SPECIAL ISSUE PAPER
A novel medical image compression using Ripplet transform
Sujitha Juliet • Elijah Blessing Rajsingh •
Kirubakaran Ezra
Received: 14 December 2012 / Accepted: 12 July 2013
� Springer-Verlag Berlin Heidelberg 2013
Abstract In spite of great advancements in multimedia
data storage and communication technologies, compression
of medical data remains challenging. This paper presents a
novel compression method for the compression of medical
images. The proposed method uses Ripplet transform to
represent singularities along arbitrarily shaped curves and
Set Partitioning in Hierarchical Trees encoder to encode
the significant coefficients. The main objective of the
proposed method is to provide high quality compressed
images by representing images at different scales and
directions and to achieve high compression ratio. Experi-
mental results obtained on a set of medical images dem-
onstrate that besides providing multiresolution and high
directionality, the proposed method attains high Peak
Signal to Noise Ratio and significant compression ratio as
compared with conventional and state-of-art compression
methods.
Keywords Medical image compression � Ripplet
transform � SPIHT � Multiresolution � Telemedicine
1 Introduction
With the great development in the field of medical imag-
ing, analysis and compression of medical images are the
major challenges in healthcare services. In telemedicine,
medical images generated from medical centers with effi-
cient image acquisition devices such as Computed
Tomography (CT), Magnetic Resonance Imaging (MRI),
Ultrasound (US), Electrocardiogram (ECG) and Positron
Emission Tomography (PET) need to be transmitted con-
veniently over the network for perusal by another medical
expert. These huge amounts of data cause a high storage
cost [1] and heavy increase of network traffic during
transmission [2]. Therefore, compression of medical ima-
ges is essential in order to reduce the storage and band-
width requirements [3, 4]. Apart from preserving vital
information in the medical images, high compression ratio
and the ability to decode the compressed images at various
qualities are the major concerns in medical image com-
pression [5].
Many advanced image compression methods have been
proposed in response to the increasing demands for medi-
cal images. Among the proposed methods, much interest
has been focused on resolving 2D singularities and
attaining the desirable characteristics such as high Peak
Signal to Noise Ratio (PSNR), and little work has been
done on efficient representation of images at different
scales and different directions. Grounded on this motiva-
tion, this paper proposes a compression method for medical
images which provides hierarchical representation of ima-
ges by representing singularities along arbitrarily shaped
curves. This method employs a recently introduced family
of transforms termed as Ripplet transform [6]. The Ripplet
transform has been proposed as an alternative to wavelet
transform to represent images at different scales and
S. Juliet (&)
Department of Information Technology, Karunya University,
Coimbatore, India
e-mail: [email protected]
E. B. Rajsingh
School of Computer Science and Technology, Karunya
University, Coimbatore, India
e-mail: [email protected]
K. Ezra
Bharat Heavy Electricals Limited, Trichy, India
e-mail: [email protected]
123
J Real-Time Image Proc
DOI 10.1007/s11554-013-0367-9
different directions. In wavelet transform, the coarser ver-
sion of an input image can be efficiently represented using
wavelet base, but discontinuities across a simple curve
affect the high frequency components and affect all the
wavelet coefficients on the curve. Hence the wavelet
transform does not handle curves discontinuities well.
When the ripplet function intersects with curves in images,
the corresponding coefficients will have large magnitude
and the coefficients decay rapidly along the direction of
singularity.
Specifically the proposed method employs Ripplet
transform and Set Partitioning In Hierarchical Trees
(SPIHT) encoder [7] to compress the medical images and
to provide efficient representation of edges in images.
Since the Ripplet transform successively approximates
images from coarse to fine resolutions, it provides hier-
archical representation of images. The magnitudes of
Ripplet transform coefficients decay faster than those of
other transforms which result in higher energy concen-
tration ability. Ripplet functions can represent scaling
with arbitrary degree and support. They have compact
support in frequency domain and decay very fast in
spatial domain that leads to good localization in both
spatial and frequency domains. With the increase of res-
olution, the ripplet functions orient at various directions.
The general scaling and support result in anisotropy of
ripplet functions which guarantees to capture singularities
along various curves.
