The research paper proposes a hybrid image compression method combining Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT), and Huffman coding for medical images to achieve higher compression rates. It discusses the advantages of using luminance-chrominance representations over RGB for better image processing and analyzes the performance of DWT and DCT at various threshold levels, concluding that while DCT performs well at lower thresholds, DWT maintains superior image quality at higher thresholds. The study emphasizes the importance of selecting appropriate threshold values for optimal image quality and compression efficacy.

1. Integrated Intelligent Research (IIR) International Journal of Web Technology
Volume: 02 Issue: 01 June 2013 Page No.25-27
ISSN: 2278-2389
25
Image Compression Using Discrete Cosine
Transform & Discrete Wavelet Transform
Mr.Anurag Tiwari1
Payal Chandrakant2
, Tripti2
, Surabhi Chaudhary2
, Anil Kumar Shukla2
1
Assistant Professor, Department of Electronics & Communication Engineering
2
Research Scholar,Department of Electronics & Communication Engineering,
Kanpur Institute of Technology, Kanpur, Uttar Pradesh, INDIA.
Email : aktitmg2007@gmail.com
Abstract -This research paper presents a proposed method for
the compression of medical images using hybrid compression
technique (DWT, DCT and Huffman coding). The objective of
this hybrid scheme is to achieve higher compression rates by first
applying DWT and DCT on individual components RGB. After
applying this image is quantized to calculate probability index
for each unique quantity so as to find out the unique binary code
for each unique symbol for their encoding. Finally the Huffman
compression is applied. Results show that the coding
performance can be significantly improved by the hybrid DWT,
DCT and Huffman coding algorithm.
Keywords- Image compression, hybrid, quantization, DWT,
DCT, Huffman encoding, medical image.
I. INTRODUCTION
In a digital true- color images, each color component is
quantized with 8 bits, and so a color is specified with 24 bits. As
a result, there are 2^24 possible colors for the image.
Furthermore, a color image usually contains a lot of data
redundancy and requires a large amount of storage space. In
order to lower the transmission and storage cost, image
compression is desired. Most color images are recorded in RGB
model, which is the most well known color model. However,
RGB model is not suited for image processing purpose. For
compression, a luminance-chrominance representation is
considered superior to the RGB representation. Therefore, RGB
images are transformed to one of the luminance-chrominance
models, performing the compression process, and then transform
back to RGB model because displays are most often provided
output image with direct RGB model.
Discrete wavelet Transform:
For the compression of image, firstly the DWT is applied on the
image using Thresholding value. Threshold values neglects the
certain wavelet coefficients.for doing this one has to decide the
value of threshold. Value of thresholf affects the quality of
compresed image. Thresolding can be of two types:
Hard threshold: If x is the set of wavelet coeficients, then
threshold value t is given by,
i.e. all the values of x which are less than threshold t are equated
to zero.
II. SOFT THRESHOLD
In this case, all the coefficients x lesser than threshold t are
mapped to zero. Then t is subtracted from all x ¸ t. This condition
is depicted by the following equation:
Fig: A Quantized Technique Can Be Applied On Few/All
OfTheseFinal Sub Images To Get The Compression
Discrete Cosine Transform
discrete Fourier transform: it transforms a signal or image from
the spatial domain to the frequency The discrete cosine
transform (DCT) helps separate the image into parts (or spectral
sub-bands) of differing importance (with respect to the image's
visual quality). The DCT is similar to the domain. A discrete
cosine transform (DCT) expresses a sequence of finitely many
data points in terms of a sum of cosine functions oscillating at
different frequencies. DCTs are important to numerous
applications in science and engineering, from lossy
compression of audio (e.g. MP3) and images (e.g. JPEG) (where
small high-frequency components can be discarded), to spectral
for the numerical solution of partial differential equations. The
use of cosine rather than sine functions is critical in these
applications: for compression, it turns out that cosine functions
are much more efficient (as described below, fewer are needed to
approximate a typical signal), whereas for differential equations
the cosines express a particular choice of boundary conditions.
In particular, a DCT is a Fourier-related transform similar to the

