A Review on Image Compression using DCT and DWT

IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 10, 2015 | ISSN (online): 2321-0613
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A Review on Image Compression using DCT and DWT
Madhu Ahuja1
Sanjivani Shantaiya2
1,2
Department of Computer Science & Engineering
1,2
DIMAT, Raipur, India
Abstract— Image Compression addresses the matter of
reducing the amount of data needed to represent the digital
image. There are several transformation techniques used for
data compression. Discrete Cosine Transform (DCT) and
Discrete Wavelet Transform (DWT) is mostly used
transformation. The Discrete cosine transform (DCT) is a
method for transform an image from spatial domain to
frequency domain. DCT has high energy compaction
property and requires less computational resources. On the
other hand, DWT is multi resolution transformation. The
research paper includes various approaches that have been
used by different researchers for Image Compression. The
analysis has been carried out in terms of performance
parameters Peak signal to noise ratio, Bit error rate,
Compression ratio, Mean square error. and time taken for
decomposition and reconstruction.
Key words: Compression, DCT, DWT, MSE, SNR, PSNR
I. INTRODUCTION
An image can be defined as a matrix of pixel or intensity
values. Image compression is used to reduce the redundancy
and randomness present in the image because to increase the
storing capacity and efficiency level of the images.
Therefore it is essential to compress the images by storing
only the required information needed to reconstruct the
image. To compress any image, redundancy must be
removed. Sometimes images having large areas of same
color will have large redundancies and similarly images that
have frequent and large changes in color will be less
redundant and harder to compress.
II. FUNDAMENTALS OF IMAGE COMPRESSION TECHNIQUES
A digital image, or "bitmap", consists of a grid of dots, or
"pixels", with each pixel defined by a numeric value that
represents its colour. A Typical characteristic of most
images is that the neighboring pixels are correlated and
therefore contain redundant information. The foremost task
then is to find less correlated representation of the image. In
general, there are three types of redundancy:
A. Coding Redundancy
Use smaller code words for the commonly used gray levels
and longer code words for the less commonly used gray
levels. This is an example of Variable Length Coding. To
reduce coding redundancy from an image we use Huffman
technique where we assign fewer bits to the more probable
gray levels than to the less probable ones to achieve
sufficient data compression[10]
B. Inter Pixel Redundancy
Another important type of data redundancy is inter pixel
redundancy, which is directly related to the inter pixel
correlations within an image. Because the value for any
given pixel can be reasonable predicted from the value of its
neighbours, the information carried by individual pixels is
relatively small. Much of the visual contribution of a single
pixel to an image is redundant; it could have been guessed
on the basis of its neighbor’s values. A variety of names,
including spatial redundancy, geometric redundancy, and
inter frame Redundancies have been given to refer to these
inter pixel dependencies.[10]
C. Psycho Visual Redundancy
Human perception of the information in an image normally
doesn't involve quantitative analysis of every pixel or
luminance value in the image. In general, an observer
searches for distinguishing features such as edges or textural
regions and mentally combines them into recognizable
groupings. The brain then correlates these groupings with
prior knowledge in order to complete the image
interpretation process. So eye doesn't respond with equal
sensitivity to all visual information. Certain information
simply has less relative importance than other information in
normal visual processing. This information is called psycho
visually redundant. To reduce psycho visual redundancy
quantizer is used. Therefore, the elimination of psycho
visually redundant.[10]
III. WHAT ARE THE DIFFERENT CLASSES OF COMPRESSION
TECHNIQUES?
Two ways of classifying compression techniques are
mentioned here.
A. Lossless vs. Lossy compression
In lossless compression schemes, After compression the
reconstructed image is numerically identical to the original
image. However lossless compression can only achieve a
modest amount of compression. In lossy compression An
image reconstructed is degraded relative to the original. This
is because lossy compression scheme completely discards
redundant information. However, lossy schemes are capable
of achieving much higher data compression. Under normal
viewing conditions, no visible loss is perceived (visually
lossless).
B. Predictive vs. Transform coding
In predictive coding, information already available or sent is
used to predict future values, and the difference is coded.
Since this is done in the image or spatial domain, it is
relatively simple to implement and is readily adapted to
local image characteristics. Differential Pulse Code
Modulation (DPCM) is an example of predictive coding[4].
Transform coding, on the other hand, first transforms the
image from its spatial domain representation to a different
type of representation using transformation techniques and
then codes the transformed values (coefficients). This
method provides greater data compression compared to
predictive methods, although at the expense of greater
computation.

