LSPIHT Algorithm for ECG Data Compression and Transmission for Telemedicine Applications

Transcription

1 Dhaa Unv. J. Sc. 60(1): 31-36, 2012 (January) LSPIHT Algorthm for ECG Data Compresson and Transmsson for Telemedcne Applcatons Tahmna Zebn, Eramul Faroo, Syeda Znath Aman and Shahda Rafque Department of Appled Physcs, Electroncs & Communcaton Engneerng, Unversty of Dhaa, Dhaa-1000, Bangladesh. *Correspondng Autoher Receved on Accepted for Publcaton on Abstract Medcal mage analyss and data compresson are rapdly evolvng felds wth growng applcatons n healthcare servces e.g. teleradology, teleconsultaton, e-health, telemedcne and statstcal analyss of medcal data. In ths paper, a Layered Set Parttonng n Herarchcal Trees (LSPIHT) algorthm for medcal data compresson and transmsson s presented. In the LSPIHT, the encoded bt streams are dvded nto a number of layers for transmsson and reconstructon. Startng from the base layer, by accumulatng bt streams up to dfferent enhancement layers, medcal data can be reconstructed wth varous sgnal-to-nose ratos (SNRs) and resolutons. Recevers wth dstnct specfcatons can then share the same source encoder to reduce the complexty of telecommuncaton networs for telemedcne applcatons. The algorthm s compared wth other algorthms for encodng ECG data, and analyss shows that the LSPIHT attans better rate-dstorton performance and low networ complexty than other encodng technques. Keywords Dscrete Wavelet Transform (DWT), ECG, Telemedcne, Layered Image Transmsson (LIT) I. Introducton Compresson of medcal magery s an mportant area of Bomedcal Engneerng. Medcal mage analyss and data compresson are rapdly evolvng felds wth growng applcatons n the healthcare servces e.g. teleradology, teleconsultaton, e-health, telemedcne and statstcal analyss of medcal data 1. Not only t has brought a drastc change n the health care systems but also t has made the concept of tele-consultaton and telemedcne a realty. For telemedcne, medcal mage compresson (MIC) and analyss may even be more useful and can play an mportant role for the dagnoss of more sophstcated and complcated mages through consultaton of experts. The useful part of the mage may be hghlghted wth more contrast and resoluton for feature extracton and dagnoss through mage enhancement and analyss. In telemedcne, vdeos and the medcal mages are transmtted through advanced telecommuncaton lns, so the help of medcal mage compresson to compress the data wthout any loss of useful nformaton s of mmense mportance for faster transfer of nformaton 2. The mage transmsson tme depends on the bandwdth and the data transfer rate, so for the optmum use of the channel bandwdth, t s necessary to transmt the medcal mage data n compressed form. Now to save ds space and management overhead for dfferent types of encoded medcal data, a scalable transmsson scheme can be used where an encoded bt stream s delvered n two or more layers. At the recevng ends, medcal data wth dfferent SNRs and/or dfferent resolutons are reconstructed by decodng bt streams accumulated up to dfferent enhancement layers from the base layer. Users wth varous SNR and resoluton requrements therefore can share the same source encoder and transmsson system. Although many algorthms are effectve for medcal data compresson 3, they can not perform scalable codng. The wavelet-based embedded 4, 5, 6 codng algorthms can be employed for realzng scalable systems. Some of these algorthms, such as JPEG and the Set Parttonng n Herarchcal Trees (SPIHT) 7 algorthm have been found to outperform many exstng methods for mage compresson. However, the SPIHT algorthm s only SNR scalable snce t always encodes and dsplays reconstructed data at a fxed resoluton level (usually the full resoluton). The JPEG2000 can be used for SNR or resoluton scalable transmsson. The algorthm allows the compresson rato (CR) at each layer to be pre-specfed. Therefore, the SNR scalablty can be attaned f the bt stream s delvered n layer-resoluton-component-poston order. Ths paper shows a layered SPIHT (LSPIHT) technque for the desgn of scalable transmsson systems 8. In the LSPIHT, the CR and resoluton assocated wth each layer can be pre-specfed before encodng. The transmtted mages are reconstructed wth CR and resoluton dentcal to those of the hghest layer accumulated by the decoder. Both the SNR and resoluton scalabltes therefore can be acheved. To satsfy both CR and resoluton constrants at each layer, startng from the base layer, the LSPIHT encodes one layer at a tme untl the desgn of the top layer s completed. The encodng of each layer s based on SPIHT whch only covers the subbands wth resoluton lower than the resoluton constrant of that layer. To enhance the performance of SPIHT at each layer, the encodng results of the prevous layers are used. In ths paper, the LSPIHT s appled to mages of recorded ECGs for scalable transmsson, where dfferent layers are assocated wth dstnct CRs and resolutons. Smulaton results show that, as compared wth other data compresson technques, the