Performances of the proposed method are evaluated and
compared with conventional and state of art methods such
as DCT, Haar wavelet, Contourlet, Curvelet and Joint
Photographic Experts Group (JPEG) compression on a set
of medical images. Experimental results demonstrate that
the proposed method outperforms the existing methods in
terms of PSNR, directionality, structural similarity index
measure (SSIM) and compression ratio.
The rest of the paper is organized as follows: A brief
review of existing image compression methods is given in
Sect. 2. Section 3 describes the basic concepts of Ripplet
transform and the SPIHT encoder. Section 4 describes the
proposed medical image compression using Ripplet trans-
form. Performance evaluations are presented in Sect. 5 and
finally the conclusions are given in Sect. 6.
2 Review of literature
Over the past decades, there has been abundant interest in
wavelet-based methods for the compression of images.
Wavelet transform is able to efficiently represent a function
with one dimensional singularity [8]. Although the discrete
wavelet transform has established an excellent reputation
for mathematical analysis and signal processing, the typical
wavelet transform is unable to resolve 2D singularities
along arbitrarily shaped curves. Since 2D wavelet trans-
form is just a tensor product of two 1D wavelet transforms,
it resolves 1D horizontal and vertical singularities,
respectively. The poor directionality of wavelet transform
has undermined its usage in many applications.
However, to overcome the limitations of wavelet
transform, Multiscale Geometric Analysis (MGA) theory
has been developed for high dimensional signals and sev-
eral MGA transforms are proposed such as ridgelet [9, 10],
curvelet [12], contourlet [15], surfacelet [18], bandelet
[19], etc. An anisotropic geometric wavelet transform,
named ridgelet transform is proposed by Candes and
Donoho [9, 10]. The ridgelet transform can resolve 1D
singularities along an arbitrary direction and it is optimal at
representing straight-line singularities. This transform with
arbitrary directional selectivity provides a key to the
analysis of higher dimensional singularities [11]. Unfortu-
nately, the ridgelet transform is not able to resolve 2D
singularities.
In order to analyze local line or curve singularities, the
idea is to partition the image, and then to apply ridgelet
transform to the obtained sub-images. This multiscale
ridgelet transform is proposed by Starck et al. [12] and
named as curvelet transform. The curvelet transform rep-
resents two dimensional functions with smooth curve dis-
continuities at an optimal rate. It is characterized by its
specific anisotropic support which obeys the parabolic
scaling law width = length2. From the view of microlocal
analysis, the anisotropic property of curvelet transforms
guarantees resolving 2D singularities along C2 curves.
Although this property is desired for compression [13, 14],
the discretization of curvelet transform turns out to be
challenging, and the resulting algorithm is highly compli-
cated. In order to optimize the scaling law, the Ripplet
transform is proposed. Ripplet transform generalizes
curvelet by adding two important parameters, i.e., support
c and degree d. The introduction of support c and degree
d provides anisotropy capability of representing singulari-
ties along arbitrarily shaped curves.
Contourlets, as proposed by Do and Vetterli [15] form a
discrete filter bank structure that can deal effectively with
piece-wise smooth images with smooth contours. This
transform is directly constructed in discrete domain, and
hence there is no need for transformation from continuous
time–space domain. Its implementation is based on a
pyramidal band-pass decomposition of the image followed
by a multiresolution directional filtering stage. Even though
contourlet transform is well suited for tasks such as image
compression [16, 17] by having lower redundancy and less
complexity, it has less clear directional features than
curvelet, which in turn leads to artifacts in image
compression.
J Real-Time Image Proc
123
Surfacelets proposed by Lu and Do [18] are 3D exten-
sions of 2D contourlets that are obtained by a higher
dimensional directional filter bank and a multi scale pyr-
amid. They can be used to represent surface-like singu-
larities in multidimensional volumetric data involving
biomedical imaging and computer vision, but they are not
able to represent images at different scales and different
directions. Penneca and Mallat [19] have introduced ban-
delet bases which decompose the image along multiscale
vectors. It defines the geometry as a vector field and
indicates the direction in which the image grey levels have
regular variations. There have been several other devel-
opments of directional wavelet systems in recent years in
order to provide optimal representation of directional fea-
tures of signals in higher dimensions. Shearlets [20] and
platelets [21] have also been proposed independently to
identify and restore geometric features. The proposed
Ripplet transform provides better performance than the
directional transforms because it localizes the singularities
more accurately and is highly directional to capture the
orientations of singularities.
