2-D ECG Compression Method Based on Wavelet Transform and Modified SPIHT

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 6, JUNE 2005 999

A 2-D ECG Compression Method Based on WaveletTransform and Modified SPIHT

Shen-Chuan Tai, Chia-Chun Sun*, and Wen-Chien Yan

Abstract—A two-dimensional (2-D) wavelet-based electrocar-diogram (ECG) data compression method is presented whichemploys a modified set partitioning in hierarchical trees (SPIHT)algorithm. This modified SPIHT algorithm utilizes further theredundancy among medium- and high-frequency subbands ofthe wavelet coefficients and the proposed 2-D approach utilizesthe fact that ECG signals generally show redundancy betweenadjacent beats and between adjacent samples. An ECG signal iscut and aligned to form a 2-D data array, and then 2-D wavelettransform and the modified SPIHT can be applied. Records se-lected from the MIT-BIH arrhythmia database are tested. Theexperimental results show that the proposed method achieveshigh compression ratio with relatively low distortion and is ef-fective for various kinds of ECG morphologies.

Index Terms—Electrocardiogram (ECG) compression, set parti-tioning in hierarchical trees (SPIHT), wavelet transform.

I. INTRODUCTION

AN electrocardiogram (ECG) is an important physiologicalsignal for heart disease diagnosis. Because of the tremen-

dous amount of ECG data generated each year, efficient methodsfor storing and retrieving ECG data are needed. Besides, howto efficiently store and transmit ECG data in digital form be-comes one of the important issues in the biomedical signal pro-cessing community. On the other hand, the characteristics ofECG waveforms are the keys to the diagnosis. For example, Pwave, QRS complex, T wave, and PR interval represent the atrialdepolarization, ventricular depolarization, ventricular repolar-ization, and AV conduction time, respectively. For this reason, ageneral goal of ECG data compression algorithms is to removeredundancy between ECG data while preserving required signalquality for clinical diagnosis.

In recent years, many wavelet transform based ECG datacompression techniques with low reconstruction error and finevisual quality have been proposed [1]–[13]. Most of thesewavelet-based ECG Compression algorithms disregard theredundancy between adjacent heartbeats and apply wavelettransform directly to the acquired one-dimensional (1-D) ECGdata. According to the techniques used in wavelet-coefficientencoding, these techniques can roughly be divided into threecategories.

Manuscript received February 12, 2004; revised October 31, 2004. Asteriskindicates corresponding author.

S.-C. Tai and W.-C. Yan are with the Department of Electrical Engineering,National Cheng Kung University, Tainan 701, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]).

*C.-C. Sun is with the Department of Electrical Engineering, National ChengKung University, No. 1 Ta-Hsueh Road, Tainan 701, Taiwan, R.O.C. (e-mail:[email protected]).

Digital Object Identifier 10.1109/TBME.2005.846727

1) Threshold methods: wavelet coefficients are compared tosome certain thresholds, and those that below the thresh-olds are discarded [10], [12].

2) Vector quantization methods: vector quantization (e.g.,dynamic vector quantization) is applied to the encodingof wavelet coefficients [13].

3) Embedded zero tree (EZW) or SPIHT methods: waveletcoefficients are encoded using the concepts of the EZWor the set partitioning in hierarchical trees (SPIHT) algo-rithm [7]–[9], [11].

By observing the ECG waveforms, a fact can be concludedthat the heartbeat signals generally show considerable sim-ilarity between adjacent heartbeats, along with short-termcorrelation between adjacent samples. However, most existingECG compression techniques did not utilize such correlationbetween adjacent heartbeats. A compression scheme usingtwo-dimensional (2-D) transformation (e.g., DCT, DWT) is anoption to employ the correlation between adjacent heartbeatsand can thus further improve the compression efficiency. Leeand Buckley proposed a 2-D DCT based ECG compressionmethod using cut and align beats approach [14]. Uyar andIder proposed a 2-D DCT based compression algorithm forexercise ECG data [15]. Moghaddam and Nayebi presented a2-D wavelet packet ECG compression approach [16]. Bilgin etal. proposed a 2-D wavelet based ECG compression methodusing the JPEG2000 image compression standard [17]. These2-D ECG compression methods consist of following steps:1) QRS detection, 2) preprocessing (cut and align beats, pe-riod normalization, amplitude normalization, mean removal),3) transformation, and 4) coefficient encoding. Table I showsa comparison of these four methods. Generally, Period nor-malization helps utilizing the interbeat correlation but incurssome quantization errors. Mean removal helps maximizing theinterbeat correlation since dc value of each beat is different dueto baseline change.