2 32 LSPIHT algorthm attans better rate-dstorton performance for the encodng of each layer whle demandng fewer resources and lower costs. II. Wavelet Transform and Scalable Transmsson Systems A. 2-D DWT(dscrete wavelet transform) for 2-D LSPIHT Let x be an mage to be transmtted over the scalable n n system. The dmenson of x s assumed to be 2 2. Let, X be the p-stage wavelet transform matrx of x, where p n n n.then, as shown n Fg. 1(a), X s also a 2 2 matrx contanng subbands X L, X V, X H, X D ; where, = 0, Tahmna Zebn et. al + ( n p) + ( n p) 1., p-1,each wth dmenson 2 2. To be noted, n the wavelet transform matrx, the subbands X (low-pass subbands at resoluton level ), and V H L X, X, X ( where V, H, D are orentaton selectve D hgh-pass subbands at resoluton level ), are obtaned recursvely from X L + 1 wth X = x, where resoluton level p refers to the full resoluton. The decomposton of X nto four sub-bands X, X, X, X can be L +1 carred out usng a smple quadrature mrror flter (QMF) scheme 9. L p L V H D Fg. 1. a) Wavelet transform coeffcents of an mage x; b) wavelet tree; c) encodng of LIT usng SPIHT. The wavelet coeffcents can be organzed as a set of trees, called wavelet trees, for mage codng. In the wavelet doman, wth the excepton of the subbands at lowest resoluton level, every coeffcent at a gven resoluton level can be related to a set of coeffcents of the same orentaton at the next hgher resoluton level. The coeffcent at the lowest resoluton level s called the parent, and all the coeffcents at the same spatal locaton and of the same orentaton at the next hgher resoluton level are called chldren. For the lowest resoluton subband, X, n Fg. L P 3 1.(b), the parent-chld relatonshp s defned such that each parent node has three chldren, one n each subband at the same resoluton level and spatal locaton havng dfferent orentaton. B. Layered Image Transmsson (LIT) System Typcal mplementaton of the scalable transmsson systems s based on the structure of the layered mage transmsson (LIT) system shown n Fg. 2. In the LIT, the CR and resoluton assocated wth each layer are desred to be prespecfed. In addton, the layers are arranged n such a way that layers havng lower resoluton are placed n lower postons. That s, I j I ; for j The low-pass subband X LI s also encoded at layer. However, the encodng process at each layer s not performed ndependently snce X LIj s a low pass sub-band of X LI, when j.the encoder at layer can utlze the encodng results at the prevous layers to reduce the overhead for scalable transmsson. To reconstruct medcal data at each layer, the decoder has to accumulate bt streams up to that layer startng from the base layer. The transmsson s assumed to be lossless. The resoluton of the reconstructed medcal data after decodng s the resoluton of the layer n the hghest poston among the layers decoded by the recever. Let the ncremental rate at layer of the LIT, denoted by τ, be the number of bts per pxel at layer. The accumulated rate r, can be obtaned by r = 1 + τ ; = 0 0 ; r r (1) Where, the ncremental rate τ s used to compute the Compresson Rato (CR) at layer, the accumulated rate r ndcates the number of bts requred for decodng at layer.