Predictive coding approach can mostly reduce the rele-
vance of pixels in time and space domain. An adaptive
prediction coding method based on wavelet transform is
proposed by Chen and Tseng [22], where the correlations
between wavelet coefficients are analyzed and the predictor
variables are evaluated to determine which relative coef-
ficients should be included in the prediction model.
Knezovic et al. [23] has also proposed a prediction-based
coding, which uses contextual error modeling for the
determination of probabilistic context in which the current
prediction error occurs. Even though the compression
performance is increased through the prediction-based
method, the computational complexity is also increased.
Hosseini et al. [24] proposed a contextual vector quan-
tization method for the compression of ultrasound images
where the contextual region of interest portion is com-
pressed with a lower compression ratio and the background
is compressed with high compression ratio. Jiang et al. [25]
proposed a vector quantization method with variable block
sizes in wavelet domain in which the variable block-size
coding segments the original image into several types of
blocks. The lowest frequency subband coefficients are
compressed using Huffman encoder and the high frequency
subbands are optimized using vector quantization with
variable block sizes. The variable block-coding method can
achieve a high visual quality and a relatively high com-
pression ratio. However, it is at the expense of complexity.
Discrete Cosine Transform (DCT) is possibly the most
popular transform used in compression of images in stan-
dards like JPEG [26, 27]. Chen [28] presented a DCT-
based subband decomposition method for the compression
of medical images. This bitrate reduced approach uses
transform function to DCT coefficients to concentrate
signal energy and a modified SPIHT algorithm to organize
data and entropy encoding. Singh et al. [29] proposed a
DCT-based compression method, in which the input image
is split into smaller blocks and each block is classified
based on adaptive threshold value of variance. Ansari et al.
[27] and Kim [30] have evaluated the performance of JPEG
compression for the compression of medical images.
However, the introduction of blocking artifacts across the
block boundaries cannot be neglected for higher com-
pression ratio. Reducing blocking artifacts by using any
smoothing filter would sacrifice the detailed information in
the image.
Beladgham et al. [31] proposed an algorithm for medical
image compression based on a biorthogonal wavelet
transform CDF 9/7 coupled with SPIHT coding and applied
lifting structure to improve the drawbacks of wavelet
transform. Although the compression performance is good,
it lacks in providing multiresolution representation of
edges in images. Minasyan et al. [32] demonstrated the
performance of Haar wavelet for image compression. Even
though Haar wavelet has less computational complexity
suitable for efficient transmission of images, it does not
provide sparse representation of edges in images.
Several wavelet-based encoding methods have been
proposed and reported in the literature. These coders are
developed to provide high image quality at high com-
pression rates. The effectiveness of wavelet-based image
coding is first demonstrated by Shapiro’s Embedded Ze-
rotree Wavelet (EZW) [33], and it is the first subband
coding algorithm by zerotree. Later, the research by Said
and Pearlman [7, 34] on SPIHT improved upon EZW
coding and applied successfully to both lossy and lossless
compression of images. SPIHT is a tree-based fully
embedded coder which employs progressive transmission
by coding bit planes in decreasing order. This coder
exploits the dependencies between the location and value
of the coefficients across subbands. The Embedded Block
Coding with Optimized Truncation (EBCOT) algorithm
proposed by Taubman [35] is a block-based coding algo-
rithm which processes the code block by bit-plane-by-bit-
plane and it is more complicated and also time-consuming
[36].
The Set Partitioned Embedded block coder (SPECK)
proposed by Pearlman et al. [37] is also a block-based
image coding algorithm which uses recursive set-parti-
tioning procedure to sort subsets of wavelet coefficients by
maximum magnitude with respect to integer powers of two
thresholds. Simard et al. [38] have proposed tarp coding
approach to significance-map coding. This coding uses a
nonadaptive arithmetic coder coupled with an explicit
probability estimate of the significance map. However, it
lacks context modeling and cross-scale aggregation of
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symbols such as zerotree structures. Pan et al. [39] pro-
posed the progressive binary wavelet-tree coder that uti-
lizes a binary wavelet transform to convert the image into
binary format and an entropy coder that uses a joint bit
scanning method and an adaptive context modeling to
encode the wavelet-transformed coefficients. Even though
this coder exploits the properties of embedded coding and
progressive transmission, the rate-distortion approach is
not as efficient when compared to other embedded coders
such as SPIHT.
