International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
Performance Evaluation of Medical Image
Compression Using Discrete Cosine and Discrete
Wavelet Transform
Anupreksha Jain1, Asstt.Prof. ShilpaDatar2,
1
PG student, Dept. of Electronics and Communication Engg., SATI, Vidisha, M.P., India
2
Asstt. Prof.,Dept.of Electronics&Instrumentation Engg., SATI, Vidisha, M.P., India
Abstract— Image compression communicates the
problem of reducing the amount of data needed to
represent a digital image. The underlying basis of the
reduction deal is the removal of redundant data. Here
we have used Medical images for compression like
brain images. Every year, terabytes of medical image
data are generated through advance imaging
modalities such as X-rays and many more recent
techniques of medical imaging. But storing and
transferring these tremendous voluminous data could
be a typical job. All these medical images require
being stored for future reference of the patients and
their hospital findings. So to reduce storage costs and
transmission time and, efficient image compression
schemes, without degradation of image quality are
needed. Generally, compression algorithms can be
categorized into two main categories: one is the
lossless category and the other is the lossy category.
This paper diagnoses some of the medical image
compression techniques that are existing as of today. A
comparison of these image compression techniques has
been made on the basis of performance parameters
like compression ratio, and PSNR for various medical
image .
Keywords— DCT (discrete cosine transform), DWT
(discrete wavelet transform), MSE (mean square
error), PSNR (peak signal to noise ratio),
CR(compression ratio).
INTRODUCTION
The term image compression concern to the process of
reducing the amount of data required to stand for a given
quantity of information. A popular characteristic of about
images is that the neighbouring pixels are correlated and
consequently contain redundant information. Image
compression has transform one of the most essential
conditions in digital electronics because of the ever
developing popularity and usage of the internet and
multimedia systems combined with the high requirements
of the bandwidth and storage space[1,3].
information needed without any appreciable loss of
information [1, 2 ,3-4].
This is the case with lossless compression while lossy
compression techniques are more cost-efficient in terms
of storage and transmission demands because of good
PSNR, compression ratio and the quality.
The quality of the image after compression is very
essential and it must be within the supportable limits
which vary from image to image and the method to
method and therefore the compression becomes more
interesting as a part of qualitative analysis of different
types of image compression techniques [8-9].There are
mainly two categories of compression namely: Lossless
or reversible compression and Lossy or irreversible
compression.
DISCRETE COSINE TRANSFORM
The Joint Photographic Experts Group (JPEG) standard is
one of the most widely used techniques for lossy image
compression. The approach recommended by JPEG is a
transform coding approach using the DCT. The JPEG
specification consists of several parts, including a
specification for both lossless and lossy encoding.
The key to the JPEG compression process is a
mathematical transformation known as the discrete cosine
transform. It takes a set of points from the spatial domain
and transforms them into an identical representation in the
frequency domain. The DCT can be used to convert
spatial information into frequency or spectral information,
With X and Y-axes representing the frequencies of the
two signals in two different directions [1-3, 4-6,5,7]. The
pictorial representation for DCT based compression
algorithm is shown in figure.
In medical image compression, diagnosis is effective only
when compression techniques preserve all the relevant
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
Fig 1 Schematic diagram of JPEG compression
ALGORITHM FOR JPEG COMPRESSION
1. The first step in JPEG compression process is to
subdivide the input image into non-overlapping pixel
blocks of size 8 x 8.
2. They are subsequently processed from left to right, top
to bottom. As each 8 x 8 block or sub-image is processed,
its 64 pixels are level shifted by subtracting
, where
is the number of gray levels.
3. Now its discrete cosine transform is computed. The
resulting coefficients are then simultaneously normalized
and quantized.
4. After each block’s DCT coefficients are quantized, the
elements of T(u, v) are reordered in accordance with a
zig-zag pattern. Now the nonzero coefficients are coded
using a variable length code. The variable length codes
are generated by the Huffman encoding.
DISCRETE WAVELET TRANSFORM
Wavelet transform has state an essential method for image
compression. Wavelet based coding gives substantial
improvement in picture quality at sufficient compression
ratios mainly due to better energy compaction property of
wavelet transforms [1,4,8]. With the increasing use of
multimedia technologies, image compression requires
advance performance as well as new features.