In this paper, we propose a 2-D approach for ECG compres-sion that utilizes the redundancy between adjacent heartbeats.The QRS complex in each heartbeat is detected for slicingand aligning a 1-D ECG signal to a 2-D data array, and then2-D wavelet transform is applied to the constructed 2-D dataarray. Finally, a modified SPIHT algorithm is applied to theresulting wavelet coefficients for further compression. The waythat the proposed algorithm differs from other 2-D algorithmsis that the proposed algorithm not only utilizes the interbeatcorrelation but also employs the correlation among coefficientsin relative subbands. This paper is organized as follows: Briefintroductions to the SPIHT and the modified SPIHT algorithmare presented in Sections II and III, respectively. The proposedmethod is described in Section IV. In Section V, the proposed

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1000 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 6, JUNE 2005

TABLE ICOMPARISON OF 2-D ECG COMPRESSION ALGORITHMS

method is tested using selected records from the MIT-BIHarrhythmia database and the simulation results are comparedwith other methods. Finally, a conclusion will be given inSection VI.

II. SHORT SUMMARY OF SPIHT

The SPIHT algorithm, introduced by Said and Pearlman [19],is an efficient method for both lossy and loss-less natural imagecoding. The SPIHT algorithm adopts a hierarchical quad-treedata structure on a wavelet-transformed image. The energy ofa wavelet-transformed image is centered on the low-frequencycoefficients and the coefficients are ordered in hierarchies andhave a parent-child relationship through subbands. By utilizingthis relationship, the SPIHT algorithm saves many bits from rep-resenting insignificant coefficients. The coding procedure of theSPIHT algorithm is briefly described as follows.

The SPIHT algorithm can be defined recursively using a se-quence of thresholds. Detailed description of the SPIHT algo-rithm can be found in [19].

1) Initialization: Set the list of significant points (LSP)as empty. Set the roots of similarity trees in the listof insignificant points (LIP) and the list of the in-significant sets (LIS). Set the threshold with

, where denotes thecoefficient at position .

2) Sorting pass in LIP: Each coefficient in the LIP is checkedand the significant coefficients are moved to the LSP. Thesign bits of the significant coefficients are encoded.

3) Sorting pass in LIS: If an entry in the LIS is significant, aone is sent and then its two offspring are checked like anentry in the LIP. If an entry in the LIS is insignificant, azero is sent.

4) Refinement pass: Each old entry of LSP is checked. If itis significant under current threshold, a one is sent andits magnitude reduced by the current threshold. If it isinsignificant, a zero is sent.

III. MODIFIED SPIHT ALGORITHM

After wavelet decomposition, the energy of an image iscentered on the wavelet coefficients in the low-low band.Accordingly, the modified SPIHT algorithm divides a wavelet-transformed image into three partitions

where indicates a wavelet coefficient at position .Partitions , and represent low-frequency, middle-fre-quency and high-frequency wavelet coefficients, respectively.Coefficients in partition are coded as the entries in the LSPin the original SPIHT algorithm. In partition , the modifiedSPIHT algorithm adopts a set to utilize the correlation amongsubbands of the same level, where indicates whether thereis at least one coefficient significant among the coefficients atcorresponding coordinates in , , and and theirdescendants. If there is at least one coefficient significant, then

is set to one and the coefficients at corresponding coordi-nates in , , and would be sent to the decoder,otherwise, nothing is sent.

For other high-frequency coefficients in partition , the mod-ified SPIHT algorithm further utilizes the redundancy amongsubbands. There are few significant coefficients in this partition,and the original SPIHT algorithm suggests using one bit to rep-resent whether there is a significant coefficient is in a quad-tree.

TAI et al.: A 2-D ECG COMPRESSION METHOD BASED ON WAVELET TRANSFORM AND MODIFIED SPIHT 1001

Fig. 1. Block diagram of the proposed ECG compression method. (a) Encoder and (b) decoder.

