2
Lagrangian Parameter Control of Subband Quantization
Selection of quantisers is a matter for the encoder only. The current Dirac encoder
uses an RDO technique to pick a quantiser by minimising a Lagrangian
combination of rate and distortion. Essentially, lots of quantisers are tried and the
best picked. Rate is estimated via an adaptively-corrected measure of zeroth-order
entropy measure Ent(q) of the quantised symbols resulting from applying the
quantisation factor q, calculated as a value of bits/pixel. Distortion is measured in
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