3 LSPIHT Algorthm for ECG Data Compresson and Transmsson for Telemedcne Applcatons 33 Fg. 2. Basc Structure of Layered Image Transmsson (LIT) System In the SPIHT and the JPEG2000 algorthms, the rate for encodng an mage X can be pre-specfed. In the LIT systems, however, the X LI ; = 1,2,.,N vewed as the subbands of x. Snce the rate allocated to these subbands can not be prespecfed n the SPIHT and JPEG2000 algorthms, t may be dffcult to control the ncremental rate at each layer usng these algorthms for the mplementaton of the LIT. Thus a Layered SPIHT (LSPIHT) algorthm descrbed n the next segment could be a better soluton for LIT. III. LSPIHT Algorthm The LSPIHT algorthm can be vewed as a sequence of operatons usng the SPIHT algorthm wth one operaton for each layer. Fg. 1(c) shows a smple example for the desgn of the LIT usng the LSPIHT technque. In Fg. 1(c), 4 4 the dmenson of an mage x s assumed to be 2 2 (.e., n = 4).The number of layers s N = 2 and resoluton levels assocated wth layer 1 and layer 2 are I 1 = 3 and I 2 = 4 respectvely. Because I 1 =3 the subbands X Lo, X VK, X HK, X DK wth = 0, 1, 2 are the subbands consttutng layer 1 (showed by shaded area n fg 1(c)). Smlar ndependent encodng can be done at layer 2 wth I 2 =4, but ths may result n large overhead. In the SPIHT and the JPEG2000 algorthms, the rate for encodng an mage X can be pre-specfed. In the LIT systems, however, the X LI ; = 1,2,.,N vewed as the subbands of x. Snce the rate allocated to these subbands can not be prespecfed n the SPIHT and JPEG2000 algorthms, t may be dffcult to control the ncremental rate at each layer usng these algorthms for the mplementaton of the LIT. Thus a Layered SPIHT (LSPIHT) algorthm descrbed n the next segment could be a better soluton for LIT. IV. LSPIHT Algorthm The LSPIHT algorthm can be vewed as a sequence of operatons usng the SPIHT algorthm wth one operaton for each layer. Fg. 1(c) shows a smple example for the desgn of the LIT usng the LSPIHT technque. In Fg. 1(c), 4 4 the dmenson of an mage x s assumed to be 2 2 (.e., n = 4).The number of layers s N = 2 and resoluton levels assocated wth layer 1 and layer 2 are I 1 = 3 and I 2 = 4 respectvely. Because I 1 =3 the subbands X Lo, X VK, X HK, X DK wth = 0, 1, 2 are the subbands consttutng layer 1 (showed by shaded area n fg 1(c)). Smlar ndependent encodng can be done at layer 2 wth I 2 =4, but ths may result n large overhead.