A one indicates that there is at least one significant coefficient ina quad-tree, and a zero represents all coefficients in a quad-treeare insignificant. According to the quad-tree concept, there iscorrelation among and , and , andand . Therefore, the modified SPIHT algorithm divides

, , , , , into three subpartitions,, , 2, and 3

A subpartition is significant if there is at least one coefficientsignificant in the corresponding subbands. The bitmap of asignificant subpartition is encoded to indicate the positionsof significant coefficients. The sign information of significantcoefficients is also encoded. A more detailed description ofthe modified SPIHT algorithm can be found in [18].

IV. PROPOSED METHOD

Heart beat signals generally show considerable similaritybetween adjacent beats, along with short-term correlationbetween adjacent samples. According to this observation,employing temporal beat alignment method may lead to moreefficient ECG compression methods. Fig. 1 shows the blockdiagram of the proposed algorithm. In summary, the proposedalgorithm is implemented in the following steps.

1) QRS detection of the 1-D ECG signal.2) 2-D ECG data array construction and block segmentation.3) Wavelet decomposition and coefficients encoding.

Below we will describe each of these steps.

A. QRS Detection

In order to utilize the correlation among adjacent heart beats,the input 1-D ECG signal have to be segmented and alignedproperly. Therefore, the input 1-D ECG signal has to be QRSdetected and then the original 1-D ECG signal can be segmented

and aligned according to the results of QRS detection. The accu-racy of a QRS detection method would affect the performanceof the proposed algorithm.

B. 2-D Array Construction and Block Segmentation

The construction of a cut and aligned beat ECG data array isillustrated in Fig. 2. Using an appropriate QRS detection algo-rithm, an input ECG signal is QRS detected, and then cut andaligned every beats to form a 2-D array ( rows). To maxi-mally utilize the beat to beat correlation, QRS complex shouldbe properly aligned. The length of each heartbeat has to be pre-served and sent to the decoder for signal reconstruction. Sincethe length of each beat is different, an appropriate number ofzeros is padded to the end of each heartbeat data sequence (Be-cause the length of each beat is preserved and sent to the de-coder, the number of padded zeros need not be preserved forthe decoding process.). The constructed 2-D array is then slicedevery samples (columns) into blocks for 2-D waveletdecomposition.

C. 2-D Wavelet Decomposition and Coefficients Encoding

Before applying 2-D wavelet decomposition to each block,mean removal is performed on each block to reduce the numberof significant wavelet coefficients. Each mean-removed block isthen decomposed by using the Daubechies (Db8) wavelet. The

wavelet coefficients of each block are then encoded usingthe modified SPIHT algorithm and stored for the reconstructionof the ECG signal.

In order to reconstruct the ECG waveforms, the compresseddata must include the following items:

1) associated beat length information;2) mean value of each block;3) encoded bit stream of MSPIHT.Beat length information is defined as the length of each

heartbeat cycle, (e.g., the duration between adjacent peaks),and is utilized for ECG period recovery. Mean value of each

block must be stored for reconstructing the amplitude ofthe segmented ECG data. The encoded bit stream of MSPIHTcontains significant information for regenerating each


Fig. 2. Construction of a 2-D ECG data array. (a) Original ECG data sequence,(b) cut and aligned ECG data, (c) gray scale mapping of a 2-D ECG data array,and (d) 2-D array segmented into blocks.

block and forms the major part of the compressed data forsignal reconstruction.

V. EXPERIMENTAL RESULTS

This section describes the results of several experimentsthat verify the effectiveness of the proposed 2-D wavelet-basedECG data compression algorithm. The proposed algorithm isalso compared to other ECG coders with their reported per-formance in the literature. The proposed algorithm was testedand evaluated using 11 selected records from the MIT-BIHarrhythmia database. The record numbers for the test datasetare 100, 101, 102, 103, 107, 109, 111, 115, 117, 118, and119. These datasets were chosen because they were used inearlier studies, and allow us to compare the performance ofthe proposed method with others. We compressed 10 min ofdata from each of theses records for various compression ratiosand compared the performance with other existing algorithms.

