Implementation of Zero-Trees in Wavelet Based Image
Compression:
Zero trees in the wavelet transform
of images provide an opportunity to compress the images. When a wavelet
transform of an image is taken, it represents the image as a set consisting of
4 elements of emphasized high frequency components and emphasized low frequency
components. The word ‘emphasized’ is used in order to bring out that neither
band is devoid of frequencies from the other band, they are just suppressed or
attenuated.
In the transform domain, most of the
content of a natural image is cluttered in the low frequency components, leaving
very little information for the high frequency emphasis band. Thus, in digital
representation, the high frequency part of the image consists of many zeros.
When the low frequency image is further converted into the transform
domain, the pixels corresponding to the same physical point tend to exhibit
similar magnitude trend as observed in the transformation at the previous
level. Looking bit-wise, a zero at a coarser level will probably imply a zero
at a detailed level of analysis. This leads to the “zero trees” as one goes
from a coarser band to a detailed band. Such zero-trees are exploited in order
to compress images.
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