Md

YDS

a

A

R

R

A

K

S

J

1

MT(Xratmnq

1d

i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725

journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls / i jmi

edical image compression using DCT-based subbandecomposition and modified SPIHT data organization

en-Yu Chen ∗

epartment of Information Management, ChengChou Institute of Technology, 6, Line 2, Sec 3,han-Chiao Rd., Yuanlin, Changhwa, Taiwan

r t i c l e i n f o

rticle history:

eceived 11 January 2005

eceived in revised form 3 July 2006

ccepted 9 July 2006

eywords:

et partitioning in hierarchical trees

PEG2000

a b s t r a c t

Objective: The work proposed a novel bit-rate-reduced approach for reducing the memory

required to store a remote diagnosis and rapidly transmission it.

Method: In the work, an 8 × 8 Discrete Cosine Transform (DCT) approach is adopted to per-

form subband decomposition. Modified set partitioning in hierarchical trees (SPIHT) is then

employed to organize data and entropy coding. The translation function can store the

detailed characteristics of an image. A simple transformation to obtain DCT spectrum data

in a single frequency domain decomposes the original signal into various frequency domains

that can further compressed by wavelet-based algorithm. In this scheme, insignificant DCT

coefficients that correspond to a particular spatial location in the high-frequency subbands

can be employed to reduce redundancy by applying a proposed combined function in asso-

ciation with the modified SPIHT.

Results and conclusions: Simulation results showed that the embedded DCT-CSPIHT image

compression reduced the computational complexity to only a quarter of the wavelet-based

subband decomposition, and improved the quality of the reconstructed medical image as

given by both the peak signal-to-noise ratio (PSNR) and the perceptual results over JPEG2000

and the original SPIHT at the same bit rate. Additionally, since 8 × 8 fast DCT hardware

implementation being commercially available, the proposed DCT-CSPIHT can perform well

in high speed image coding and transmission.

years, some American industrial standards such as ACR/NEMA

. Introduction

edical images are extensively adopted to diagnosis disease.hese imaging modalities include computerized tomography

CT), magnetic resonance imaging (MRI), ultrasonography (US),radiographs, etc. These modalities provide flexible means of

eviewing anatomical cross-sections and physiological states,nd may reduce patient radiation doses and examinationrauma. However, medical images have large storage require-

ents. An efficient data-compression scheme to reduce theumber of digital data without significantly degrading theuality of the medical image, to be interpreted by humans

∗ Tel.: +886 922638077; fax: +886 48369574.E-mail address: miscyy@tcts1.seed.net.tw.

386-5056/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights resoi:10.1016/j.ijmedinf.2006.07.002

© 2006 Elsevier Ireland Ltd. All rights reserved.

or machines. Compression may be lossy or lossless, depend-ing on system requirements. Lossless compression ensurescomplete data fidelity following reconstruction but in is typi-cally limited to compression ratios of between 2:1 and 3:1 (bitrate = 4.0–2.67 bpp). Hence, lossless techniques only a mod-est reduction file size. Lossy compression methods [1–4] arerequired to affect significantly transmission and storage cost,but losses must not be diagnostically significant. In recent

[5], and DICOM [6] have been established. All involve lossycompression. Lossy compression is the main area of ourresearch.

erved.

i c a l

cients. Third step, the significance coefficients that be foundin sorting pass are put into the refinement pass that use twobits to exact the reconstruct value for closing to real value.The front second and third steps are iterative, next iteration

718 i n t e r n a t i o n a l j o u r n a l o f m e d

Computer-aided diagnosis (CAD) schemes require digitalimage format to assist radiologists in detecting radiologi-cal features that could indicate various pathologies. Withoutimages in digital format, there would be no picture archiving,communications systems (PACS), and tele-radiology. Conven-tional medical image compression systems apply full-frameprocessing to prevent blocking, which may result in incorrectdiagnosis. However, full-frame processing is time-consumingand, worse, blurs sharp regions when the compression ratiois high. In picture archiving and communication systems,lossy techniques with compression ratios of around 10:1 (bitrate = 0.80 bpp) are commonly adopted; compression is con-ducted by full-frame processing.