TABLE IICORRELATION AMONG MIDDLE-FREQUENCY SUB-BANDS, WITH VARIOUS

BLOCK SIZES FOR ALL RECORDS IN THE MIT-BIH DATABASE

The sample rate and the resolution are 360 Hz and 11 bits, andhence total bit-rate is 3960 bps. The distortion between theoriginal and the reconstructed signal was measured by percentroot mean square difference (PRD). PRD is easy to calculateand compare, and is widely used in the ECG compressionliterature. The PRD is given by

(3)

where denotes the original data, denotes the recon-structed data, and , the number of samples. Since a baseline of1024 is added for the storage purpose in the MIT-BIH database,a level of 1024 is subtracted from each sample to give inthe PRD formula. The performance of the proposed algorithmwas compared with two 2-D ECG compression algorithms andseveral wavelet-based ECG compression algorithms. The com-pression ratio (CR) is calculated as the number of bits in theoriginal signal over the number of bits in the compressed signal.

In the first experiment, we will see redundancy among sub-bands and an appropriate wavelet decomposition level will bedecided. All records in the MIT-BIH database were tested andthe statistics for interband correlation were gathered. Table IIshows the correlation among , , and (partition

) for 3-level decomposition along with the correlation among, , and for 4-level decomposition. Table III shows

the correlation among LH bands ( and for 3-leveldecomposition or , , and for 4-level decomposi-tion), HL bands and HH bands. The modified SPIHT algorithmwas designed to utilize the interband correlation to achievebetter compression performance. As shown in Tables II andIII, the 3-level decomposition produces a smaller percentage ofsignificant coefficients. For instance, for a 32 256 block size,there are 49% middle-frequency coefficients significant for the


TABLE IIICORRELATION AMONG HIGH-FREQUENCY SUB-BANDS, WITH VARIOUS

BLOCK SIZES FOR ALL RECORDS IN THE MIT-BIH DATABASE

3-level decomposition ( ).For the 4-level decomposition, there are 61% middle-frequencycoefficients significant ( ).In the case of high-frequency subbands, there are 40% coef-ficients significant ( )for the 3-level decomposition and 54% coefficients signifi-cant ( ) for the4-level decomposition. Obviously, there are fewer interbandcorrelation and more significant coefficients for the 4-levelwavelet decomposition. Therefore, in the proposed algorithm,the wavelet decomposition level is set to be 3.

Since the modified SPIHT algorithm utilizes interbandcorrelation well to improve coding efficiency, it is reasonableto assume that the proposed algorithm achieves better per-formance with the modified SPIHT algorithm than with theoriginal SPIHT algorithm. Table IV shows the performancecomparison of the original SPIHT and the modified SPIHT al-gorithm. As shown in Table IV, even using a 32 32 block sizethat produce less interband correlation, the modified SPIHTalgorithm outperforms the original SPIHT algorithm in theproposed method.

In the second experiment, we verified the performance of theproposed algorithm with two different QRS detection schemes.The accuracy of the QRS detection process may affect the per-formance of a 2-D transform-based ECG compression method.Here we describe two existing QRS detection algorithms inthe literature and discuss the influence on the performanceof the 2-D ECG compression method. The Okada algorithm[20] utilizes digital filtering techniques in the problem of QRSdetection. The difference between 1) a three-point movingaverage of the ECG signal and 2) a low-pass filtering of theECG signal is computed. The difference signal is then squaredand multiplied by a nonlinearly filtered version of itself. Falsepeaks can be removed by searching the output of the 3 pointmoving average filter for local peaks. Shubha et al. proposeda wavelet transform-based QRS complex detector [21]. In this

TABLE IVPERFORMANCE COMPARISON (PRD) OF THE ORIGINAL SPIHT AND THE

MODIFIED SPIHT ALGORITHM WITH BLOCK SIZE 32� 32

Fig. 3. The performance of the proposed algorithm with different block sizesusing different QRS detection schemes (CR = 10).

method, a multiresolution approach is utilized. The input ECGsignal is segmented and decomposed using dyadic wavelet


