Journal of Signal and Information Processing, 2013, 4, 364-369
Published Online November 2013 (
Open Access JSIP
Compression of MR Images Using DWT by Comparing
RGB and YCbCr Color Spaces
Agrawal Jayprkash1*, Ritu Vijay2
1Department of Electronics and Communication Engineering, Jagnnath Gupta Institute of Engineering and Technology, Jaipur, India;
2AIM & ACT, Banasthali University, Vanasthali, India.
Email: *
Received August 6th, 2013; revised September 6th, 2013; accepted September 16th, 2013
Copyright © 2013 Agrawal Jayprkash, Ritu Vijay. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper consists of a lossy image compression algorithm dedicated to the medical images doing comparison of RGB
and YCbCr color space. Several lossy/lossless transform coding techniques are used for medical image compression.
Discrete Wavelet Transform (DWT) is one such widely used technique. After a preprocessing step (remove the mean
and RGB to YCbCr transformation), the DWT is applied and followed by the bisection method including thresholding,
the quantization, dequantization, the Inverse Discrete Wavelet Transform (IDWT), YCbCr to RGB transform of mean
recovering. To obtain the best compression ratio (CR), the next step encoding algorithm is used for compressing the
input medical image into three matrices and forward to DWT block a corresponding containing the maximum possible
of run of zeros at its end. The last step decoding algorithm is used to decompress the image using IDWT that is applied
to get three matrices of medical image.
Keywords: Magnetic Resonance Image (MRI); RGB; YCbCr Transform; Block-Based DWT; Transform Coding
1. Introduction
The basic objective of image compression is to reduce
the size of image data for transmission or store in an effi-
cient manner, while maintaining the suitable quality of
reconstructed images [1-3]. The easy and reliable digital
transmission and storage of biomedical images would be
a tremendous boon to the medical practices. This can
help in instant availability of earlier imaging studies
when patients are re-admitted [4-6]. Both Medical and
surgical teams indulging on patient care could have
simultaneous access to imaging studies on monitors
throughout the hospital. This long-term digital archiving
or rapid transmission is prohibitive without the use of
image compression to reduce the file sizes.
There are two basic types of image compression
The first lossless compression scheme encodes and
decodes the data perfectly and the reconstructed image
matches exactly with the original image, which means
there is no loss of data with no degradation. In this
scheme the coding techniques are Huffman encoding,
entropy encoding, and run length ending.
The second lossy compression scheme is used for the
sake of using a minimum storage space. In this scheme
there is a trade-off between compression and image qual-
ity. In lossy compression, the final decompressed image
must be visually lossless and consist of removing the
redundant information in adjacent pixels to minimize the
number of bits [7-9].
In preprocessing step, many decorrelating transforms
like YCbCr, YUV, YIQ [10-12] are used to reduce the
correlation between the R, G and B plane. We can pref-
erably use one of these color space transforms before the
application of wavelet transform. In this paper we are
considering the YCbCr transform to reduce the correla-
tion between the R, G and B space [13].
Block-based DWT [9,14] Shown in Figure 1, decom-
poses a broadband signal into two subbands with smaller
bandwidths and slower sample rates. A series of HP and
LP FIR filters are used to repeatedly divide the input
frequency range. The input signals are in the form of
frames having a frame size as multiple of 2n, where n is
the number of levels. Each unit consists of an LP and HP
FIR filter pair. The halfband filters with a cutoff fre-
*Corresponding author.
Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces 365
quency of Fs/4 are obtained by decimating the output of
each LP and HP filter by a factor of 2.
The aim of this paper is to evaluate the performance of
lossy medical image compression wavelet transforms
followed by wavelet encoders experiments which were
performed by using magnetic resonance images (MRI) as
test images. The performances of the medical images
were evaluated in terms of peak signal-to-noise ratio
(PSNR), bit rate (bpp) and the compression ratio (CR). In
the last step, decoding algorithm is used to decompress
the image using IDWT which is applied to get three ma-
trices of medical image.
2. Methodology
The block diagram of DWT based medical image com-
pression/decompression model shown in Figure 2. In
this paper, the method is dedicated to lossy medical im-
age compression DWT based and two phases of com-
pression/decompression. The input to the system is a
medical image and the output is the compressed one. The
compression technique is built with several steps and
each will be explained in details.
2.1. RGB to YCbCr Transformation
RGB is not very efficient when dealing with real-word
images. All three RGB components need to be of equal
bandwidth to generate any color within the RGB color
cube. The result of this is a frame buffer that has the
same pixel depth and display resolution for each RGB
component. The processing an image with the RGB color
space is usually not the most efficient method. To modify
the intensity or color of a given pixel, the three RGB
values must be read from the frame buffer, with the steps
of intensity or color calculation, performing desired
modifications, calculating new RGB values and at last
returning back to the frame buffer. If the system had ac-
Figure 1. Block-based DWT.
Figure 2. Compression algorithm scheme. (a) Compression
phase; (b) Decompression phase.
cess to an image stored directly in the intensity and color
format, some processing steps would be faster. For these
and other reasons, many video standard uses luma and
two color difference signals. The most common are the
YUV, YIQ and YCbCr color spaces [10-12].
In this paper the RGB to YCbCr transformation, the
mean value of three plane images R, G and B are re-
moved and the almost signal energy of the new trans-
formed YCbCr image is contained in the Y plane. Con-
sequently, we can achieve high compression ratio in the
Cb and Cr without losses in quality of compressed image
when returned to the original RGB space.
The transformation from RGB to YCbCr performed
respecting to
Y1665.738 129.05725.064R
Cb12837.94574.494 112.439G
Cr128112.43994.15418.285 B
 