The challenges posed by medical imaging require devel-oping compression algorithms that are nearly lossless fordiagnoses, yet support high compression ratios to reduce theamount of storage, transmission and processing required. Thisis particularly important in applications such as remote diag-nosis. In this paper we develop and evaluate an algorithmfor image compression that is based on the SPIHT algorithm.First we introduce the basic signal processing techniques onwhich the algorithm is based, i.e. the discrete cosine trans-form and the original SPIHT algorithm. Next we describe ourproposal for an efficient and good quality modified SPIHT algo-rithm. We describe a number of experiments and compare theperformance of our algorithm with that of a few well-knownalgorithms for compression. Finally we discuss our results andpresent the conclusions of our work.

2. Discrete Cosine Transform

Transform coding first became popular following the introduc-tion of the Discrete Cosine Transform (DCT) [7], an efficientapproximation to the theoretically optimal but highly complexKarhunen–Loeve transform (KLT). DCT is extensively adoptedin many practical image/video compression systems, becauseof its compression performance and computational efficiency.DCT has been successfully employed as the first step in severalcoding system, including JPEG [8], MEPG [9] and H.26x [10,11],because it exhibits favorable energy distribution in the fre-quency domain.

One basic DCT function (1) and its inverse function (2) areshown below:

F(u, v) = C(u)C(v)4

7∑u=0

7∑v=0

f (j, k) cos

((2j + 1)u�

16

)

× cos

((2k + 1)v�

16

)(1)

f (i, j) =7∑

u=0

7∑v=0

f (u, v)C(u)c(v) cos

((2j + 1)u�

16

)

( )

× cos

(2k + 1)v�

16(2)

where C(w) =

⎧⎨⎩

1√2

, if w = 0

0, otherwise.

i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725

The computation of full-frame DCT in whole image is heavyso the image is usually divided into non-lapped sub-images(8 × 8) for furthermore processing in many DCT-based com-pression algorithms. Although the complexity of a direct DCTis as high as O(N3), by using fast DCT algorithms it can bereduced to O(N2log N) [12].

3. Original SPIHT algorithm

In recently, the wavelet-based image encoding algorithmsconsiderably improve the compression rate and the visualquality, therefore many researches proposes many differentmethods for encoding the wavelet-based images. The SPIHT[13] algorithm is an efficient method for lossy and lossless cod-ing of natural images. The SPIHT algorithm adopts a hierarchi-cal quad-tree [14,15] data structure on wavelet-transformedimage. The energy of a wavelet-transformed image is con-centrated on the low frequency coefficients. A tree structure,called spatial orientation tree (SOT), naturally defines the spa-tial relationship of the hierarchical pyramid. Fig. 1 shows howa spatial orientation tree is defined in a pyramid constructedwith recursive four subbands splitting. The coefficients areordered in hierarchies. According to this relationship, theSPIHT algorithm saves many bits that specify insignificantcoefficients.

The flowchart of SPIHT is presented in Fig. 2. First step,the original image is decomposed into 10 subbands. Thenthe method finds the maximum and the iteration number.Second step, the method puts the DWT coefficients into sort-ing pass that finds the significance coefficients in all coef-ficients and encodes the sign of these significance coeffi-

Fig. 1 – Parent–child relationship.

i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725 719

cha

dvc

iwtmpo(cnct

wasn

4

TbTfscr

gaabittiee

4

E4t

Fig. 2 – Flow

ecreases the threshold (Tn = Tn−1/2) and the reconstructivealue (Rn = Rn−1/2). Forth step, the encoding bits access entropyoding and then transmit [16,17].