Although several encoders have been reported for image
compression, to the extent of authors’ knowledge, SPIHT is
considered as an efficient entropy encoder for image
compression due to its salient features such as intensive
progressive capability, SNR scalability, low computational
complexity and compact output bit stream with large bit
variability [40].
3 Backgrounds
3.1 Ripplet transform
The Ripplet transform proposed by Xu et al. [6] is an
attempt to break the inherent limitations of wavelet trans-
form. It is a higher dimensional generalization of wavelet
transform capable of representing images or two dimen-
sional signals at different scales and different directions.
Similar to curvelet, ripplet is also optimal for representing
objects with C2 singularities. Thus, edges within images
have a sparse representation in ripplet space. Ripplet gen-
eralizes curvelet by adding two important parameters i.e.
support c and degree d. The introduction of support c and
degree d provides anisotropy capability of representing
singularities along arbitrarily shaped curves [41]. Each
coefficient in the ripplet expansion of an image is the result
of convolution of the associated ripplet and the image.
The ripplet function can be generated as:
qab~hðx~Þ ¼ q
a0~0ðRhðx~� b~ÞÞ ð1Þ
where Rh ¼cos h sin h� sin h cos h
� �is the rotation matrix, which
rotates h radians. x*
and b~ are 2D vectors. qa0~0ð�Þ is the
mother function of ripplet in frequency domain. The set of
functions fqab~hg is defined as ripplet functions, because in
spatial domain these functions have ripple-like shapes. The
major axis referred as effective length pointing in the
direction of ripplet and the minor axis referred as effective
width which is orthogonal to the major axis represent the
effective region. The effective region satisfies the property
for its length and width as width � c� lengthd where
c defines the support of ripplets and d determines the
degree of ripplets. This property provides ripplets the
capability of capturing singularities along arbitrary curves.
In the ripplet system, the analyzed effective region
describes the characteristics of pixels at various scales,
locations and directions.
The effective region tuned by support c and degree d is
an evidence for the most distinctive property of ripplets
known as general scaling. For c ¼ 1 and d ¼ 1; both axis
directions are scaled in the same way. So, ripplet with
d ¼ 1 will not have the anisotropic behavior. For d [ 1;
the anisotropic property is reserved for the Ripplet trans-
form. For d ¼ 2; ripplets have parabolic scaling; for d ¼ 3;
ripplets have cubic scaling; and so forth. Therefore, the
anisotropy provides ripplets the capability of capturing
singularities along arbitrary curves. For each scale, ripplets
have different compact supports such that ripplets can
localize the singularities more accurately.
For a 2D integrable function f ðx~Þ; the continuous Rip-
plet transform is defined as the inner product of f ðx~Þ and
ripplets qab~hðx~Þ; as given below:
Rða; b~; hÞ ¼ f ; qab~h
� �¼Z
f ðx~Þqab~hðx~Þdx~ ð2Þ
where Rða; b~; hÞ are the ripplet coefficients.
The discretization of continuous Ripplet transform is
based on the discretization of the parameters of ripplet
functions. The parameters a; b~ and h are substituted as
aj; b~k and hl, respectively, and satisfy that aj ¼ 2�j; b~k ¼c� 2�j � k1; 2
�j=d � k2
� �Tand hl ¼ 2p
c� 2�½jð1�1=dÞ� � l,
where k~¼ ½k1; k2�T and j; k1; k2; l 2 Z � ð�ÞT denote the
transpose of a vector.
The discrete Ripplet transform of an M 9 N image
f ðx; yÞ is given as:
Rj;k~;l ¼
XM�1
x¼0
XN�1
y¼0
f ðx; yÞ � qj;k~;l x; yð Þ ð3Þ
where Rj;k~;l are the ripplet coefficients and q
j;k~;lðx; yÞ are the
ripplets of scale j at position index k with angle index l in
discrete domain, ð�:Þ denotes the conjugate operator.
3.2 Encoding process
In transform-based compression methods, the dependencies
between the transformed coefficients are exploited before
entropy coding to improve the compression performance.
Many encoding methods have been recently developed to
exploit the dependencies between the location and value of
the coefficients across the subbands. One of the most
efficient methods that fulfill the goal of superior low-bit
rate performance, SNR scalability and progressive trans-
mission by pixel accuracy is SPIHT method [7].
