MPEG video compression - The MPEG - page 189

The lossy coding consists of quantizing the parameters to reduce their wordlength. Coarse quantisation may be
employed on a base level bitstream, whereas an enhancement bitstream effectively transmits the quantizing error
of that coarse quantization.
The wavelet transform produces a decomposition of the image which is ideal for compression. Each sub-band
represents a different band of spatial frequencies, but in the form of a spatial array. In real images, the outline of
every object consists of an edge which will contain a wide range of frequencies. There will be energy in all sub-
bands in the case of a sharp edge. As each sub-band is a spatial array, edge information will be found in the same
place in each sub-band. For example, an edge placed one quarter of the way across the picture will result in
energy one quarter of the way across each sub-band.
This characteristic can be exploited for compression if the sequence in which the coefficients are coded starts at a
given coefficient in the lowest sub-band and passes through each sub-band in turn. Figure 5.70 shows that for
each coefficient in a given sub-band there will be four children in the next, sixteen descendants in the next and so
on, in a tree structure. In the case of a sharp edge, all the relevant coefficients will generally lie on a single route
through the tree. In plain areas containing only low frequencies, the corollary of this characteristic is that generally if
a given coefficient has value zero, then all of the coefficients in higher sub-bands will frequently also have value
zero, producing a zerotree . [ 3 ] Zerotrees are easy to code because they simply need a bit pattern which is
interpreted as meaning there are no further non-zero coefficients up this tree.
Figure 5.70: In wavelet coding, every coefficient at a given resolution corresponds to four coefficients at the next
highest level.
Figure 5.71 shows how zerotree coding works. Zero frequency coefficients are coded separately using predictive
coding, so zerotree coding starts with coefficients in the lowest AC sub-band. Each coefficient represents the root
of a tree and leads to four more nodes in the next sub- band and so on. At nodes, one of four codes may be
applied. ZTR means that this node is at the bottom of a zerotree and that this all further coefficients up the tree are
zero and need not be coded. VZTR means that this coefficient is non-zero but all its descendants are. In this case
only the valid coefficient at the foot of the tree is sent. IZ means that this coefficient is zero but it has non-zero
descendants and the scan must continue. Finally VAL means a non-zero coefficient with non-zero descendants.
This coefficient and subsequent ones must be coded.