Analysis of Efficient Wavelet Based Volumetric Image Compression

Krishna Kumar, Basant Kumar & Rachna Shah
International Journal of Image Processing (IJIP), Volume (6) : Issue (2) : 2012 113
Analysis of Efficient Wavelet Based Volumetric Image
Compression
Krishna Kumar krishnanitald@gmail.com
Department of ECE,
Motilal Nehru NIT
Allahabad, India
Basant Kumar singhbasant@mnnit.ac.in
Department of ECE,
Motilal Nehru NIT
Allahabad, India
Rachna Shah rachna.shah27@gmail.com
Department of CSE,
NIT Kurukshetra, India
Abstract
Recently, the wavelet transform has emerged as a cutting edge technology, within the field of
image compression research. Telemedicine, among other things, involves storage and
transmission of medical images, popularly known as Teleradiology. Due to constraints on
bandwidth and storage capacity, a medical image may be needed to be compressed before
transmission/storage. This paper is focused on selecting the most appropriate wavelet
transform for a given type of medical image compression. In this paper we have analyzed the
behavior of different type of wavelet transforms with different type of medical images and
identified the most appropriate wavelet transform that can perform optimum compression for a
given type of medical imaging. To analyze the performance of the wavelet transform with the
medical images at constant PSNR, we calculated SSIM and their respective percentage
compression.
Keywords: JPEG, CT, US, MRI, ECG, Wavelet Transforms, Medical Image Compression
1. INTRODUCTION
With the steady growth of computer power, rapidly declining cost of storage and ever-
increasing access to the Internet, digital acquisition of medical images has become increasingly
popular in recent years. A digital image is preferable to analog formats because of its
convenient sharing and distribution properties. This trend has motivated research in imaging
informatics [1], which was nearly ignored by traditional computer-based medical record systems
because of the large amount of data required to represent images and the difficulty of
automatically analyzing images. Besides traditional X-rays and Mammography, newer image
modalities such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) can
produce up to several hundred slices per patient scan. Each year, a typical hospital can
produce several terabytes of digital and digitized medical images.
2. IMAGE COMPRESSION
Both JPEG and wavelet belong to the general class of “transformed based lossy compression
techniques.” These techniques involved three steps: transformation, quantization, and
encoding. Transformation is a lossless step in which image is transformed from the grayscale
values in the special domain to coefficients in some other domain. No loss of information occurs
in the transformation step. Quantization is the step in which loss of information occurs. It
attempts to preserve the more important coefficients, while less important coefficients are
roughly approximated, often as zero. Finally, these quantized coefficients are encoded. This is
also a lossless step in which the quantized coefficients are compactly represented for efficient
storage or transmission of the image [20].

2.1 JPEG Compression
The JPEG specification defines a minimal subset of the standard called baseline JPEG, which
all JPEG-aware applications are required to support. This baseline uses an encoding scheme
based on the Discrete Cosine Transform (DCT) to achieve compression. DCT is a generic
name for a class of operations identified and published some years ago. DCT-based algorithms
have since made their way into various compression methods. DCT-based encoding algorithms
are always lossy by nature.
FIGURE 2.1: JPEG Compression & Decompression
2.2 Wavelet Compression
The Fourier transform is a useful tool to analyze the frequency components of the signal.
However, if we take the Fourier transform over the whole time axis, we cannot tell at what
instant a particular frequency rises. Short-time Fourier transform (STFT) uses a sliding window
to find spectrogram, which gives the information of both time and frequency. But still another
problem exists: The length of window limits the resolution in frequency. Wavelet Transform
seems to be a solution to the problem above. Wavelet transforms are based on small wavelets
with limited duration. The translated-version wavelets locate where we concern. Whereas the
scaled version wavelets allow us to analyze the signal in different scale. It is a transform that
provides the time -frequency representation simultaneously.
2.3 Decomposition Process
The image is high and low-pass filtered along the rows. The results of each filter are down-
sampled by two. Each of the sub-signals is then again high and low-pass filtered, but now along
the column data and the results is again down-sampled by two.
FIGURE 2.3.1: One Decomposition Step of the Two Dimensional Images
Hence, the original data is split into four sub-images each of size N/2 by N/2 and contains
information from different frequency components. Fig. 2.3.2 shows the block wise
representation of decomposition step.
FIGURE 2.3.2: One DWT Decomposition Step

The LL subband contains a rough description of the image and hence called the approximation
subband. The HH Subband contains the high-frequency components along the diagonals. The
HL and LH images result from low-pass filtering in one direction and high-pass filtering in the
other direction. LH contains mostly the vertical detail information, which corresponds to
horizontal edges. HL represents the horizontal detail information from the vertical edges. The
subbands HL, LH and HH are called the detail subbands since they add the high-frequency
detail to the approximation image.
2.4 Composition Process
Fig. 2.4 corresponds to the composition process. The four sub-images are up-sampled and
then filtered with the corresponding inverse filters along the columns. The result of the last step
is added together and we have the original image again, with no information loss.
FIGURE 2.4: One Composition Step of the Four Sub Images
3. WAVELET FAMILIES
There are many members in the wavelet family, Haar wavelet is one of the oldest and simplest
wavelet.
FIGURE 3: Different Types of Wavelets
Daubechies wavelets are the most popular wavelets. They represent the foundations of wavelet
signal processing and are used in numerous applications.The Haar, Daubechies, Symlets and
Coiflets are compactly supported orthogonal wavelets. These wavelets along with Meyer
wavelets are capable of perfect reconstruction. The Meyer, Morlet and Mexican Hat wavelets
are symmetric in shape. The wavelets are chosen based on their shape and their ability to
analyze the signal in a particular application. Biorthogonal wavelet exhibits the property of
linear phase, which is needed for signal and image reconstruction. By using two wavelets, one
for decomposition (on the left side) and the other for reconstruction (on the right side) instead of
the same single one, interesting properties are derived.