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This method groups the insignificant coefficients in trees
that span across the subbands and code them with zero
symbols. It creates a pyramid structure based on the
wavelet decomposition of an image. There is a strong
spatial relationship of wavelet coefficients with their chil-
dren at the top of the pyramid. Its efficiency is based on
iteratively searching for significant pixels throughout the
pyramid tree and ordering the coefficients according to a
significance test.
4 The proposed compression method
The block diagram of the proposed compression method is
illustrated in Fig. 1. The input medical image f ðx; yÞ of size
256� 256 is first decomposed into a set of multiresolution
subbands P0; ðDs; s [ 0Þ through wavelet transform with
biorthogonal 9/7 wavelet filter. The decomposed input
image is given as:
f ðx; yÞ7!ðP0f ðx; yÞ;D1f ðx; yÞ;D2f ðx; yÞ; . . .Þ ð4Þ
where P0f ðx; yÞ is the approximation lowest frequency
component and fD1f ðx; yÞ;D2f ðx; yÞ; . . .g 2 Dsf ðx; yÞdenote high frequency components and Dsf ðx; yÞ contain
details about 2�2s wide. The frequency domain is parti-
tioned into three subbands, indexed by s ¼ 1; 2; 3. Usually
discrete wavelet transform would offer eight sub bands on
256� 256 image at levels j ¼ 0; 1; 2; ::; 7. The ripplet
subband s ¼ 1 corresponds to wavelet subbands j ¼0; 1; 2; 3 and subband s ¼ 2 corresponds to wavelet sub-
bands j ¼ 4; 5. Subband s ¼ 3 corresponds to wavelet
subbands j ¼ 6; 7. Hence, the decomposed wavelet bands j
are partially reconstructed into ripplet subbands s as
j 2 f2s; 2sþ 1g. Figure 2 shows the decomposition of
T2WI-axial view of MRI brain into subbands.
The high frequency subbands are dissected into small
partitions by multiplying with the smooth window function
wQðx1; x2Þ localized around dyadic squares Q. By doing
this for all Q ¼ Qðs; k1; k2Þ with k1 and k2 varying and s
fixed, produces a smooth dissection of the function into
squares. Multiplying the high frequency band with a win-
dowing function produces a smooth dissection of the
function into squares of side 2�s � 2�s. The windowing wQ
and the filtering Ds are constructed to ensure that all these
steps result in perfect reconstruction [42]. The window
function is a non-negative function, which provides parti-
tion of energyP
k1;k2w2ðx1 � k1; x2 � k2Þ � 1; 8ðx1; x2Þ:
Now each subband Dsf ðx; yÞ is smoothly partitioned into
squares as shown in Fig. 3. There are either squares which
do not intersect the edge or a ripplet fragment. The empty
squares have no energy and can be ignored. The resulting
dyadic squares are then renormalized. Renormalization
is centering each dyadic square to the unit square ½0; 1� �½0; 1� in order to have a system of elements at all
lengths and all finer widths. It results in an aspect ratio
of width � length2. For a dyadic square Q, let
Input image f(x,y)
Wavelet transform
Lowest frequency subbands
)),(( 0 yxfP
High frequency subbands
)),(( yxfsΔ
Smooth partitioning
Renormalization
Ripplet domain
SPIHT encoding
Compressed Image
Ripplet Transform
Fig. 1 Block diagram of the
proposed compression method
J Real-Time Image Proc
123
ðTQf ðx; yÞÞðx1; x2Þ ¼ 2sf ð2sx1 � k1; 2sx2 � k2Þ denote the
operator which transports and renormalizes f ðx; yÞ, so that
the part of the input supported near Q becomes the part of
the output supported near ½0; 1�2. Each resulting dyadic
square is then renormalized to unit scale
gQ ¼ ðTQÞ�1ðwQ � Dsf ðx; yÞÞ. Each pixel in renormalized
square is represented as ripplets in spatial domain. The
major axis referred as effective length pointing in the
direction of ripplet and the minor axis referred as effective
width which is orthogonal to the major axis represent the
effective region. The effective region is analyzed in the
ripplet system. The effective region satisfies the property
for its length and width as width � c� lengthd where
c defines the support of ripplets and d determines the
degree of ripplets. This property provides ripplets the
capability of capturing singularities along arbitrary curves.