All of the wavelet-based-image encoding algorithmsmprove the compression rate and the visual quality, but theavelet-transform computation is a serious disadvantage of

hose algorithms. One study concluded that wavelet-basedethods such as SPIHT are subjectively superior to JPEG com-

ressed at moderately high bit rate [18]. However, SPIHT devel-ped ringing artifacts with compression ratios above 12:1

bit rate < 0.67 bpp), impacting diagnostic acceptability. Imagesoded at medium bit rate suffer from loss of detail and sharp-ess, as well as various coding artifacts. Ringing, one of theoding artifacts, appears as small ripples around the edge ofhe image.

In the work of Xiong et al. [19], they compare this techniqueith wavelet and SPIHT. In their study the DCT has not been

ssessed that positive. This work designs the algorithm, whichuccessfully enhances the quality of medical images codedear lossless.

. Proposed algorithm

raditional transform-based image coders such as JPEG areased on Block-based Discrete Cosine Transform (BDCT).he image is divided and transformed by 8 × 8 BDCT for

urther processing. A BDCT coder can apply only a verymall fraction of the transform coefficients and ratheroarsely quantize the rest, still offering satisfactory reconst-uction.

Most medical images are dominated by a dark back-round. A few medical image features in the 8 × 8 blocksre observed on the dark background. All of the pixels havepproximate gray scale values in the 8 × 8 blocks. Theselocks exhibited of similarities that could be further exploitedn the novel approach to reduce the bit rate. Therefore,his algorithm adopted the translation function to reorderhe DCT domain data for all individual blocks and mod-fied the SPIHT algorithm that was designed initially toncode the DWT coefficients to enable DCT coefficients to bencoded.

.1. Translation function

ach 8 × 8 DCT-transformed image was broken down into four× 4 blocks. The translation function is an important part of

he proposed system. It relates the spectral data of all for the

rt of SPIHT.

8 × 8 individual blocks:

for (l = 0; l < 8; l + +) / ∗ #x-band ∗ /

for (m = 0; m < 8; m + +) / ∗ #y-band ∗ /

for (i = 0; i < N/8; i + +) / ∗ x-band index ∗ /

for (j = 0; j < N/8; j + +) / ∗ y-band index ∗ /

T : �l, m

i, j= kl+i×8,m+j×8

(3)

Herein, k is the buffer that stores the individual spectral dataof the original f and N in order, and is of size f. The trans-lation process collocates all of the spectral data in the samefrequency band. In Eq. (3), i is the order of the band and j is theindex in the band i.

Clearly, the complexity of the translated sequences � is lessthan of the original individual block-based signal k, becausetransformation decomposes the original signal into variousfrequency domains. After one instance of the preceding trans-lation processing, the original k buffer is decomposed into four‘�’s, each corresponding to a single band. Each � has the trans-form coefficients with the frequency band of k. Such bandclustering yields a multi-resolution image. The high bandscontain almost only random noises and very little informa-tion, which can be discarded in the reconstruction procedurewithout appreciable distortion. Therefore, the use of the trans-lation function T reduces the data complexity below the orig-inal k.

The coefficients from LL, LH, HL, and HH subbands of 4 × 4across all 8 × 8 DCT blocks are grouped, respectively, to formfour subbands of the entire image in the frequency domain.The second-level decomposition depends on the first transfor-mation of the grouped LL subband back to the spatial domain.Since each 4 × 4 LL subband represents the frequency con-tent of the corresponding 8 × 8 original block, each individual4 × 4 LL subband can be simply transformed back to the spa-tial domain. Fig. 3 presents this technique. The algorithm is asfollows:

Input. Original medical image.Output. ˚(L,L), ˚(L,H), ˚(H,L), and ˚(H,H).Step 1. Applying 8 × 8 DCT to all image data in order; storethe resulting spectrum to k.Step 2. Apply translation function T to k, yielding �(L,L), �(L,H),�(H,L), and �(H,H).