TABLE VPERFORMANCE OF THE ECG COMPRESSION METHOD WITH/WITHOUT QRS DETECTION WITH BLOCK SIZE 32� 256

transform. QRS complexes could be detected by tackling peaksin its across successive dyadic scales. The primaryadvantages of the over existing techniques are 1) itsrobust noise performance and 2) its flexibility in analyzingthe time-varying morphology of ECG data [21]. Fig. 3 showsthe performance of the two QRS detection schemes describedabove with different block sizes. As shown in Fig. 3, the per-formance is better with larger block sizes. The result impliesthat smaller block sizes are more sensitive to the accuracyof QRS detection than larger block sizes. Fig. 3 also revealsthat the performance begins to saturate at a 32 256 blocksize with an accurate QRS detection scheme. According tothe results shown in Fig. 3, a 32 256 block size is selectedin the following experiments.Table V shows the compressionperformance with the above two QRS detection techniques andwithout QRS detection. Without applying QRS detection, the1-D ECG data is sliced and aligned every 512 samples. If QRSdetection is applied, the 1-D ECG data is sliced according tothe fiducial points detected. As shown in Table V, while noQRS detection is applied, the correlation between adjacentheartbeats can not be fully utilized, thus the performance iscomparatively worse at high compression ratio. On the otherhand, while at low compression ratio, the performance of theproposed method with QRS detection is a little worse thanthat without QRS detection. There are two probable reasonsthat may lead to such situation. The first reason is that whileno QRS detection is applied, there isn’t any side information(beat length) needed to be sent. Therefore, many bits are savedespecially at low compression ratio. In other words, more bitscan be used for encoding the wavelet coefficients. Second, theaverage beat length of the tested ECG records of the MIT-BIT

database according to the results of QRS detection is about 250samples, which implies that the length of segmentation (512samples) we adopted is about twice the detected average beatlength, i.e., the ECG data is somewhat aligned. According tothe results listed in Table V, we adopt the wavelet based QRSdetector throughout the rest of this paper.

The objective of the third experiment is to verify the effectof block size on the performance of the proposed algorithm. All11 selected records in the test dataset were used as test signals.Because the wavelet decomposition level is 3, the block size ischosen to be a multiple of 8. Each beat length is presented using10 bits, and the extracted mean value of each block ispresented using 9 bits.Table VI shows the compression ratios forvarious block sizes with identical PRD values for the selectedrecords from the MIT-BIH database. The results show that theperformance of the proposed algorithm is better with a largeblock size and the results remain consistent with different ECGsignals. According to the results shown in Table VI and Fig. 3,a 32 256 block size is recommended since with accurate QRSdetection, the performance of the proposed algorithm will notimprove significantly with a block size larger than 32 256.

In the fourth experiment, the proposed algorithm was com-pared with two 2-D ECG compression algorithms. The first 2-Dalgorithm was proposed by Lee and Buckley in 1999, which isa 2-D DCT based algorithm [14]. The algorithm proposed byLee is tested on ECG signals with 12-b resolution and 250-Hzsampling rate and the block size used is 32 32. Therefore, thecomparison was carried out using two selected records 100 and119 from the MIT-BIH database (all signals were converted to12-b resolution and a 250-Hz sampling rate) and the result isshown in Table VII. The second 2-D algorithm was proposed


TABLE VICRS FOR DIFFERENT BLOCK SIZES OF THE 11 SELECTED RECORDS FROM THE MIT-BIH DATABASE

TABLE VIICOMPARISON OF THE PROPOSED ALGORITHM AND THE 2-D DCT BASED ALGORITHM WITH BLOCK SIZE 32� 32

by Bilgin et al. in 2003, which apply the well known JPEG2000image coding standard on the ECG compression [17]. Identicaldataset was used in the experiment and the result is shown inFig. 4. The results show that the proposed algorithm has betterperformance than other 2-D algorithms.

In the fifth experiment, the proposed method was comparedwith other wavelet-based algorithms [1], [4], [7], [9]. The testdataset containing 11 selected records of the MIT-BIH data-base was encoded to evaluate the performance of the proposedmethod. Fig. 5 shows the PRD values versus compression ratios


Fig. 4. Comparison of performance of the proposed algorithm and otheralgorithms in the literature.