 
 
 
 
 
where R, G and B take the typical values from 0 to 255
(8-bit precision), Y is the same range (0 - 255), and Cb,
Cr components are into the range (16 - 240).
The inverse transformation is expressed by
R1.0 0.0001.371Y
G1.00.3360.698 Cb
B1.0 1.7320.000Cr
 
 
 
 
 
 
A original MRI image shown in Figure 3(a) and we
define the RGB to YCbCr transformation for removing
the mean values of R, G, and B plane. Figures 3(b)-(d)
are the block displays which show an M-by-N matrix
element values to specified range of RGB colors. Fig-
ures 3(e)-(g) are the block displays which specified
range of YCbCr colors. It confirms that RGB to YCbCr
transformation approach is necessary to get superier per-
2.2. Block Based DWT Transform
For any color image, after the RGB to YCbCr transfor-
mation, each one of the new three planes YCbCr are par-
titioned to blocks and each block is transformed by DWT.
The DWT blocks perform a single-level one-dimen-
sional wavelet decomposition with respect to either a
particular wavelet (Daubechies, Coiflets, Symlets, Dis-
crete Meyer, Biorthogonal, Reverse Biorthogonal) [9,
14] or particular wavelet LP and HP decomposition fil-
As shown in Figure 4 the original signals are firstly
decomposed into two subspaces, low-frequency subband
and high frequency subband. It first scanned in a hori-
zontal direction and passed through LP and HP decom-
position filters producing low frequency as well as
high-frequency data in the horizontal direction. Filtered
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Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces
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Figure 3. (a) Original test MRI image; (b)-(d) are the block displays an M × N matrix element values to specified range of
RGB colors; (e)-(g) are the block displays specified range of YCbCr colors.
Figure 4. Pyramidal algorithm of one-level forward DWT
output data are then scanned in a vertical direction and
again these filters are applied separately to generate dif-
ferent frequency subbands. The transform generates sub-
bands LL, LH, HL and HH each with one-fourth the size
of the original image. Most of the energy is concentrated
in low-frequency subband LL, whereas higher-frequency
subbands LH, HL and HH contain detailed information
of the image in vertical, horizontal and diagonal direc-
tions, respectively. For higher level decomposition, DWT
can be applied again to the LL subband recursively in a
similar way to further compact energy into fewer low-
frequency coefficients. The appropriate choice of filters
for the transform is very important to achieve high cod-
ing efficiency.
2.3. Quantization and Transform Coding
A transform coder decomposes a signal in an orthogonal
basis and quantizes the decomposition coefficients [15].
The distortion of the restored signal is minimized by op-
timizing the quantization, the basis, and the bit allocation.
It is desirable to perform quantization by dividing the
transformed coefficients by quantization value. For low
frequency, coefficients are divided by smaller values
while the high frequency coefficients are divided by lar-
ger values
In this paper, we code the data using transform coding
scheme of following steps:
Source coding is to represent information in bits, with
the natural aim of using a small number of bits. The “in-
formation” is denoted by a real column vector
or a sequence of such vectors. A vector might be formed
from pixel values in an image; K. N pixels can be ar-
ranged as a sequence of K vectors of length N. The vec-
tor length N is defined such that each vector in a se-
quence is encoded independently.
Transform codes are the most used source codes be-
cause they are easy to apply at any rate and even with
very large values of N. The essence of transform coding
is the modularization shown in the Figure 5 first, an in-
vertible linear transform of the source vector x is com-
puted, producing y = Tx. Each component of y is called a
transform coefficient. The N transform coefficients are
then quantized independently of each other by N scalar
A quantizer q is a mapping from a source alphabet
to a reproduction code. It can be decomposed into
two operations
. The lossy encoder
is specified by a partition of into partition cells
  and the reproduction de-
coder is . If N = 1, the quantizer is called a
scalar quantizer and if N ˃ 1, it is vector quantizer.
Several quality measures can be found in open litera-
ture of the field. The mean square error (MSE) and the
Peak signal to noise ratio (PSNR) are the most used
Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces 367
Figure 5. Transform coding scheme: A source code can be
decomposed so that the encoder is a linear transform T and
a set of N scalar quantizer encoders. In decoder are N sca-
lar quantizer decoders and another linear transform U.
Usually U = T1.
Mean square error (MSE) is the some sort of average
or sum of the squares of the error between two images.
For M × N images u(m, n) and û(m, n), the least square
error (LSE) is,
LSE, ,
umn umn
MN 
 (3)
and average LSE is called the Mean square error (MSE),
MSE, ,
Eumn umn
MN 
 (4)
where u(m, n) and û(m, n) are the original and recon-
structed intensities belonging to R, G and B plane. The
PSNR is defined in decibels (dB) as,
where 2
is the variance of the original image. For
medical image we used the relation given as
  