Finally, the resulting ripplet coefficients and the coeffi-
cients in the coarsest subband are further coded using
SPIHT algorithm which exploits the dependencies between
the location and value of the coefficients across subbands.
This algorithm orders the resulting coefficients according
to the significance test (5) and stores the information in
three separate sets of lists: list of insignificant sets (LIS),
list of insignificant pixels (LIP) and list of significant pixels
(LSP). After the initialization, this algorithm takes two
stages for each level of threshold: sorting stage and
refinement stage. During the sorting stage, the pixels in LIP
are tested using significance test and those that become
significant are moved to the LSP. The sets are sequentially
evaluated following the LIS order and when the set is
found to be significant it is removed from the list and
partitioned. The new subsets with more than one element
are added back to the LIS, while the single-coordinate sets
are added to the end of LIP or LSP, depending upon
whether they are insignificant or significant, respectively.
LSP now contains the coordinates of the pixels that are
visited in the refinement pass, which outputs the nth most
significant bit of snðumÞ. The value of n is decreased by 1
and the sorting and refinement stages are repeated. When
all the coefficients are processed completely, the com-
pressed image is taken as the output.
snðumÞ ¼1; maxjCi;jj � 2n
0; otherwise
(ð5Þ
where snðumÞ is the significance of a set of coordinates and
Ci;j represents the combination of Ripplet-transformed
coefficients and the coarsest coefficients at coordinates
ði; jÞ.The inherent properties of Ripplet transform in con-
junction with the coding of coefficients using SPIHT
algorithm provide efficient representation of edges in
images.
The proposed compression procedure is formulated as
follows:
Step 1 Input the medical image f ðx; yÞ of size
256 9 256.
Step 2 Decompose the input image into a set of fre-
quency subbands.
f ðx; yÞ7!ðP0f ðx; yÞ;D1f ðx; yÞ;D2f ðx; yÞ; . . .Þ ð6Þ
where P0f ðx; yÞ is the lowest frequency component and
fD1f ðx; yÞ;D2f ðx; yÞ; . . .g 2 Dsf ðx; yÞ represent high fre-
quency components.
The decomposed wavelet bands j are partially recon-
structed into ripplet subbands s as j 2 f2s; 2sþ 1g.
Fig. 2 Subband decomposition
of T2WI-axial view of MRI
brain
Fig. 3 Smooth partitioning
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123
Step 3 Dissect the high frequency band into small par-
titions by defining a grid of dyadic square.
Qðs;k1;k2Þ ¼k1
2s;
k1 þ 1
2s
h i� k2
2s;
k2 þ 1
2s
h i2 Qs ð7Þ
where Qs defines dyadic squares of the grid. Multiplying
the high frequency band Dsf ðx; yÞ with a windowing
function wQ produces a smooth dissection of the function
into squares of side 2�s � 2�s.
hQ ¼ wQ � Dsf ðx; yÞ ð8Þ
Step 4 Renormalize each resulting dyadic square by
centering each square to the unit square ½0; 1� � ½0; 1�. For
each Q, the operator TQ is defined as:
ðTQf ðx; yÞÞðx1; x2Þ ¼ 2sf ð2sx1 � k1; 2sx2 � k2Þ ð9Þ
Each square is renormalized as:
gQ ¼ T�1Q hQ ð10Þ
Step 5 Analyze each square in the ripplet domain.
RðQ;ab~hÞ ¼ hgQ; qab~hi ¼Z
gQðx~Þqab~0ðx~Þdx~ ð11Þ
where RðQ;ab~hÞ are ripplet coefficients and qab~h is the ripplet
function which is generated as:
qab~hðx~Þ ¼ q
a0~0ðRhðx~� b~ÞÞ ð12Þ
where Rh ¼cos h sin h� sin h cos h
� �is the rotation matrix, which
rotates h radians. x*
and b~ are 2D vectors. qa0~0ð�Þ is the
mother function of ripplet in frequency domain.
The discrete Ripplet transform is given as:
Rj;k~;l ¼
XM�1
x¼0
XN�1
y¼0
gQðx; yÞqj;k~;l x; yð Þ ð13Þ
where Rj;k~;l are the ripplet coefficients and q
j;k~;lðx; yÞ are the
ripplets or ripplet functions in discrete domain, ð��Þ denotes
the conjugate operator.
