A VLSI PROGRESSIVE CODING FOR WAVELET

BASED IMAGE
COMPRESSION
Description:
This paper describes the hardware design flow of lifting based 2

D Forward Discrete Wavelet Transform (FDWT)
processor for JPEG 2000. In order to build high quality image of JPEG 2000 codec, an effective 2

D FDWT
algorithm has been performed on input image
file to get the decomposed image coefficients. The Lifting Scheme
reduces the number of operations execution steps to almost one

half of those needed with a conventional
convolution approach. Initially, the lifting based 2

D FDWT algorithm has been develo
ped using Mat lab. The
FDWT modules were simulated using XPS(8.1i) design tools. The final design was verified with Matlab image
processing tools.
Comparison of simulation results Matlab was done to verify the proper functionality of the developed module.
The
motivation in designing the hardware modules of the FDWT was to reduce its complexity, enhance its
performance and to make it suitable development on a reconfigurable FPGA based platform for VLSI
implementation. Results of the decomposition for test i
mage validate the design. The entire system runs at 215
MHz clock frequency and reaches a speed performance suitable for several realtime applications. The result of
simulation displays that lifting scheme needs less memory requirement.
Introduction
A
majority of today’s Internet bandwidth is estimated to be used for images and video. Recent multimedia
applications for handheld and portable devices place a limit on the available wireless bandwidth. The bandwidth
is limited even with new connection stand
ards. JPEG image compression that is in widespread use today took
several years for it to be perfected. Wavelet based techniques such as JPEG2000 for image compression has a
lot more to offer than conventional methods in terms of compression ratio. Current
ly wavelet implementations are
still under development lifecycle and are being perfected. Flexible energy

efficient hardware implementations that
can handle multimedia functions such as image processing, coding and decoding are critical, especially in hand

held portable multimedia wireless devices.
Background
Data compression is, of course, a powerful, enabling technology that plays a vital role in the information age.
Among the various types of data commonly transferred over networks, image and video
data comprises the bulk
of the bit traffic. For example, current estimates indicate that image data take up over 40% of the volume on the
Internet. The explosive growth in demand for image and video data, coupled with delivery bottlenecks has kept
compress
ion technology at a premium.
Among the several compression standards available, the JPEG image compression standard is in wide spread
use today. JPEG uses the Discrete Cosine Transform (DCT) as the transform, applied to 8

by

8 blocks of image
data. The n
ewer standard JPEG2000 is based on the Wavelet Transform (WT). Wavelet Transform offers multi

resolution image analysis, which appears to be well matched to the low level characteristic of human vision. The
DCT is essentially unique but WT has many possibl
e realizations. Wavelets provide us with a basis more suitable
for representing images.
This is because it cans represent information at a variety of scales, with local contrast changes, as well as larger
scale structures and thus is a better fit for ima
ge data.
Aim of the project
The main aim of the project is to implement and verify the image compression technique and to investigate the
possibility of hardware acceleration of DWT for signal processing applications. A hardware design has to be
provi
ded to achieve high performance, in comparison to the software implementation of DWT. The goal of the
project is to
. Implement this in a Hardware description language (Here VHDL).
. Perform simulation using tools such as Xilinx ISE 8.1i.
. Check the c
orrectness and to synthesize for a Spartan 3E FPGA Kit.
The STFT represents a sort of compromise between the time

and frequency

based views of a signal. It provides
some information about both when and at what frequencies a signal event occurs. However,
you can only obtain
this information with limited precision, and that precision is determined by the size of the window.
While the STFT compromise between time and frequency information can be useful, the drawback is that once
you choose a particular siz
e for the time window, that window is the same for all frequencies. Many signals
require a more flexible approach
—
one where we can vary the window size to determine more accurately either
time or frequency.
Problem Present in Fourier Transform
The Fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers feel that
using wavelets means adopting a whole new mind