The JPEG 2000 is the standard which will be
based on wavelet decomposition..However, at lower rates
there is a distinct degradation in the quality of the
reconstructed image. To correct this and other
shortcomings, the JPEG committee initiated work on
another standard, commonly known as JPEG 2000.
Fig 2 Schematic diagram of JPEG2000 compression
ALGORITHM FOR JPEG 2000
COMPRESSION
1. The Discrete Wavelet Transform is first applied on the
input image.
2. The transform coefficients are then quantized.
3. Finally the entropy encoding technique is used to
generate the output. The Huffman encoding and run
length is generally used for this purpose.
Orthogonal or Bi orthogonal wavelet transform has often
been used in many image processing applications,
because it makes possible multi- resolution analysis and
does not yield redundant information.
DECOMPOSITION LEVEL SELECTION
The number of operations, in the computation of the
forward and inverse transform increases with the number
of decomposition levels. In applications like, searching
image databases on transmitting images for progressive
reconstruction, the resolution of the stored or transmitted
images and the scale of the lowest useful approximations
normally determine the number of transform levels.
SELECTION OF WAVELET
The wavelets chosen as the basis of the forward and
inverse transforms .The ability of the wavelet to compact
information into a small number of transform coefficients
find outs its compression and reconstruction performance,
affect all aspects of wavelet coding system design and
performance.
They affect directly the computational complexity of the
transforms and the system’s ability to compress and
reconstruct images of satisfactory error.
The most widely used expansion functions for waveletbased compression are the Daubechies wavelets.
ISSN: 2231-5381
HUFFMAN CODING
Huffman coding is an efficient source coding algorithm
for source symbols that are not equally probable. A
variable length encoding algorithm was suggested by
Huffman in 1952, based on the source symbol
probabilities P(xi), i=1,2…….,L . The algorithm is
optimal in the sense that the average number of bits
required to represent the source symbols is a minimum
provided the prefix condition is met. The most popular
technique for removing coding redundancy is due to
David Huffman. It creates variable length codes that are
an integral number of bits. Huffman codes have unique
prefix attributes which means that they can be correctly
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
decoded despite being variable lengths. The Huffman
codes are based on two observations regarding optimum
prefix codes: 1-In an optimum code, symbols that occur
more frequently (have higher probability of occurrence)
will have shorter code words than symbols that occur less
frequently and 2-In an optimum code, the two symbols
that occur least often will have the same length. It is
simple to see that the first observation is correct. If
symbols that occur more frequently had code words that
were longer than the code words for the symbol that
occurred less often, the average number of bits per
symbol would be larger if the condition were reversed [1,
3].
PERFORMANCE PARAMETERS
Image compression research aims to reduce the number of
bits required to represent an image by removing the
spatial and spectral redundancies as much as possible.
1) MSE
Mean Squared Error (MSE) is defined as the
square of differences in the pixel values between the
corresponding pixels of the two images. N * M size
image is the mean square error (MSE) and is given by.
And data redundancy of the original image can be specify
as
PROPOSED METHODOLOGY
Uses of various compression techniques our aim is to
provided the approximate compression ratio with
sufficient PSNR. The commonly used two techniques i.e.
JPEG and JPEG2000 are good sufficient for the
compression but we may get improvisation in its
performances by the changing the encoding technique.
We get good PSNR in JPEG2000 technique compare to
JPEG.
In the preceding two techniques, the Huffman encoding is
generally used. In the proposed work, a change in the
coding technique has been comprised in the existing
techniques.
We have add Run length coding in the both techniques.
We have used the Run Length encoding followed by the
Huffman encoding and the significant coefficients are
encoded separately using the Huffman encoding. This
encoding technique provides an improvisation in the
PSNR with sufficient the compression ratio.
For the thresholding we used a parameter alpha, where
alpha can be selected manually from 0 to 1.
Threshold level is decided by the formula:
2) PSNR Peak signal-to-noise ratio often
abbreviated PSNR, is an engineering name, for the ratio
between the maximum possible power of a signal and the
power of corrupting noise that affects the fidelity of its
3) COMPRESSION RATIO
Data redundancy is the centric release in digital image
compression. If n1 and n2 denote the number of
information carrying units in original and encoded image
respectively, then the compression ratio, CR can be
specify as
Where:
Max I= Maximum intensity value present in the image.