Step 6 Encode the resulting coefficients using SPIHT
encoder.
Step 7 Measure the resulting image quality in terms of
PSNR, Bitrate, SSIM and Compression ratio.
5 Performance evaluations
The performances of the proposed method are evaluated on
a set of eight medical images of size (256 9 256, 8 bits per
pixel) and the quality of the compressed images has been
assessed in terms of PSNR (dB), Bitrate (bpp), SSIM,
compression ratio and computational complexity. The
efficiency of the proposed method is evaluated on com-
parison with DCT [28], Haar wavelet [32], contourlet [16],
Fig. 4 Set of medical images used for evaluation. a T1WI-ankle MRI, b T2WI-axial-1 view of brain, c T2WI-axial-2 view of brain, d sagittal
stir axial view of cerebral, e T1-weighted MRI lungs, f MRI abdomen, g CT-axial view of pancreas and h sagittal stir axial view of head
J Real-Time Image Proc
123
curvelet [13] based compression methods, encoded using
SPIHT encoder and JPEG compression method [26]. Fig-
ure 4 shows the set of input medical images used for
evaluation. In order to implement the proposed method, the
image processing toolbox of MATLAB software is used.
The following subsections present thorough experimental
investigations of the overall behavior of the proposed
method.
Four sets of experimental results are obtained. The first
set evaluates the image quality of the proposed and existing
methods in terms of PSNR and the second set evaluates the
image quality in terms of SSIM. The third set tabulates the
compression ratio achieved and the fourth set describes the
computational complexity of the proposed and existing
methods.
5.1 Evaluation of image quality based on PSNR
The major design objective of compression method is to
obtain the best visual quality with minimum bit utilization.
PSNR is one of the most adequate parameters to measure
the quality of compression. If the PSNR values are higher,
the quality of compression is better and vice versa. It is
defined as:
a b
c d
e f
Fig. 5 PSNR (dB) achieved for test images using different methods. a T1WI-MRI ankle, b T2WI-axial-1 view of brain, c sagittal stir axial view
of head, d sagittal stir axial view of cerebral, e T1-weighted MRI lungs and f CT-axial view of pancreas
J Real-Time Image Proc
123
PSNR ¼ 10� log10ð2552=MSEÞ ð14Þ
MSE in Eq. (14) represents the mean squared error of
the image defined as:
MSE ¼ 1
M � N�
XM�1
x¼0
XN�1
y¼0
ðf ðx; yÞ � Fðx; yÞÞ2" #
ð15Þ
where M � N represent the size of the image, f ðx; yÞdenotes original image and Fðx; yÞ denotes compressed
image. Bitrate (bpp) is defined as the ratio of the size of the
compressed image in bits to the total number of pixels.
It is seen from Figs. 5a–f and 6 that, in the proposed
method, the non-negative windowing function and the
subband filtering procedures yield exact reconstruction,
resulting in high PSNR. In contourlet-based method,
aggressive sub-sampling can lead to artifacts in signal
reconstruction. DCT and JPEG also suffer from blocking
artifacts caused by discontinuities. Since the anisotropy
capability of the Ripplet transform is able to capture 2D
singularities along a family of curves in images which also
provides efficient representation of images, the proposed
method achieves high PSNR as compared to existing
methods.
5.2 Evaluation of image quality based on SSIM
The SSIM is an objective image quality metric used to
measure the similarity between two images based on the
characteristics of the human visual system. It measures the
structural similarity rather than error visibility between two
images. SSIM is defined as:
SSIMðx; yÞ ¼ð2lxly þ C1Þð2rxy þ C2Þ
ðl2x þ l2
y þ C1Þðr2x þ r2
y þ C2Þð16Þ
where x and y are spatial patches (windows), lx and ly are
the mean intensity values of x and y, respectively. r2x and
r2y are standard deviations of x and y, respectively; and C1
and C2 are constants.
From Fig. 7a–d, it is clear that the proposed method
yields better SSIM value (close to 1) than existing methods.
Since Ripplet transform has superior reconstruction prop-
erty, the SSIM value is higher than that of other methods.
5.3 Evaluation of compression ratio
Compression ratio is used to enumerate the minimization in
image representation size produced by the compression
algorithm. It is defined as the ratio of the number of bits in
the original image to that of the compressed image. Table 1
shows the compression ratio achieved by the proposed and
existing methods for different images at 1.2 bpp.
