A novel medical image compression using Ripplet transform

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


K. Ezra

Bharat Heavy Electricals Limited, Trichy, India


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.


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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].


123

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


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


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


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


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


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,

c T2WI-axial-2 view of brain and d T1-weighted MRI lungs

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.


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A novel medical image compression using Ripplet transform

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