Step 3. Apply 4 × 4 IDCT to �(L,L); store the resulting spectrumto k′.Step 4. Apply 8 × 8 DCT to k′, yielding ˚(L,L), ˚(L,H), ˚(H,L), and˚(H,H).

720 i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725

osit

Fig. 3 – Subband decomp

Fig. 3 presents the application of the proposed translationfunction to the medical image. The translation function pyra-mids the image to generate the multi-resolution model. Thistranslation function aims to concentrate the energy of the LLsuband coefficients. Each value in ˚(L,L) is an average of theoriginal 4 × 4 gray data, and the other bands contain the con-tour information of the original image data.

4.2. Combined function

The proposed methods applied the combined function toremove the correlation in the other subbands (in LH2, HL2,HH2, LH1, HL1, HH1) that are the leaf of the SOT tree. Thosesubbands include few significant coefficients, and the origi-nal SPIHT algorithm suggests the use of one bit to representwhether the significant coefficient is in the quad-tree. Thefact that a quad-tree includes at least one significant coeffi-cient is represents as 1. That all of the nodes in the quad-treeare insignificant coefficients is presented as 0. The subbandsoriginally neglected by the SPIHT algorithm neglected exhibitsquite a large correlation among the same level subbands, andthe proposed algorithm presents the dictator to solve thisproblem. According to the quad-tree concept, a correlationexists between LH1 and LH2. Equally the correlation existsbetween HL1 and HL2. Equally the correction exists between

HH1 and HH2. Therefore, LH2, LH1, HL2, HL1, HH2 and HH1 aredivided into three partitions, Qt, t = 1–3:

Q1 = {LH2 ∪ LH1} (4)

Fig. 4 – The proposed algorithm uses the concep

ion on the whole image.

Q2 = {HL2 ∪ HL1} (5)

Q3 = {HH2 ∪ HH1} (6)

The set Su, u = 1–3 is defined. The set Su indicates whetherthat the subtree coefficients in Qt are significant. S1 is modifiedby the following conditions in the set Q1:

S1(I, J) = 1, if LH1(x, y) = 1, I =⌊

x

4

⌋and J =

⌊y

4

⌋. (7)

S1(I, J) = 1, if LH1(x, y) = 1, I =⌊

x

2

⌋and J =

⌊y

2

⌋. (8)

S1(I, J) = 0, otherwise. (9)

Q2 and Q3 in the same steps result in S2 and S3. The cor-relation among the three sets (S1, S2, S3) is greater, so theproposed algorithm creates the combined function that deter-mines which subband has significant coefficients. The com-bined function d will decide what needs to be sent:

d = {d(m, n)|S1(m, n) ∪ S2(m, n) ∪ S3(m, n)} (10)

Fig. 4 shows the concept and framework of the combinedfunction. The oblique-line block is the set S , u = 1–3. This way

u

saves the bits required to represent insignificant coefficients.From d, the subband with significant coefficients can be identi-fied. If d(m, n) = 0 that means there is no significance coefficientin the leaf of these three SOT trees, nothing is sent to the

t and framework of the combined function.

i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725 721

Fig. 5 – Proposed algorithm for DCT coefficients flowchart.

Fig. 6 – Angiogram test image: (a) original test image; (b) compressed by JPEG2000, bit rate = 0.1 bpp, PSNR = 44.1 dB; (c)compressed by DCT-CSPIHT, bit rate = 0.1 bpp, PSNR = 45.2 dB; (d) difference image between (a and c).

i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725

Table 1 – PSNR for the original SPIHT, JPEG2000, andDCT-CSPIHT at various bit rates in an angiogram testimage

Bit rate (bpp) SPIHT (dB) JPEG2K (dB) DCT-CSPIHT (dB)

0.025 33.4 36.1 39.50.10 40.3 44.1 45.20.24 45.4 47.6 48.40.50 49.8 50.5 52.0

Table 2 – PSNR values for the original SPIHT, JPEG2000,and DCT-CSPIHT at various bit rates in a sonogram testimage

Bit rate (bpp) SPIHT (dB) JPEG2K (dB) DCT-CSPIHT (dB)

0.35 31.5 34.5 35.0

722 i n t e r n a t i o n a l j o u r n a l o f m e d

decoder. If d(m, n) = 1 that means there are as least one sig-nificance coefficient in the leaf of these three SOT trees, thedetail about how to record the significance coefficient locationin next section.