Fig. 5. PRD versus CR of selected records of the MIT-BIT database.

for each record of the test dataset with a 32 256 block size. Wecan see in Fig. 5 that the results for all test records are close toeach other. This implies that the proposed method is suitable forvarious morphologies of ECG data. The average PRD values ofthis experiment are presented in Fig. 4. A comparison betweenthe wavelet-based SPIHT ECG coder [7], the EZW ECG coder[9], and the proposed method is also given in Fig. 4. The re-sults show that the proposed method outperforms the other twocoders, especially at high compression ratio. There are two rea-sons that make the proposed algorithm perform better. The firstreason is that the proposed method utilizes the interbeat corre-lation of ECG signals using a 2-D strategy. The second reason

TABLE VIIIAVERAGE PRD’S OF ALL RECORDS IN THE MIT-BIH DATABASE WITH

DIFFERENT COMPRESSION RATIOS

Fig. 6. Original and reconstructed ECG signal of MIT-BIH record 102. (a) Theoriginal signal. (b) Reconstructed signal at 200 bps (PRD = 2:53%, block size32� 256). (c) Error signal.

is that the modified SPIHT algorithm used in the proposed al-gorithm further utilizes the interband correlation of the wavelettransformed 2-D array. All other records in the MIT-BIH data-base were also tested and the averages are listed in Table VIII.

There are other wavelet-based coders presented in the litera-ture. Hilton [4] reported the PRD value of 2.6% with CR 8:1 forrecord 117 and compared with the best previous coder reportedin [1] of 3.9%. Lu [7] reported the PRD value of 1.18% for thesame record and CR. The PRD value of the proposed method is0.94% for the same record and CR, which is considered betterthan the coders in [1], [4], and [7]. To reveal the visual qualityof the reconstructed signals, 1500 samples of the original signaland the reconstructed signals decoded at bit-rates of 200 of




Fig. 9.Original and reconstructed ECG signal of MIT-BIH record 119. (a) Theoriginal signal. (b) Reconstructed signal at 200 bps (PRD = 2:35%, block size32� 256). (c) Error signal.

selected records are reproduced in Figs. 6–9, respectively. Thereconstructed and original signals were examined by two car-diologists and they were asked if there are major errors thatwill affect the clinical diagnosis in the reconstructed signals.They commented that all the clinical information is preserved.As can be seen in Figs. 6–9, the characteristic features are wellpreserved in the reconstructed signals and the error signals arealmost uniformly distributed. The main effect of the proposedalgorithm is the smoothing of background noise.

VI. CONCLUSION

In this paper, we proposed a 2-D wavelet-based ECG com-pression approach, which utilized the long-term and short-termcorrelation of heartbeat signals. By coding several records inthe MIT-BIH arrhythmia database, the performance of theproposed method was tested. The performance of the pro-posed method was also compared with several wavelet-basedECG coders. The results show that the 2-D method proposedperformed better than the 1-D methods in the literature. Theexperimental results also show that the proposed method hasbetter performance than other 2-D methods for utilizing in-terband correlation of the wavelet transformed 2-D array. Theexperiments showed that the performance of a QRS detectionscheme may greatly affect the performance of a 2-D ECG com-pression method. Besides, the performance of a QRS detectoris affected by various noises and by varying morphologies.Therefore, an accurate QRS detector invariant to different noisesources and varying morphologies is essential to the proposed


method. Continuing our research, we will try to find an accu-rate wavelet based QRS detection scheme which can integratewith the latter wavelet decomposition stage.

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Shen-Chuan Tai received the B.S. and M.S. degreesin electrical engineering from National TaiwanUniversity, Taipei, Taiwan, R.O.C., in 1982 and1986, respectively, and the Ph.D. degree in computerscience from the National Tsing Hua University,Hsinchu, Taiwan, in 1989.

He is currently a Professor of electrical engi-neering in the Department of Electrical Engineering,National Chen Kung University, Tainan, Taiwan. Histeaching and research interests include data com-pression, DSP VLSI array processors, computerized

electrocardiogram processing, multimedia systems, and algorithms.

Chia-Chun Sun was born in Kaohsiung, Taiwan,R.O.C., in 1974. He received the B.S. and M.S.degrees in electrical engineering from the NationalChen Kung University, Tainan, Taiwan, in 1996 and1998, respectively. Currently, he is a Ph.D. degreecandidate in the Department of Electrical Engi-neering, National Chen Kung University, Tainan.

His research interests include data compressionand computerized electrocardiogram processing.

Wen-Chien Yan received the B.S. degree in informa-tion and computer engineering from the Chung YungChristian University, Chung Li, Taiwan, R.O.C., in2001. She received the M.S. degree from the NationalChen Kung University, Tainan, Taiwan, in 2003.

Her research interests include image compressionand image processing.

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2-D ECG Compression Method Based on Wavelet Transform and Modified SPIHT