Min I= Minimum intensity present in the image.
In the quantization stage, we have moderated the levels to
. Where n is number of bits corresponds to each pixel
of compressed image. We have used the n=4,5,6 in
measurement in the coding .
RESULT AND ANALYSIS
The results are shown below for the two methods, for the
different images, in the tabular form.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
Table 1 Result of image compression using DCT for
medical image 1
Number of bits
corresponds to the
each pixel of
compressed
image(Tbits)
4
5
6
PSNR of the
reconstructed image
Compression ratio
16.4135
7.0252
18.2842
7.0618
17.1680
6.0284
19.9230
6.3243
19.9358
5.0596
21.8884
5.4122
Number of bits
corresponds to the
each pixel of
compressed
image(Tbits)
Table 3 Result of image compression using DCT for
medical image2
Number of bits
corresponds to the
each pixel of
compressed
image(Tbits)
4
5
7.8571
27.9549
6.3454
27.3930
6.8094
28.6344
5.1512
28.1381
5.4801
Table 4 Result of image compression using DWT for
medical image2
7.4449
8.2631
27.4606
6.0817
6.1520
27.1471
6.6447
4.9325
27.8837
5.0527
27.5361
5.4832
6.9782
20.0251
6.0363
Number of bits
corresponds to the
each pixel of
compressed
image(Tbits)
4
5
6
4.9439
(b)
7.3144
26.6518
26.3388
6.9301
18.5403
(a)
6
27.1235
26.5946
21.0794
21.6737
5
Compression ratio
Compression ratio
Compression ratio
21.7731
6
4
PSNR of the
reconstructed image
PSNR of the
reconstructed image
PSNR of the
reconstructed image
20.4479
Table 2 Result of image compression using DWT for
medical image 1
(c)
(d)
Fig. 3 (a) Original Image (medical image 1 –brain image) and (b) Reconstruct image at Tbits =4 (c) Reconstruct image at Tbits =5 (d)
Reconstruct image at , Tbits =6. Images by DCT
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
(a)
(b)
(c)
(d)
Fig. 4 (a) Original Image (medical image 1 –brain image) and (b) Reconstruct image at Tbits =4 (c) Reconstruct image at Tbits =5 (d)
Reconstruct image at , Tbits =6. Images by DWT
(a)
(b)
(c)
(d)
Fig. 5 (a) Original Image (medical image 2 –brain image) and (b) Reconstruct image at Tbits =4 (c) Reconstruct image at Tbits =5 (d)
Reconstruct image at Tbits =6. Images by DCT
(a)
(b)
(c)
(d)
Fig. 6 (a) Original Image (medical image 2 –brain image) and (b) Reconstruct image at Tbits =4 (c) Reconstruct image at Tbits =5 (d)
Reconstruct image at Tbits =6. Images by DWT
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 6 – Aug 2014
Another governing factor is the number of bits corresponding
to each pixel of compressed image (Tbits). For the higher
value of Tbits the number of levels in the compressed image is
higher so PSNR is higher but the compression ratio is lower.
[7]
[8]
[9]
CONCLUSION
We have seen the various compression methods that are most
frequently and commonly used for the image compression.
The JPEG compression scheme is a standard technique that
uses DCT, but have blocking effect ,whereas JPEG2000 used
the DWT and provides the results that are good enough and no
blocking effect. But for both JPEG and JPEG2000, we may
use the improved encoding technique to get the better results.
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We have used the run-length encoding followed by Huffman
encoding and the significant coefficients are encoded
separately using the Huffman encoding. With the use of good
encoding technique the compression ratio remains unaffected
but the PSNR get increased.
We have also seen the results for the different number of bits
corresponding to each pixel of the compressed image (Tbits).
With lowering of Tbits value the PSNR decreases but the
compression ratio increases. Thus we may select the desired
level of compression with the corresponding PSNR.
Here we have compared the value of PSNR at approximate
compression ratio . We get good PSNR using DWT as
compared to the DCT. So we can say DWT gives good image
quality instead DCT.
Our implemented strategies work sufficiently well, to provide
improvisation in the PSNR with the desired compression ratio.
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