(IJSRD/Vol. 3/Issue 10/2015/032)
IV. VARIOUS COMPRESSION TECHNIQUES
A. DCT-Based Image Coding Standard
Discrete Cosine Transform (DCT) exploits cosine functions,
it transform a signal from spatial representation into
frequency domain. The DCT represents an image as a sum
of sinusoids of varying magnitudes and frequencies. DCT
has the property that, for a typical image most of the
visually significant information about an image is
concentrated in just few coefficients of DCT .
1) Forward DCT
1 1
0 0
2 (2 1) (2 1)
( , ) ( ) ( ) ( , )cos cos
2 2
for 0,..., 1 and 0,..., 1
1/ 2 for 0
where 8 and ( )
1 otherwise
N N
x y
x u y v
F u v C u C v f x y
N N N
u N v N
k
N C k
  
 
    
    
   
   
 
  


2) Inverse DCT:
1 1
0 0
2 (2 1) (2 1)
( , ) ( ) ( ) ( , )cos cos
2 2
for 0,..., 1 and 0,..., 1 where 8
N N
u v
x u y v
f x y C u C v F u v
N N N
x N y N N
  
 
    
    
   
    

Nageswara Rao Thota et al. (2008) [3] proposes Image
Compression Using Discrete Cosine Transform. DCT
images are divided into blocks of 8x8 or 16x16 or bigger.
The problem with these blocks is that when the image is
reduced to higher compression ratios, these blocks become
visible One of the main problems and the limitation of the
DCT is the blocking effect. The following table1 shows the
test reports in the image compression using DCT
The following table1 shows the test reports in the
image compression using DCT
Maneesha Gupta et al. ( 2012) [5] proposes some
simple functions to compute the DCT and to compress
images. Image Compression is studied using 2-D DCT. The
original image is transformed in 8-by-8 blocks and then
inverse transformed in 8-by-8 blocks to form the
reconstructed image. The inverse DCT would be performed
using the subset of DCT coefficients. The error image (the
difference between the original and reconstructed image)
would be displayed. The results shows that DCT exploits
inter pixel redundancies to render excellent decorrelation for
most natural images. Therefore all transform coefficients
can be encoded independently without compromising
coding efficiency. In addition, the DCT packs energy in the
low frequency coefficients. Therefore, some of the high
frequency coefficients can be discarded without degradation
in image quality.
B. Image Compression by Wavelet Transform:
A "wavelet" mathematical function is used to divide a given
function or continuous-time signal into different wave
signals. It is the delegation of a function by wavelets. The
Haar wavelet is the simplest wavelet. The limitation of the
Haar wavelet is that it is not continuous, and therefore not
differentiable. The Haar wavelet's mother wavelet function
ψ(t) can be described as
and its scaling function φ(t) can be described as
Sonja Grgic, et al. (2009) [6] proposes a set of
wavelet functions (wavelets) for implementation in image
compression system and to highlight the benefit of this
transform relating to new methods. The consequences of
different wavelet functions, image contents and compression
ratios are assessed. A comparison with a discrete-cosine-
transform-based compression system is given. The final
choice of optimal wavelet in image compression application
depends on image quality and computational complexity.
Amina Khatun et al. (2012) [7] have proposed the
new image compression scheme with pruning based on
discrete wavelet transformation (DWT). The effectiveness
of the algorithm has been justified over some real images,
and the performance of the algorithm has been compared
with different common compression standards.
Experimental results demonstrate that the proposed
technique provides sufficient high compression ratios
compared to different compression techniques. A new image
compression scheme based on discrete wavelet transform is
proposed which provides high compression ratios with no
considerable degradation of image quality. The effectiveness
and robustness of this approach has been justified using a set
of real images. To demonstrate the performance of the
proposed method, a comparison between the proposed
technique and other common compression techniques has
been revealed. From the experimental results it is evident
that, the proposed compression technique gives better
performance compared to other traditional techniques. Both
DCT and DWT are very popular compression techniques for
colour and grey level images. There are many flavours in
each technique. In this a hybridised form of the techniques
are implemented for compressing images.
Aisha Fernandes, Wilson Jeberson et al(2014)[11]
proposes wavelet transform and the Antonini 7/9 filter [5]
for compressing an image. It is thus seen that images
compressed decompressed using the proposed wavelet based
compression algorithm (WCP) produces consistently better
images and a higher PSNR (Peak signal to noise ratio) than
the jpeg compression algorithm at the same compression
percentage.
(a) (b) (c)

