Bonfring International Journal of Advances in Image Processing, Vol. 1, Special Issue, December 2011 6
ISSN 2250 – 1053 | © 2011 Bonfring
Abstract--- In this paper, the digital data can be
transformed using Discrete Wavelet Transform. The images
need to be transformed without loosing of information. The
Discrete Wavelet Transform was based on time-scale
representation, which provides efficient multi-resolution. The
lifting based scheme (5, 3) filters give lossless mode of
information as per the JPEG 2000 Standard. The lifting based
DWT are lower computational complexity and reduced
memory requirements. Since Conventional convolution based
DWT is area and power hungry which can be overcome by
using the lifting based scheme. The DWT is being increasingly
used for image coding. This is due to the fact that DWT
supports features like progressive image transmission (by
quality, by resolution), ease of transformed image
manipulation, region of interest coding, etc. DWT has
traditionally been implemented by convolution. Such an
implementation demands both a large number of computations
and a large storage features that are not desirable for either
high-speed or low-power applications. Recently, a lifting-
based scheme that often requires far fewer computations has
been proposed for the DWT. In this paper, the design of
Lossless 2-D DWT using Lifting Scheme Architecture will be
modeled using the Verilog HDL and its functionality were
verified using the Modelsim tool and can be synthesized using
the Xilinx tool.
Keywords--- Fourier Transform (FT), Short Time FT
(STFT), Discrete Wavelet Transform (STFT), Multi-resolution
Analysis (MRA).
I. INTRODUCTION
HE fundamental idea behind wavelets is to analyze
according to scale. Indeed, some researchers in the
wavelet field feel that, by using wavelets, one is adopting a
perspective in processing data. Wavelets are functions that
satisfy certain mathematical requirements and are used in
representing data or other functions. This idea is not new.
Approximation using superposition of functions has existed
since the early 1800's, when Joseph Fourier discovered that he
could superpose sines and cosines to represent other functions.
However, in wavelet analysis, the scale that we use to look at
data plays a special role. Wavelet algorithms process data at
S. Suresh, Assistant Professor, Department of ECE, Don Bosco Institute
of Tech & Science
K. Rajasekhar, Assistant Professor, Department of ECE, Narasaraopeta
Engineering College
M. Venugopal Rao, Professor and HOD, Narasaraopeta Engineering
College.
Dr. Bv Rammohan Rao, Professor and Principal, Narasaraopeta
Engineering College.
R. Samba Siva Nayak, Professor and HOD, Don Bosco Institute of Tech
& Science, E-mail: sambanayak@gmail.com
different scales or resolutions.
FT with its fast algorithms (FFT) is an important tool for
analysis and processing of many natural signals. FT has
certain limitations to characterize many natural signals, which
are non-stationary (e.g. speech). Though a time varying,
overlapping window based FT namely STFT is well known
for speech processing applications, a time-scale based Wavelet
Transform is a powerful mathematical tool for non-stationary
signals.
Wavelet Transform uses a set of damped oscillating
functions known as wavelet basis. WT in its continuous
(analog) form is represented as CWT. CWT with various
deterministic or non-deterministic basis is a more effective
representation of signals for analysis as well as
characterization. Continuous wavelet transform is powerful in
singularity detection. A discrete and fast implementation of
CWT is known as the standard DWT.With standard DWT,
signal has a same data size in transform domain and therefore
it is a non-redundant transform. A very important property
was Multi-resolution Analysis allows DWT to view and
process.
II. DWT
The discrete wavelet transform became a very versatile
signal processing tool after Mallat proposed the multi-
resolution representation of signals based on wavelet
decomposition. The method of multi-resolution is to represent
a function (signal) with a collection of coefficients, each of
which provides information about the position as well as the
frequency of the signal (function). The advantage of the DWT
over Fourier transformation is that it performs multi-resolution
analysis of signals with localization both in time and
frequency, popularly known as time-frequency localization.
As a result, the DWT decomposes a digital signal into
different sub bands so that the lower frequency sub bands have
finer frequency resolution and coarser time resolution
compared to the higher frequency sub bands. The DWT is
being increasingly used for image compression due to the fact
that the DWT supports features like progressive image
transmission, ease of compressed image manipulation region
of interest coding, etc. Because of these characteristics, the
DWT is the basis of the new JPEG2000 image compression
standard.
1-D DWT: Any signal is first applied to a pair of low-pass
and high-pass filters. Then down is applied to these filtered
coefficients. The filter pair (h, g) which is used for
decomposition is called analysis filter-bank and the filter pair
which is used for reconstruction of the signal is called
synthesis filter bank.(g`, h`).The output of the low pass filter
after down sampling contains low frequency components of
the signal which is approximate part of the original signal and
Three-D DWT of Efficient Architecture
S. Suresh, K. Rajasekhar, M. Venugopal Rao, Dr.B.V. Rammohan Rao and R. Samba Siva Nayak
T