18-06-2012, 01:53 PM
Performance Analysis of Image Compression Using Wavelets
[attachment=24712]
Abstract
The aim of this paper is to examine a set of wavelet
functions (wavelets) for implementation in a still image compression
system and to highlight the benefit of this transform relating
to today’s methods. The paper discusses important features of
wavelet transform in compression of still images, including the
extent to which the quality of image is degraded by the process
of wavelet compression and decompression.
INTRODUCTION
IN RECENT years, many studies have been made on
wavelets. An excellent overview of what wavelets have
brought to the fields as diverse as biomedical applications,
wireless communications, computer graphics or turbulence,
is given in [1]. Image compression is one of the most visible
applications of wavelets. The rapid increase in the range and
use of electronic imaging justifies attention for systematic
design of an image compression system and for providing the
image quality needed in different applications.
WAVELET TRANSFORM
Wavelet transform (WT) represents an image as a sum of
wavelet functions (wavelets) with different locations and scales
[17]. Any decomposition of an image into wavelets involves a
pair of waveforms: one to represent the high frequencies corresponding
to the detailed parts of an image (wavelet function
) and one for the low frequencies or smooth parts of an image
(scaling function ).
Fig. 1 shows two waveforms of a family discovered in the late
1980s by Daubechies: the right one can be used to represent detailed
parts of the image and the left one to represent smooth
parts of the image. The two waveforms are translated and scaled
on the time axis to produce a set of wavelet functions at different
locations and on different scales. Each wavelet contains
the same number of cycles, such that, as the frequency reduces,
the wavelet gets longer. High frequencies are transformed with
short functions (low scale). Low frequencies are transformed
with long functions (high scale). During computation, the analyzing
wavelet is shifted over the full domain of the analyzed
function. The result ofWTis a set of wavelet coefficients, which
measure the contribution of the wavelets at these locations and
scales.
DWT IN IMAGE COMPRESSION
Image Content
The fundamental difficulty in testing an image compression
system is how to decide which test images to use for the evaluations.
The image content being viewed influences the perception
of quality irrespective of technical parameters of the system
[9]. Normally, a series of pictures, which are average in terms
of how difficult they are for system being evaluated, has been
selected. To obtain a balance of critical and moderately critical
material we used four types of test images with different
frequency content: Peppers, Lena, Baboon, and Zebra. Spectral
activity of test images is evaluated using DCT applied to the
whole image. DCT coefficients as a result of DCT show frequency
content of the image. Fig. 4 shows the distributions of
image values before and after DCT. The distribution of DCT coefficients
depends on image content (white dots represent DCT
coefficients, arrows indicate the increase of horizontal and vertical
frequency).
DWT COMPRESSION RESULTS
The choice of optimal wavelet function in an image compression
system for different image types can be provided in
a few steps. For each filter order in each wavelet family, the
optimal number of decompositions can be found. The optimal
number of decompositions gives the highest PSNR values in
the wide range of compression ratios for a given filter order.
Table II shows some of the results for DW and image Lena.
For lower filter orders, better results are reached with more
decompositions than for higher filter orders.
CONCLUSIONS
In this paper, we presented results from a comparative study
of different wavelet-based image compression systems. The effects
of different wavelet functions, filter orders, number of decompositions,
image contents, and compression ratios are examined.
The final choice of optimal wavelet in image compression
application depends on image quality and computational
complexity.We found thatwavelet-based image compression
prefers smooth functions of relatively short length. A suitable
number of decompositions should be determined by means
of image quality and less computational operation.
[attachment=24712]
Abstract
The aim of this paper is to examine a set of wavelet
functions (wavelets) for implementation in a still image compression
system and to highlight the benefit of this transform relating
to today’s methods. The paper discusses important features of
wavelet transform in compression of still images, including the
extent to which the quality of image is degraded by the process
of wavelet compression and decompression.
INTRODUCTION
IN RECENT years, many studies have been made on
wavelets. An excellent overview of what wavelets have
brought to the fields as diverse as biomedical applications,
wireless communications, computer graphics or turbulence,
is given in [1]. Image compression is one of the most visible
applications of wavelets. The rapid increase in the range and
use of electronic imaging justifies attention for systematic
design of an image compression system and for providing the
image quality needed in different applications.
WAVELET TRANSFORM
Wavelet transform (WT) represents an image as a sum of
wavelet functions (wavelets) with different locations and scales
[17]. Any decomposition of an image into wavelets involves a
pair of waveforms: one to represent the high frequencies corresponding
to the detailed parts of an image (wavelet function
) and one for the low frequencies or smooth parts of an image
(scaling function ).
Fig. 1 shows two waveforms of a family discovered in the late
1980s by Daubechies: the right one can be used to represent detailed
parts of the image and the left one to represent smooth
parts of the image. The two waveforms are translated and scaled
on the time axis to produce a set of wavelet functions at different
locations and on different scales. Each wavelet contains
the same number of cycles, such that, as the frequency reduces,
the wavelet gets longer. High frequencies are transformed with
short functions (low scale). Low frequencies are transformed
with long functions (high scale). During computation, the analyzing
wavelet is shifted over the full domain of the analyzed
function. The result ofWTis a set of wavelet coefficients, which
measure the contribution of the wavelets at these locations and
scales.
DWT IN IMAGE COMPRESSION
Image Content
The fundamental difficulty in testing an image compression
system is how to decide which test images to use for the evaluations.
The image content being viewed influences the perception
of quality irrespective of technical parameters of the system
[9]. Normally, a series of pictures, which are average in terms
of how difficult they are for system being evaluated, has been
selected. To obtain a balance of critical and moderately critical
material we used four types of test images with different
frequency content: Peppers, Lena, Baboon, and Zebra. Spectral
activity of test images is evaluated using DCT applied to the
whole image. DCT coefficients as a result of DCT show frequency
content of the image. Fig. 4 shows the distributions of
image values before and after DCT. The distribution of DCT coefficients
depends on image content (white dots represent DCT
coefficients, arrows indicate the increase of horizontal and vertical
frequency).
DWT COMPRESSION RESULTS
The choice of optimal wavelet function in an image compression
system for different image types can be provided in
a few steps. For each filter order in each wavelet family, the
optimal number of decompositions can be found. The optimal
number of decompositions gives the highest PSNR values in
the wide range of compression ratios for a given filter order.
Table II shows some of the results for DW and image Lena.
For lower filter orders, better results are reached with more
decompositions than for higher filter orders.
CONCLUSIONS
In this paper, we presented results from a comparative study
of different wavelet-based image compression systems. The effects
of different wavelet functions, filter orders, number of decompositions,
image contents, and compression ratios are examined.
The final choice of optimal wavelet in image compression
application depends on image quality and computational
complexity.We found thatwavelet-based image compression
prefers smooth functions of relatively short length. A suitable
number of decompositions should be determined by means
of image quality and less computational operation.