Fig. 1: Comparison of visual image quality for the test
image cameraman.bmp at a compression ratio of 9:1. (a)
Original image (b) wcp compressed image (c) Jpeg
compressed image.
C. Hybridised DCT and DWT Compression
Prabhakar.Telagarapu, A.Lakshmi.Prasanthi, G.Vijaya
Santhi, V.Jagan Naveen et al (2011)[1] proposes an DCT
and DWT for image compression and decompression. By
taking several images as inputs, it is observed that Mean
Square Error is low and Peak Signal to Noise Ratio is high
in DWT than DCT based compression. From the results it is
concluded that on the basis of compression ratio overall
performance of DWT is better than DCT. In Discrete Cosine
Transform image need to be “blocked”, correlation is found
across the block boundaries which can't eliminated which
results in noticeable and annoying, blocking artifacts‟
particularly at low bit rates. Wavelets are good to represent
the point singularities and it cannot represent line
singularities.
(a) (b)
Fig. 2: shows (a) Original Image (b) Original Histogram
(a) (b)
Fig 3: shows (a) DCT decompressed image (b) DCT
decompressed histogram
(a) (b)
Fig. 4: shows (a) DWT decompressed image (b) DWT
decompressed histogram
Vellaiappan Elamaran et al. (2012) [2] proposes a
Comparison of DCT and Wavelets in Image coding. Fourier
based transforms (e.g. DCT and DFT) are efficient in
exploiting the low frequency nature of an image. The high
frequency coefficients are coarsely quantized, and therefore
the reconstructed image at the edges will have poor quality.
On the other hand, wavelets are efficient in representing non
stationary signals because of the adaptive time-frequency
window. So the Discrete Wavelet Transform (DWT) is
applied in an image and the PSNR of both DCT and DWT is
compared. A comparison and analysis and of image
compression using DCT and DWT is demonstrated.
K.Saraswathy et al. (2013) [4] have proposes an orthogonal
approximation for the 8 point Discrete Cosine Transform
(DCT). The proposed transformation matrix contains only
ones and zeros. Bit shift operations and multiplication
operations are absent. The approximate transform of DCT is
obtained to meet the low complexity requirements. The
hybrid results obtained from the work will shows clearly the
efficiency of the proposed transform in image compression.
Finally, the new approximation offers the users another
options for mathematical analysis and circuit
implementations. The new approximate transform matrix
has rows constructed from a different mathematical structure
when compared to DCT. These rows can be considered in
the design of hybrid algorithm which take advantage of the
best matrix rows from the existing algorithm aiming at novel
improved approximate transform.
According to Author Ch.Sathi Raju and D.V.Rama
Koti Reddy et al (2015) [12] Compression is a serious
problem in capsule endoscopy applications. It dictates the
power consumption characteristics and the capsule life. In
this paper a hybrid DCT and DWT compression method is
employed to capitalise the advantages of both the
techniques. It involves in applying a three level DWT on the
input image. The DWT compressed image is taken for
quantization and further zeros are eliminated from the
matrices. Further is subjected to compression using
arithmetic coding(AC). Now 1D DCT is applied to the LL3
image and followed by the process of quantization and
eliminating zeros and applying arithmetic coding is repeated
for satisfactory compression. The color data is extracted
from the compressed image. This color data is further serves
as input to the decompression section. The decompression
process is simply reverse to the compression process. The
results pertaining to the simulated experiment are presented
in this section. Lena images are considered initially and the
proposed technique is applied on it. The corresponding
original and decompressed images are presented in Fig.5
(a) (b)
Fig. 5: 'Lena' image (a) Original and (b) decompressed
V. CONCLUSION AND FUTURE WORK
This paper represents the concept of compression and varied
technologies used in the image compression comparing the
performance of compression technique identical data sets
and performance measure are used. In this paper

comparative analysis of varied Image compression
techniques for different images is done based parameters
mean square error (MSE), peak signal to noise ratio (PSNR).
DWT produces higher results without losing more
information of image. Pitfall of DWT is, it requires more
processing power. DCT overcomes this disadvantage since
it needs less processing power, but it produces less
compression ratio. DCT based standard JPEG uses blocks of
image. In wavelet, there is no need to block the image.
REFERENCES
[1] Telagarapu, Prabhakar, et al. "Image Compression
Using DCT and Wavelet Transformations."
International Journal of Signal Processing, Image
Processing and Pattern Recognition 4.3 (2011).
[2] Elamaran, V., and A. Praveen. "Comparison of DCT
and wavelets in image coding." Computer
Communication and Informatics (ICCCI), 2012
International Conference on. IEEE, 2012.
[3] NageswaraRaoThota, Srinivasa Kumar Devireddy.
"Image Compression Using Discrete Cosine
Transform." Georgian Electronic Scientific Journal:
Computer Science and Telecommunications 3 (2008).
[4] Saraswathy, K., D. Vaithiyanathan, and R.
Seshasayanan. "A DCT approximation with low
complexity for image compression." Communications
and Signal Processing (ICCSP), 2013 International
Conference on. IEEE, 2013.
[5] Gupta, Maneesha, and Amit Kumar Garg. "Analysis Of
Image Compression Algorithm Using DCT." (2012).
[6] Grgic, Sonja, Mislav Grgic, and Branka Zovko-Cihlar.
"Performance analysis of image compression using
wavelets." Industrial Electronics, IEEE Transactions
(2001).
[7] Chowdhury, M. Mozammel Hoque, and Amina Khatun.
"Image Compression Using Discrete Wavelet
Transform." International Journal of Computer Science
(2012).
[8] Deshlahra, Archana, G. S. Shirnewar, and A. K. Sahoo.
"A Comparative Study of DCT, DWT & Hybrid
(DCTDWT) Transform." (2013).
[9] Harjeetpal singh, Sakhi Sharma. “Hybrid Image
Compression Using DWT, DCT & Huffman Encoding
Techniques” vol. 2, issue 10 (2012).
[10]Chander mukhi , Pallavi Nayyar, Mandeep Singh Saini
“Improved Image Compression using Hybrid
Transform” International Journal of Science and
Research (IJSR), India Online ISSN: 2319-7064.

A Review on Image Compression using DCT and DWT

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