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\title{Efficient Image Compression Scheme Using Tree Structure
Wavelet Transforms}
\author{Jiaming Li and Jesse S. Jin\\
School of Computer Science and Engineering, \\
The University of New South Wales, Sydney 2052, Australia}
\date{}
\maketitle
Most recent research on applying wavelet transform(WT) in image coding has 
shown that WT-based methods generally outperform all other methods 
including discrete cosine transform (DCT) based approaches. In comparison
to other transform-based image coding schemes, the most attractive feature 
of WT is that it offers a flexible image representation with multiple
resolutions. Among various versions of WT-based coding algorithms it has
been claimed that the embedded zerotree wavelet (EZW) coding proposed by
Shapiro [1993] can produce a consistent compression rate that is competitive
with virtually all known compression algorithms (by 1993) over a set of 
conventional test images. Much effort has been made to elevate the
performance of the tree-structure-related algorithm of which the main idea
is: the coefficient tree is encoded recursively if the absolute value of
a WT coefficient is greater than a threshold, otherwise the tree is rejected
and zero coefficients are implied. In the course of finding ways to improve
the performance of EZW coding, we realize that the purpose of image 
compression is to achieve low bit rate representation of images with a
minimum perceived loss of image quality, and that the final observer of
the processed image is a human being.  We incorporate the characteristics
of human visual system (HVS) into the coding process so that the algorithm
is adapted to the sensitivity of visual perception and produces subjectively
less noise in images. The core of the perceptual weighting is that human
viewer can hardly perceive details in the high frequency region and it is
desirable to use more bits to represent the viewer sensitive part and less
bits to represent the insensitive part. In this paper, we propose a novel
image coding scheme based on the properties of the embedded zerotree wavelet
image coding algorithm, the characteristics of HVS, and the unique structure
correlation of wavelet transform (i.e. the subimages in same orientation
of different levels have similar structure).  In a WT-based image coding 
system, there exist three major components, i.e., the WT, the quantization
of the WT coefficients, and the entropy coding of the quantized coefficients.
The major error is the quantization error introduced in EZW coding. This 
error can be interpreted as a noise signal which will be interpolated and 
filtered by the synthesis filters and weighted by human eyes.  We applied
the perceptual characteristics of HVS to the WT domain before doing EZW 
coding, so that the algorithm is adapted to the sensitivity of human visual
perception and produces subjectively less noisy in images.  To further 
take advantage of structure correlation in WT, perceptually important
high spatial frequency components are detected and used to enhance weighting.
The improvement of Image quality has been observed subjectively with the
compression rate ranging from 1 to 128 and confirmed through the calculation
of weighted-signal-to-noise-ratio (WSNR).

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