09-08-2014, 03:05 PM
Image Compression using Wavelet and SPIHT Encoding Scheme
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Abstract
The traditional image coding technology uses the
redundant data in an image to compress it. But these methods
have been replaced by digital wavelet transform based
compression method as these methods have high speed, low
memory requirements and complete reversibility. Now in this
work we are considering SPIHT as a placement for wavelet
compression methods. We are comparing it with wavelet
encoding scheme and comparing the final results in terms of bit
error rate, PSNR and MSE.
INTRODUCTION
The discrete cosine transform [1] is a technique for
converting a signal into elementary frequency components. It
is used widely for image compression. Here we have
developed some MATLAB code to calculate DCT and
compress images through it.
In recent years, wavelet transform has become a much
applied and researched method among mathematicians [2],
[3]. A very important property of wavelet is its ability of
frequency and time localization. Localization is the process of
defining the range for total time, T, and frequency range ω
that will be used in image analysis. The main difference is that
wavelets are well localized in both time and frequency domain
whereas the standard Fourier transform is only localized in
frequency domain. The Short-time Fourier transform (STFT)
is also time and frequency localized but there are issues with
the frequency time resolution and wavelets often give a better
signal representation using Multiresolution analysis Walnut[4]
[5]. So wavelets transform are better than Fourier transform or
DCT. So it has been utilized a lot in image processing and
image compression. However, different wavelets have
different merits and demerits and thus their selection is also an
important criterion
SPIHT ALGORITHM
A. Description of the SPIHT Algorithm
The SPIHT algorithm is a more efficient implementation of
EZW (Embedded Zero Wavelet) [6] [8] algorithm which was
presented by Shapiro. After applying wavelet transform to an
image, the SPIHT algorithm partitions the decomposed
wavelet into significant and insignificant partitions based on
the following function:
ܵ
(ܶ) = ൜
1, ݉ܽݔ(,)ఢ்{หܿ,
ห} ≥ 2
݁ݏ݅ݓݎ݁ℎݐܱ,0
Here Sn(T) is the significance of a set of coordinates T, and
ci,j is the coefficient value at coordinate (i, j). There are two
passes in the algorithm- the sorting pass and the refinement
pass. The SPIHT encoding process utilizes three lists
LIP (List of Insignificant Pixels) – It contains individual
coefficients that have magnitudes smalle
Merits of SPIHT
SPIHT provides higher PSNR than EZW because of a special
symbol that indicates significance of child nodes of a
significant parent, and separation of child nodes from second
generation descendants. The SPIHT algorithm depends on
Spatial Orientation Trees (SOT) defined on dyadic subband
structure, so some problems will arise because of its
adaptation to WP decomposition. One of them is the so-called
parental conflict [9] that occurs when in the wavelet packet
tree one or more of the child nodes are at the lower resolution
than the parent node. It must be resolved in order that SOT
structure with well-defined parent–child relationships for
arbitrary wavelet decomposition can be created.
ACKNOWLEDGMENT
The heading of the Acknowledgment section and
the References section must not be numbered.
Causal Productions wishes to acknowledge
Michael Shell and other contributors for developing
and maintaining the IEEE LaTeX style files which
have been used in the preparation of this template.
To see the list of contributors, please refer to the top
of file IEEETran.cls in the IEEE LaTeX
distribution.