4. MEDICAL IMAGES
Computed tomography (CT) , is a medical imaging procedure that uses x-rays to show cross-
sectional images of the body. A CT imaging system produces cross-sectional images or "slices"
of areas of the body, like the slices in a loaf of bread. These cross-sectional images are used
for a variety of diagnostic and therapeutic purposes. Magnetic resonance imaging (MRI) is an
imaging technique used primarily in medical settings to produce high quality images of the
inside of the human body. ECG (electrocardiogram) is a test that measures the electrical
activity of the heart. The heart is a muscular organ that beats in rhythm to pump the blood
through the body. The signals that make the heart's muscle fibres contract come from the
sinoatrial node, which is the natural pacemaker of the heart. In an ECG test, the electrical
impulses made while the heart is beating are recorded and usually shown on a piece of paper.
Mammography can be used for diagnosis or for screening asymptomatic patients.
Mammography is a highly effective imaging method for detecting, diagnosing, and managing a
variety of breast diseases, especially cancer. It is an application where an emphasis on patient
dose management and risk reduction is required. This is because of a combination of two
factors. First, breast tissue has a relatively high sensitivity to any adverse effects of radiation,
and second, mammography requires a higher exposure than other radiographic procedures to
produce the required image quality. Retinal (eye fundus) images are widely used for diagnostic
purposes by ophthalmologists. The normal features of eye fundus images include the optic
disc, fovea and blood vessels. Ultrasound imaging is a common diagnostic medical procedure
that uses high-frequency sound waves to produce dynamic images (sonograms) of organs,
tissues, or blood flow inside the body.
5. FIDELITY CRITERIA
It is natural to raise the question of how much an image can be compressed and still preserve
sufficient information for a given clinical application. This section discusses some parameters
used to measure the trade-off between image quality and compression ratio. Compression ratio
is defined as the nominal bit depth of the original image in bits per pixel (bpp) divided by the
bpp necessary to store the compressed image. For each compressed and reconstructed image,
an error image was calculated. From the error data, maximum absolute error (MAE), mean
square error (MSE), root mean square error (RMSE), signal to noise ratio (SNR), and peak
signal to noise ratio (PSNR) were calculated.
The maximum absolute error (MAE) is calculated as [21]
(5.1)
Where f (x, y) is the original image data and f*(x, y) is the compressed image value. The
formulae for calculating image matrices are:
(5.2)
(5.3)
(5.4)
(5.5)
Structural Similarity Index Measurement (SSIM):
Let x, y R” where n >2. We define the following empirical quantities: the sample mean
(5.6)
The sample variance
(5.7)
and the sample cross-variance

(5.8)
We define and similarly. The SSIM index is defined as,
(5.9)
Where , i=1, 2. The SSIM index ranges between -1 and 1, where positive values closed
to 1 indicates a small perceptual distortion. We can define a distortion “measure” as one minus
the SSIM index, that is,
d(x,y) (5.10)
which ranges between 0 and 2 where a value closed to 0 indicates a small distortion. The SSIM
index is locally applied to N×N blocks of the image. Then, all block indexes are averaged to
yield the SSIM index of the entire image. We treat each block as an n-dimensional vector where
n= .
Compression ratio, where, n, m is the image size.
Percentage compression =
(5.11)
6. PROPOSED METHOD
In this proposed method we have analyzed the different medical images with different wavelet
transforms at constant PSNR and computed the percentage compression and SSIM.
FIGURE 6: Proposed Algorithm
7. SIMULATION & RESULTS
CT Scan ECG Fundus Infrared Image
FIGURE 7.1.1: Original images

Mammography MRI US Image X-Ray
FIGURE 7.1.2: Original images
FIGURE 7.2: Compressed Images after Haar Transform at 2-Level Decomposition
FIGURE 7.3: Compressed Images after Daubechies Transform at 2-Level Decomposition
FIGURE 7.4.1: Compressed Images after Coiflets Transform at 2-Level Decomposition

FIGURE 7.4.2: Compressed Images after Coiflets Transform at 2-Level Decomposition
FIGURE 7.5: Compressed Images after Biorthogonal Transform at 2-Level Decomposition
Images Wavelet Transforms
HAAR Daubechie
s
Biorthogon
al
Coiflet
s
CT 67.541
5
75.4188 78.1819 80.323
1
MRI 77.146
9
79.6038 76.7343 74.327
5
ECG 44.473
3
41.0012 31.3784 30.635
1
Infrared 84.268
2
87.0825 85.7940 85.530
3
Mammograph
y
75.959
8
84.5384 86.0533 86.236
9
Fundus 62.417
6
69.2187 68.5846 67.199
9
Ultra Sound 71.231
1
78.5077 79.2452 79.467
8
X-Ray 78.421
0
86.1492 87.0921 86.019
8

TABLE 7.1: Percentage Compression for Different Medical Images with Wavelet Transforms
FIGURE 7.6: Percentage Compression for Different Medical Images with Wavelet Transforms
FIGURE 7.7: PSNR (dB) for Different Medical Images with Wavelet Transforms
FIGURE 7.8: SSIM for Different Medical Images with Wavelet Transforms

8. CONCLUSION
In this paper we have analyzed that the Coiflets transform gives a higher percentage of
compression for CT, US and Mammography images, Daubechies transform gives a higher
percentage of compression for MRI, Fundus and Infrared images, Haar transform gives a
higher percentage of compression for ECG images and Biorthogonal transform gives a higher
percentage of compression for X-ray images at constant PSNR.
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