The proposed algorithm differs from the SPIHT algorithmin transform and reducing redundancy of the same level sub-bands. Fig. 5 presents the complete block diagram of theencoder for compressing still images.

5. Simulation results

The proposed algorithm for DCT coefficients is compared withSPIHT and JPEG2000. Various kinds of medical images areselected as test data. They include angiogram (Fig. 6(a)), sono-gram (Fig. 7(a)), and X-ray (Fig. 8(a)). All are gray level imageswith a size of 512 × 512 pixels with 8 bpp. The proposed algo-rithm is compared with JPEG2000, which adopts original SPIHTand trellis coded quantization (TCQ). The performance is eval-uated by peak signal-to-noise ratio (PSNR). PSNR is mathemat-ically evaluated as

PSNR = 10 log102552

(1/T)∑n−1

i=0

∑n−1j=0 (xi,j − x′

i,j)2

(11)

Fig. 7 – Sonogram test image: (a) original test image; (b) comprescompressed by DCT-CSPIHT, bit rate = 1.4 bpp, PSNR value = 43.3 d

0.80 37.4 37.9 38.41.40 41.2 40.6 43.32.77 49.3 48.0 50.6

PSNR has been accepted as a widely used measure of qual-ity in the field of image compression. From Figs. 6–8 and

Tables 1–3, at a given bit rate, all of the DCT-CSPIHT PSNR val-ues are higher than these of the original SPIHT and JPEG2000.

Fig. 9(a) shows a size of 512 × 512 in the Lena test imagethat has more image context complex than the previous med-

sed by JPEG2000, bit rate = 1.4 bpp, PSNR value = 40.6 dB; (c)B; (d) difference image between (a and c).

i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725 723

Fig. 8 – X-ray test image: (a) original test image; (b) compressed bcompressed by DCT-CSPIHT, bit rate = 0.8 bpp, PSNR value = 43.6 d

Table 3 – PSNR values for the original SPIHT, JPEG2000,and DCT-CSPIHT at various bit rates in an X-ray testimage

Bit rate (bpp) SPIHT (dB) JPEG2K (dB) DCT-CSPIHT (dB)

0.15 34.2 37.0 37.2

imaJ

higher than the JPEG, JPEG2000, and SPIHT standard system

0.37 37.6 39.4 39.80.80 42.1 41.9 43.62.00 49.3 47.7 50.0

cal images. The contours of natural image contents haveore edge than those of medical image contents. Table 4

nd Fig. 9 show reporting PSNR values for the original SPIHT,PEG2000, Ref. [19], JPEG, and DCT-CSPIHT at various bit rates

Table 4 – PSNR values for the original SPIHT, JPEG2000, Ref. [19]image

Bit rate (bpp) SPIHT (dB) JPEG2000 (dB)

0.25 34.1 32.30.50 37.2 35.20.75 39.0 36.91.00 40.4 38.1

y JPEG2000, bit rate = 0.8 bpp, PSNR value = 41.9 dB; (c)B; (d) difference image between (a and c).

in a Lena test image. Simulation results show that the PSNRperformance of the DCT-CSPIHT is much better (1–2 dB) thanJPEG. For SPIHT, the PSNR of DCT-CSPIHT is average 0.6 dBlower than the wavelet-based SPIHT for image Lena. Generallyspeaking, the DCT-CSPIHT has comparable PSNR performancewith wavelet coder, yet with lower complexity. The subjectiveimage quality is almost unnoticeable when there is about 1 dBdifference between DCT-CSPIHT and SPIHT.