The size of the compressed image is evaluated with the
CR or Bit-rate per pixel (BPP), defined by
Original image size in bits
CR compressed image in bits
The various steps during compression and decompres-
sion algorithms are summarized as follows:
Compression algorithm:
1) Input: Medical image I(RGB);
2) Break the input image into three matrices I(R), I(G)
and I(B);
3) Transformation of the I(R), I(G) and I(B) matrices
into I(Y), I(Cb) and I(Cr);
4) Perform DWT transform of sub-band I(Y), I(Cb)
and I(Cr) separately;
5) Transform coder decomposes and quantizes the de-
composition coefficients;
6) Output: Compressed medical image I(YCbCr).
Decompression algorithm:
1) Input: Compressed medical image I(YCbCr);
2) Inverse sub-band transform and dequantization of
reproduction code;
3) IDWT is applied and get Î(Y), Î(Cb) and Î(Cr);
4) Transformation of the Î(Y), Î(Cb) and Î(Cr) into
Î(R), Î (G) and Î (B);
5) Convert Î(R), Î(G) and Î(B) to Î(RGB);
6) Output: Decompressed medical image Î(RGB).
3. Results
Various results got hold of and summarized after per-
forming different experiment with YCbCr color space on
standard medical MR images (Figure 6). The YCbCr
transform applied in RGB color space and the respective
reconstructed images are shown in Figure 7. Different
size images were tested on the different color images
both in the RGB space and in the YCbCr color space.
Table 1 shows the results demonstrating, the superior-
ity of performance of the proposed technique when
working in the YCbCr domain. From the Table, it ob-
serve that PSNR in YCbCr color space increased and the
percentage of increased PSNR in Cb and Cr color space
is high. Similarly it is observed that, bpp is high in
YCbCr color space as compare to RGB color space.
4. Discussion
The major objective of image compression is to reduce
the size of the image data for transmission or to obtain
the best visual quality with minimum bit utilization. The
(a) (b) (c) (d) (e)
(f) (i) (j)
Figure 6. Original test medical MR images. (a) MR1; (b)
MR2; (c) MR3; (d) MR4; (e) MR5; (f) MR6; (g) MR7; (h)
MR8; (i) MR9 and (j) MR10.
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
Figure 7. Reconstructed medical MR images. (a) MR1; (b)
MR2; (c) MR3; (d) MR4; (e) MR5; (f) MR6; (g) MR7; (h)
MR8; (i) MR9 and (j) MR10.
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Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces
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Table 1. PSNR, and bpp for different test medical images of RGB and YCbCr color space.
PSNR bpp
Images R G B Y Cb Cr R G B Y Cb Cr
MR1 11.83 11. 83 11. 84 12.91 57.93 58.63 0.279 0.279 0.278 0.301 0.502 0.502
MR2 13.28 13.28 13.25 14.26 50.52 47.54 0.225 0.226 0.205 0.253 0.491 0.503
MR3 14.66 14.61 14.76 15.85 36.02 34.1 0.293 0.289 0.287 0.310 0.500 0.504
MR4 11.66 11. 54 11. 57 12.49 43.85 41.85 0.226 0.223 0.226 0.255 0.503 0.503
MR5 16.84 16.84 16.84 18.08 42.94 60.78 0.226 0.223 0.226 0.255 0.503 0.503
MR6 17.4 17.29 17.24 18.47 52.93 51.08 0.075 0.082 0.088 0.131 0.505 0.498
MR7 18.37 18.37 18.37 19.61 147 147 0.118 0.118 0.118 0.163 0.502 0.502
MR8 18.38 18.38 18.38 19.61 147 147 0.141 0.141 0.141 0.183 0.502 0.502
MR9 18.62 18.62 18.62 19.85 147 147 0.140 0.140 0.140 0.182 0.502 0.502
MR10 16.57 16.57 16.57 17.81 147 147 0.268 0.268 0.268 0.292 0.502 0.502
15.761 15.733 15.744 16.894 87.21988.1980.188 0.190 0.189 0.223 0.502 0.502
parameters PSNR and bpp are generally used for assess-
ing the quality of the reconstructed image. Earlier studies
[1-8,13,14] discussed the image compression and [4-6]
addressed the compression of images. The results were
obtained in the present study, using the preprocessing
step followed by the bisection method including thresh-
olding, the quantization, dequantization and the IDWT
were compared with the 3-D transforms, such as discrete
Hartley transform (DHT), discrete cosine transform
(DCT) and discrete Fourier transform (DFT) [6]. From
Table 1 high bit rate result improved the quality of the
reconstructed image. The performance of the MRI com-
pression using algorithm yielded better results than other
transforms. It can be concluded that YCbCr color space
was found to be better PSNR than the RGB color space.
The user can improve the bit rate and CR depending on
his reconstructed image quality requirements.
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