The proposed method outperforms other methods on the
compression of T2WI-axial view of brain image, T1-
weighted MRI lungs, CT-axial view of pancreas and sag-
ittal stir axial view of head. This is due to the fact that the
Ripplet transform successively approximates images from
coarse to fine resolutions and is highly directional to cap-
ture the orientations of singularities. However, for T1WI—
MRI ankle, contourlet-based method performs well
because it deals effectively with piece-wise smooth images
with smooth contours. For sagittal stir axial view of cere-
bral and for MRI abdomen, Haar wavelet performs better
because the approximation component contains most of the
energy and the coefficients are reduced with input permu-
tation of variables. From Table 1, it is understood that the
average compression ratio achieved by the proposed
method is 11.37. It outperforms DCT by 5.13 %, Haar
wavelet by 5.47 %, contourlet-based method by 6.96 %,
curvelet-based method by 9.43 % and JPEG compression
by 7.46 %.
5.4 Computational complexity considerations
The performance evaluations are concluded with a brief
discussion regarding the complexity of the proposed and
existing methods. The implementation of contourlet
transform is based on a pyramidal band-pass decomposi-
tion of the image followed by a multiresolution directional
filtering stage. Since this transform is directly constructed
in discrete domain, there is no need for transformation
from continuous time–space domain which leads to less
complexity of OðnÞ for n� n image. Similarly, Haar
wavelet is also computationally attractive because it has the
complexity of Oðlog2ðnÞÞ. The computational complexities
of DCT and JPEG methods are Oðn logðnÞÞ and Oðn2Þ,respectively. Ripplet and curvelet methods have little
higher complexity, since they run in Oðn2 log nÞ flops for
an n� n image.Fig. 6 PSNR (dB) obtained for test images using different compres-
sion methods
J Real-Time Image Proc
123
6 Conclusions
In this paper, a novel ripplet-based compression method for
medical images is presented. The main focus of the proposed
method is to provide high quality compressed images by
representing images at different scales and directions and to
achieve high compression ratio. The novelty of this method
is that it uses Ripplet transform with anisotropy capability to
represent singularities along arbitrarily shaped curves and
combines with an SPIHT encoder to improve the compres-
sion performance. Experimental results demonstrate that
besides providing high PSNR and high directionality, the
proposed method outperforms DCT by 5.13 %, Haar
wavelet by 5.47 %, contourlet-based method by 6.96 %,
curvelet-based method by 9.43 % and JPEG compression by
7.46 % in terms of compression ratio.
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Fig. 7 SSIM values for the test images at various bit rates using different methods. a CT-axial view of pancreas, b T2WI-axial-1 view of brain,
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Table 1 Compression ratio achieved for different medical images at 1.2 bpp
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Author Biographies
Sujitha Juliet is an Assistant Professor at the Department of
Information Technology, Karunya University, India. She received
her B.E. degree from Bharathiar University, India in 2001 and
Masters in Applied Electronics from Karunya University, India.
Currently, she is pursuing her Ph.D. at Karunya University, India. Her
principal research interests are medical image lossy and lossless
compression and telemedicine networking.
Elijah Blessing Rajsingh is the Professor and Director for the School
of Computer Science and Technology, Karunya University, India. He
received his Master of Engineering with Distinction from the College
of Engineering, Anna University, India, where he also received the
Ph.D. degree in Information and Communication Engineering in
2005. He has very strong research background in the areas of Network
Security, Mobile Computing, Wireless and Ad hoc Networks and
Image Processing. He is an Associate Editor for International Journal
of Computers and Applications, Acta Press, Canada.
Kirubakaran Ezra is an Additional General Manager, Outsourcing
Department, BHEL—Trichy, India. He received his B.E. (Honours.)
degree from Regional Engineering College, India in 1978 and
obtained M.E. in Computer Science in 1984. In 1999, he obtained his
Ph.D. degree in Computer Science from Bharathidasan University,
India. He has 31 years of experience in designing, developing and
maintenance of Software Systems at BHEL. He is a member of the
Academic Council of Anna University Tiruchirappalli, member of the
Academic Council of Anna University Chennai and Syndicate
Member in Bharathidasan University nominated by His Excellency
the Governor of Tamil Nadu.
J Real-Time Image Proc
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