4 34 Tahmna Zebn et. al Fg. 3. Flowchart and Algorthm for the Layered Set Parttonng n Herarchcal Trees (LSPIHT) algorthm. In contrast, usng the encodng results at layer 1 for the encodng operaton at layer 2 can effectvely reduce ths overhead. Now to descrbe 2-D LSPIHT, the concept of wavelet has been recalled 10. A wavelet coeffcent W s sad to be sgnfcant for bt depth m f W 2 m, otherwse t s sad to be nsgnfcant. Moreover, a wavelet tree s sad to be sgnfcant for bt depth m f some of ts coeffcents have absolute value larger than 2 m. The orgnal SPIHT algorthm repeatedly employs a set parttonng algorthm for dentfyng and refnng sgnfcant wavelet coeffcents untl the rate budget s exhausted. Each successve applcaton of the set parttonng operaton decreases the bt depth m by one. For each m, the set parttonng operaton conssts of two passes: the sortng pass and the refnng pass. To effectvely realze these two passes, three lsts of nformaton, termed Lst of Sgnfcant Pxels (LSP), Lst of Insgnfcant Pxels (LIP) and Lst of Insgnfcant Sets (LIS), are mantaned at any pont of codng. The lsts LSP and LIP contan the locatons of sgnfcant and nsgnfcant wavelet coeffcents, respectvely. The lst LIS contans the root node of the nsgnfcant wavelet tree. The overall flowchart and steps for the LSPIHT algorthm s shown n Fg. 3. V. Performance Analyss Table 1 shows the performance of the LIT system realzed by LSPIHT for varous ECGs. The ECGs are taen from the MIT-BIH arrhythma database 11 records 100, 117 and 119, sampled at 360 Hz and 11-bt precson. Table. 1. Performance of the ECG transmsson systems realzed by the LSPIHT and SPIHT algorthms System LSPIHT bases LIT System SPIHT based Smulcast System[6] (layer number) Layer 1 Layer 2 Layer 1 Layer 2 I (resoluton at level ) CR (Compresson rato) 16:1 32:3 16:1 32:3 SNR MIT mn of data from each of these records has been encoded for ths wor. To obtan the wavelet coeffcents of ECG, each record s segmented nto non-overlappng and contguous vectors havng dentcal dmenson Each vector s then ndependently encoded usng the LSPIHT. Therefore, the full resoluton level s n=10. The number of layers n the transmsson system s N = 2. The resoluton level of layers 1 and 2 are I 1 = 9, I 2 =10, and respectvely.

5 LSPIHT Algorthm for ECG Data Compresson and Transmsson for Telemedcne Applcatons 35 The performances at each layer are percent root mean square dfference (PRD) and CR. For the case of ECG compresson, let X be the ECG to be encoded, then the lowpass subband X LI s the desred ECG to be reconstructed n the layer. Let Xˆ be the reconstructed mage n the layer and D be LI the mean squared dstance between X and LI Xˆ LI.Then the PRD n the layer, s defned as: D PRD = 100 (2) E where E denotes the energy of X LI. The CR n the layer s defned as: CR B = Bˆ (3) Where B and Bˆ are the total number of bts used for representng X and Xˆ respectvely 12. LI LI In ths paper, the CR at layers 1 and 2 are gven by 16:1 and 32:3, respectvely. Fg. 4 shows the orgnal and reconstructed versons of the ECGs coded by LSPIHT at each layer. The ECGs n the layer 1 are of lower resoluton and, therefore, are smaller n sze. They are zoomed n/up to have same sze mage as n layer 2 for easy comparson. From Fg. 4, the major effect of compresson s observed, especally n layer 1, s the smoothng of the bacground nose. Otherwse, the features of the waveform appear to be fathfully preserved. Fg. 4. Orgnal and reconstructed ECGs of MIT-BIH 117 at each layer of LIT shown n Table 1. a) Orgnal ECG 11. (b) Reconstructed ECG at layer 1.(c) Reconstructed ECG at layer 2. Table 1 also shows the perfor mances of a two-layer smulcast system for encodng ECG sgnals. Snce the JPEG2000 s used only for the mage compresson, only the performance of the SPIHT-based smulcast system s ncluded n table 1. The CR and resoluton assocated wth each layer of the system s dentcal to those of LSPIHTbased LIT system shown n the table. Consequently, the LIT and smulcast systems have the same performance at layer 1 because both systems employ the SPIHT over the X wth the same rate at that layer. LI 1 VI. Concluson Ths paper utlzes LSPIHT technque for the scalable medcal data compresson and transmsson. The technque allows the resoluton and the compresson rato (CR or the rate) at each layer to be predefned before the desgn. The encodng process s then executed based on those specfcatons. The algorthm s based on a sequence of SPIHT algorthms and, therefore, s smple to mplement. Based on the same resoluton and CR at each layer, the algorthm outperforms other methods for the compresson of ECG data. Because of ts effectveness and smplcty, the

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