set or perspective in processing data. Wavelets are functions
that satisfy certain mathematical require
ments and are used in representing data or other functions. This idea is
not new. Approximation using superposition of functions has existed since the early 18OOs, when Joseph Fourier
discovered that he could superpose sines and cosines to represent other
functions.
However, in wavelet analysis, the scale used to look at data plays a special role. Wavelet algorithms process
data at different scales or resolutions. Looking at a signal (or a function) through a large “window,” gross features
could be notice
d. Similarly, looking at a signal through a small “window,” small features could be noticed. The
result in wavelet analysis is to see both the forest and the trees, so to speak.
This makes wavelets interesting and useful. For many decades scientists have
wanted more appropriate
functions than the sines and cosines, which are the basis of Fourier analysis, to approximate choppy signals.’ By
their definition, these functions are non

local (and stretch out to infinity). They therefore do a very poor job in
a
pproximating sharp spikes. But with wavelet analysis, we can use approximating functions that are contained
neatly in finite domains. Wavelets are well

suited for approximating data with sharp discontinuities.
The wavelet analysis procedure is to adopt a
wavelet prototype function, called an analyzing wavelet or mother
wavelet. Temporal analysis is performed with a contracted, high

frequency version of the prototype wavelet, while
frequency analysis is performed with a dilated, low

frequency version of th
e same wavelet. Because the original
signal or function can be represented in terms of a wavelet expansion (using coefficients in a linear combination
of the wavelet functions), data operations can be performed using just the corresponding wavelet coeffici
ents.
And if wavelets best adapted to data are selected, the coefficients below a threshold is truncated, resultant data
are sparsely represented. This sparse coding makes wavelets an excellent tool in the field of data compression.
Other applied fields t
hat are using wavelets include astronomy, acoustics, nuclear engineering, sub

band coding,
signal and image processing, neurophysiology, music, magnetic resonance imaging, speech discrimination,
optics, fractals, turbulence, earthquake prediction, radar, h
uman vision, and pure mathematics applications such
as solving partial differential equations.
Basically wavelet transform (WT) is used to analyze non

stationary signals, i.e., signals whose frequency
response varies in time, as Fourier transform (FT) is
not suitable for such signals. To overcome the limitation of
FT, short time Fourier transform (STFT) was proposed. There is only a minor difference between STFT and FT.
In STFT, the signal is divided into small segments, where these segments (portions) of
the signal can be
assumed to be stationary. For this purpose, a window function "w" is chosen. The width of this window in time
must be equal to the segment of the signal where its still be considered stationary. By STFT, one can get time

frequency respons
e of a signal simultaneously, which can’t be obtained by FT.
Scaling
We’ve seen the interrelation of wavelets and quadrature mirror filters. The wavelet function
is determined by the
high pass filter, which also produces the details of the wavelet d
ecomposition.
There is an additional function associated with some, but not all wavelets. This is the so

called scaling function.
The scaling function is very similar to the wavelet function. It is determined by the low pass quadrature mirror that
iterati
vely up

sampling and convolving the high pass filter produces a shape approximating the wavelet function,
iteratively up

sampling and convolving the low pass filter produces a shape approximating the scaling
function.We’ve already alluded to the fact that
wavelet analysis produces a time

scale view of a signal and now
we’re talking about scaling and shifting wavelets.
What exactly do we mean by scale in this context?
Scaling a wavelet simply means stretching (or compressing) it. To go beyond colloquial d
escriptions such as
“stretching,” we introduce the scale factor, often denoted by the letter a.
If we’re talking about sinusoids, for example the effect of the scale factor is very easy to see:
One

Stage Decomposition
For many signals, the low

freque
ncy content is the most important part. It is what gives the signal its identity. The
high

frequency content on the other hand imparts flavor or nuance. Consider the human voice. If you remove the
high

frequency components, the voice sounds different but y
ou can still tell what’s being said. However, if you
remove enough of the low

frequency components, you hear gibberish. In wavelet analysis, we often speak of
approximations and details. The approximations are the high

scale, low

frequency components of th
e signal. The
details are the low

scale, high

frequency components. The filtering process at its most basic level looks like this:
The original signal S passes through two complementary filters and emerges as two signals. Unfortunately, if we
actually per
form this operation on a real digital signal, we wind up with twice as much data as we started with.
Suppose, for instance that the original signal S consists of 1000 samples of data. Then the resulting signals will
each have 1000 samples, for a total of 2
000. These signals A and D are interesting, but we get 2000 values
instead of the 1000 we had. There exists a more subtle way to perform the decomposition using wavelets.
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