Fig. 10 shows that the compression rate of the proposedalgorithm for DCT coefficients in the test image is absolutely

and furthermore the image quality of the proposed algorithmfor DCT coefficients is closer to JPEG2000 at the same bit rateand fewer blocking effect than JPEG.

, JPEG, and DCT-CSPIHT at various bit rates in a Lena test

Ref. [19] (dB) JPEG (dB) DCT-CSPIHT (dB)

32.3 31.6 33.336.1 34.9 36.638.1 36.6 38.539.7 37.9 40.1

724 i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725

Fig. 9 – Lena test image: (a) original test image; (b) compressed by JPEG2000, bit rate = 0.50 bpp, PSNR value = 35.2 dB; (c)compressed by DCT-CSPIHT, bit rate = 0.50 bpp, PSNR value = 36.6

Fig. 10 – Comparison proposed algorithm DCT-CSPIHT withJPEG, JPEG2000, and SPIHT in the test images.

6. Conclusions

A new medical images compression technique with the com-pression ratio of more than 20 (bit rate < 0.4 bpp) is devised.

dB; (d) difference image between (a and c).

From the literature, we know that wavelet transform codinglead to higher compression ratios, at a cost of high computa-tion complexity. Most of the discrete cosine transform-basedcoding methodology, such as that of JPEG, use 8 × 8 or 16 × 16coding size to get a trade-off between the computationalburden and characteristic preservation. But the reconstructedimages suffer from the blocking effect when the compressionratio is high. The challenges posed by imaging involve thedevelopment of compression algorithm reduced computa-tion complexity to only quarter of wavelet transform, yetsupport discrete wavelet transform base high compressionratios to reduce storage, transmission, and processing. Thealgorithm uses transform function to the DCT coefficients toconcentrate signal energy and proposes combined functionto eliminate the correlation in the same level subband forencoding the DCT-based images. The proposed algorithm issimilar to SPIHT, but the differences between the proposedalgorithm and SPIHT are transform and the sorting pass.The coding complexity of the proposed algorithm for DCTcoefficients is just close to JPEG but the performance is higherthan JPEG2000. The simulation results indicate that the

proposed technique can produce a reconstructed image withbetter image. The PSNR values of our proposed method arebetter than the PSNR values of SPIHT and JPEG2000 at a givenbit rate.

i n t e r n a t i o n a l j o u r n a l o f m e d i c a l i n

Summary points

What was already known on the subject:

• Since lossy compression methods were unable toachieve an increased compression ratio, and mostlyachieved a compression ratio of only 10 or 12, therewere inadequate for use in hospitals from data storageperspective. Numerous investigations demonstratethat the compression ration of lossy compression inmedical images is up to 10 or higher, and does notinfluence tested image quality.

• The SPIHT algorithm is an efficient method for lossyand lossless coding of natural images.

• The computational complexity of the DWT is morethan that of the DCT.

What study has added to our knowledge on the topic:

• The proposed technique aims to achieve a compres-sion ratio of up to 10 or 20 without a noticeable artifacteffect in reconstruction image.

• The algorithm aims to concentrate the energy of DCTdomain data for all 8 × 8 blocks and modifies theSPIHT algorithm that was designed initially to encodethe DWT coefficients to enable DCT coefficients to beencoded.

• Medical imaging requires developing compressionalgorithms that are nearly lossless for diagnoses, thealgorithm supports high compression ratios to reducethe amount of storage, transmission and processing

skcaihHTis

A

Ttr

r

space-frequency compression of ultrasound images, IEEETrans. Inform. Technol. Biomed. 5 (4) (2001) 300–310.

required.