2. Integrated Intelligent Research (IIR) International Journal of Web Technology
Volume: 02 Issue: 01 June 2013 Page No.21-24
ISSN: 2278-2389
26
discrete Fourier transform (DFT), but using only real numbers.
DCTs are equivalent to DFTs of roughly twice the length,
operating on real data with even symmetry (since the Fourier
transform of a real and even function is real and even), where in
some variants the input and/or output data are shifted by half a
sample. There are eight standard DCT variants, of which four are
common
Comprassion Analysis Between DWT and DCT
( BASIS FUNCTION OF 8X8 DCT MATRIX)
The steps of the proposed compression algorithm based on
DWT are described below:
Decompose
Choose a wavelet; choose a level N. Compute the wavelet.
Decompose the signals at level N.
Threshold detail coefficients
For each level from 1 to N, a threshold is selected and hard
thresholding is applied to the detail coefficients
.
Reconstruct
Compute wavelet reconstruction using the original
approximation coefficients of level N and the modified detail
coefficients of levels from 1 to N.
The Result Of Taking The Dct. The Numbers In Red Are The
Coefficients That Fall Below TheSpecified Threshol
III. IMAGE QUALITYEVOLUTION
Image quality is measured using signal to noise
ratio(PSNR)And mean square error(MSE) represent the
cumulative Squared error between the compressed and the
original Image .the lower value of MSE, the lower and better
Picture quality.
To calculate PSNR Peak Signal –to-noise ratio is the ratio
between the maximum possible power of a signal to the power of
corrupting noise that affects the fidelity of its representation.
Comparative Study of DCT & DWT
Table 1. shows comparative study between DCT and DWT in
terms of PSNR (in Bb) and MSE at different threshold values
for different test images. A plot between PSNR and threshold is
drawn for different test images as shown in Fig.4 which shows
that the performance of DCT is almost similar to DWT at lower
threshold values but for higher threshold DWT gives gives better
visual image quality than DCT
IV. CONCLUSION
In this paper a comparison of PSNR values for 8x8 DCT gives
similar results as DWT but for higher threshold,the quality of
images compressed using DWT slowly degrades,while the
quality of 8x8 DCT compressed images deteriorates rapidly. At
lower threshold DCT should be used but at higher threshold
DCT cannot be used because of poor image quality.There are
noticeable blocking artifacts in the DCT images at higher
threshold values.However,DWT maintains good visual quality
at high threshold.
(a)

3. Integrated Intelligent Research (IIR) International Journal of Web Technology
Volume: 02 Issue: 01 June 2013 Page No.25-27
ISSN: 2278-2389
27
Comparison Of Psnr Values At Different Thresholds For Dct And
Dwt For Test Images (A) Cameraman (B) Lena (C)Woman (D)
Woman Dark Hair (E) Elaine
Figure 5: Comparison Of Visual Image Quality Of Reconstructed
Image For Dct And Dwt For Test Images (A) Cameraman For
Threshold 30 (B) Lena For Threshold 40 (C) Elaine For Threshold
60 (D) Woman For Threshold 70 (E)Woman Dark Hair
REFREENCES
[1] Sonja Grgic,Mislav Gric,”Performance Analysis of Image Compression
Using Wavelets,”IEEE transcations on industrial
electronics,vol.48,no.3,June 2001
[2] Kamrul Hasan Talukder and Koichi Hrada,”Discrete Transform for Image
Compression and A Model of Parallel Image Compreesion Scheme for
Formal Verification”,Proceedings of the world Congress on Engineering
2007 Vol1,WCE 2007,July 2-4,2007,London,UK.
[3] Kamrul Hasan Talukder and Koichi Hrada,”Haar Wavelet Based
Approach for Image Compression and Quality Assessment of Compressed
Image,”IAENG International Journal of Applied Mathematics,36:1,IJAM
36 1 9,Advance omline publication: 1 February 2007
[4] Javed Akhtar,Dr Muhammad Younus Javed.”Image Compression with
Different Types of Wavelets”,IEEE-ICET 2006 2nd international
conference on emerging technologies,Peshawar,Pakistan13-14 November
2006.
[5] Nikolay Ponomarenko,Vladimir Lukin, Karen Egiazarian,Jaakko
Astola,”DCT Based High Quality Image Compression”,Proceedings of
14th Scandinavian Conference on Image Analysis,SCIA 2005,Joensuu,
Finland.
[6] DannyBlanco,Elliot Ng,Charlie Ice,BryanGrandy,”Compression-
Dropping
theDCTCOEFFICIENTS”Connexionsmodule:m13173,Version1.6:Dec21
,20054:17pmUS/Centralyhttp://creativecommons.org/licenses/by/2.0/
[7] K.Sarita,V.Ritu,Meel V.S”Performance Analysis of Image Compression
with Different Wavelet Families,”2nd National Conference Mathematical
Techniques:Emerging Paradigms for Electronics and IT
Industries,September 26-28,2008, MATEIT-2008,New Delhi