We propose a new algorithm for medical image compres-ion that is based on the SPIHT algorithm. This algorithm isnown for it is good performance. For application in the medi-al domain, some adaptations are needed to make the resultscceptable. In our modified SPIHT algorithm, the correlationn the frequency domain is taken into account as to achieveigh compression rates combined with good image quality.igh image quality of decoded images prevents misdiagnosis.he good compression ratio makes the management of med-

cal images more effective because of reduced bandwidth andtorage requirements.

cknowledgement

he author would like to thank the National Science Council ofhe Republic of China, Taiwan, for financially supporting thisesearch under Contract No. NSC94-2213-E-235-001.

f o r m a t i c s 7 6 ( 2 0 0 7 ) 717–725 725

e f e r e n c e s

[1] Y.G. Wu, S.C. Tai, Medical image compression by discretecosine transform spectral similarity strategy, IEEE Trans.Inform. Technol. Biomed. 5 (3) (2001) 236–243.

[2] J. Wang, H.K. Huang, Medical image compression by usingthree-dimensional wavelet transformation, IEEE Trans. Med.Imaging 15 (4.) (1996).

[3] A. Baskuet, H. Benoit-Cattin, C. Odet, On a 3-D medicalimage coding method using a separable 3-D wavelettransform, SPIE Med. Imag. 2431 (1995) 173–183.

[4] S.C. Lo, J. Xuan, H. Li, M.T. Freedman, S.K. Mun, Arithmeticwavelet decompositions in radiological image compression,in: Proc. SPIE Med. Imaging Conf., 1997, p. 3031.

[5] American College of Radiology (ACR)/National ElectricalManufacturers Association (NEMA) Standards Publicationfor Data Compression Standards, NEMA Publication PS-2,Washington, DC, 1989.

[6] Digital Imaging and Communication in Medicine (DICOM),version 3, American College of Radiology (ACR)/NationalElectrical Manufacturers Association (NEMA) StandardsDraft, December 1992.

[7] N. Ahmed, T. Natarajan, K.R. Rao, Discrete cosine transform,IEEE Trans. Comput. C-23 (1974) 90–93.

[8] W.B. Pennebaker, J.L. Mitchell (Eds.), JPEG-Still Image DataCompression Standard, Van Norstrand Reinhold, New York,1993.

[9] D.J. Le Gall, The MPEG video compression algorithm, SignalProcess.: Image Commun. 4 (1992) 129–140.

[10] ITU Recommendation H.261, Video Codec for Audio VisualServices at p × 64 kbits/s, March 1993.

[11] ITU Telecom, Standardization Sector of ITU, Video Codingfor Low Bitrate Communication, Draft ITU-TRecommendation H.263 Version 2, January 1998.

[12] N.I. Cho, S.U. Lee, Fast algorithm and implementation of 2-DDCT, IEEE Trans. Circuits Syst. Video Technol. 38 (3) (1991)297–305.

[13] A. Said, W.A. Pearlman, A new, fast, and efficient imageCodec based on set partitioning in hierarchical trees, IEEETrans. Circuits Syst. Video Technol. 7 (3) (1996) 243–250.

[14] G.J. Sullivan, R.L. Baker, Efficient quadtree coding of imagesand video, IEEE Trans. Image Process. 3 (3) (1994)327–331.

[15] A. Brian, Banister, R. Thomas, Fischer, Quadtreeclassification and TCQ image coding, IEEE Trans. CircuitsSyst. Video Technol. 1 (1) (2001) 3–8.

[16] Z. Xiong, K. Ramchandran, M. Orchard, Space-frequencyquantization for wavelet image coding, IEEE Trans. ImageProcess. 6 (5) (1997) 677–693.

[17] A. Munteanu, J. Cornelis, G.V.D. Auwera, P. Cristea, Waveletimage compression—the quadtree coding approach, IEEETrans. Technol. Biomed. 3 (3) (1999) 176–185.

[18] Ed Chiu, M. Jacques Vaisey, Stella Atkins, Wavelet-based

[19] Z. Xiong, K. Ramchandran, M.T. Orchard, Y. Zhang, Acomparative study of DCT- and wavelet-based image coding,IEEE Trans. Circuits Syst. Video Technol. 9 (5) (1999) 692–695.