Encyclopedia of Healthcare Information Systems

Transcription

1 Ecyclopedia of Healthcare Iformatio Systems Nilmii Wickramasighe Illiois Istitute of Techology, USA Eliezer Geisler Illiois Istitute of Techology, USA Volume I A-D Medical Iformatio sciece referece Hershey New York

2 Acquisitios Editor: Developmet Editor: Seior Maagig Editor: Maagig Editor: Assistat Maagig Editor: Copy Editor: Typesetter: Cover Desig: Prited at: Kristi Kliger Kristi Roth Jeifer Neidig Jamie Savely Carole Coulso Laura Kochaowski, Jeaie Porter, ad Sue Vader Hook Jeff Ash ad Sea Wozicki Lisa Tosheff Yurchak Pritig Ic. Published i the Uited States of America by Iformatio Sciece Referece (a imprit of IGI Global) 71 E. Chocolate Aveue, Suite 2 Hershey PA 1733 Tel: Fax: cust@igi-global.com Web site: ad i the Uited Kigdom by Iformatio Sciece Referece (a imprit of IGI Global) 3 Herietta Street Covet Garde Lodo WC2E 8LU Tel: Fax: Web site: Copyright 28 by IGI Global. All rights reserved. No part of this publicatio may be reproduced, stored or distributed i ay form or by ay meas, electroic or mechaical, icludig photocopyig, without writte permissio from the publisher. Product or compay ames used i this set are for idetificatio purposes oly. Iclusio of the ames of the products or compaies does ot idicate a claim of owership by IGI Global of the trademark or registered trademark. Library of Cogress Catalogig-i-Publicatio Data Ecyclopedia of healthcare iformatio systems / Nilmii Wickramasighe ad Eliezer Geisler, editors. p. ; cm. Icludes bibliographical refereces. Summary: This book provides a extesive ad rich compilatio of iteratioal research, discussig the use, adoptio, desig, ad diffusio of iformatio commuicatio techologies (ICTs) i healthcare, icludig the role of ICTs i the future of healthcare delivery; access, quality, ad value of healthcare; ature ad evaluatio of medical techologies; ethics ad social implicatios; ad medical iformatio maagemet --Provided by publisher. ISBN (h/c) 1. Medical iformatics--ecyclopedias. I. Wickramasighe, Nilmii. II. Geisler, Eliezer, [DNLM: 1. Iformatio Systems--Ecyclopedias--Eglish. W 13 E ] R858.E dc British Cataloguig i Publicatio Data A Cataloguig i Publicatio record for this book is available from the British Library. All work cotributed to this ecyclopedia set is origial material. The views expressed i this ecyclopedia set are those of the authors, but ot ecessarily of the publisher. If a library purchased a prit copy of this publicatio, please go to for iformatio o activatig the library's complimetary electroic access to this publicatio.

3 Biomedical Sigal Compressio Pedro de A. Berger Uiversity of Brasilia, Brazil B Fracisco A. de O. Nascimeto Uiversity of Brasilia, Brazil Leoardo R. A. X. de Meezes Uiversity of Brasilia, Brazil Adso F. da Rocha Uiversity of Brasilia, Brazil Joao L. A. Carvalho Uiversity of Souther Califoria, USA ItroductIo Digitizatio of biomedical sigals has bee used i several areas. Some of these iclude ambulatory moitorig, phoe lie trasmissio, database storage, ad several other applicatios i health ad biomedical egieerig. These applicatios have helped i diagostics, patiet care, ad remote treatmet. Oe example is the digital trasmissio of ECG sigals, from the patiet s house or ambulace to the hospital. This has bee prove useful i cardiac diagoses. Biomedical sigals eed to be digitally stored or trasmitted with a large umber of samples per secod, ad with a great umber of bits per sample, i order to assure the required fidelity of the waveform for visual ispectio. Therefore, the use of sigal compressio techiques is fudametal for cost reductio ad techical feasibility of storage ad trasmissio of biomedical sigals. The purpose of ay sigal compressio techique is the reductio of the amout of bits used to represet a sigal. This must be accomplished while preservig the morphological characteristics of the waveform. I theory, sigal compressio is the process where the redudat iformatio cotaied i the sigal is detected ad elimiated. Shao (1948) defied redudacy as the fractio of uecessary iformatio, ad therefore repetitive i the sese that if it was missig, the the iformatio would still be essetially complete, or it could at least be recovered. Sigal compressio has bee widely studied durig the past decades, ad several refereces discuss this subject (Gersho & Gray, 1992; Jayat & Noll, 1982; Sayood, 1996). Sigal compressio techiques are commoly classified i two categories: lossless ad lossy compressio. Lossless compressio meas that the decoded sigal is idetical to the origial oe. I lossy compressio, a cotrolled amout of distortio is allowed. Lossy sigal compressio techiques show higher compressio gais tha lossless oes. Backgroud lossless compressio Lossless sigal compressio techiques are less efficiet with respect to compressio gais. They may be used i combiatio with lossy compressio techiques, especially i cases where the maximum allowed distortio has bee reached, ad additioal compressio is eeded. Amog several lossless compressio techiques, we highlight etropy codig (Gersho & Gray, 1992), Ru- Legth, Huffma (Huffma, 1952), arithmetic codig (Witte, 1987), ad delta codig (Ke, 1985). Ru-Legth Codig Data files frequetly preset sequetially repeated characters (a character ru). For istace: text files use several spaces to separate seteces ad paragraphs. Digital sigals may cotai the same value, or the same character represetig that value i its data file, repeated Copyright 28, IGI Global, distributig i prit or electroic forms without writte permissio of IGI Global is prohibited.

4 may times sequetially. This idicates that the sigal is ot chagig, as i the isoelectric segmets of ECG sigals, for example. Figure 1 shows a example of Ru-Legth codig of a data set that cotais rus of zeros. Each time the coder fids a zero i the etry data, two values are writte i the output data. The first of these values is a zero idicatig that the Ru-Legth codificatio started. The secod value is the amout of zeros i the sequece. If the ru of zeros i the iput data set is i average larger tha two, the the Ru-Legth coder will achieve data compressio. Huffma Codig I Huffma codig, the data are represeted as a set of variable legth biary words. The legths deped o the occurrece frequecy of the symbols used for represetig each sigal value. Characters that are used ofte are represeted with fewer bits, ad those that are seldom used are represeted with more bits. Figure 2 shows a example of how a Huffma code is geerated, give a data set X ad its characteristic probability of occurrece p(x). The character codes are geerated by combiig the bits of a tree with ramificatios, addig their probabilities ad restartig the process util oly oe character remais. This process geerates a three with ramificatios liked to bits ad 1. The codes for each character are take i the iverse path of these ramificatios. Note that iitial character arragemet is ot relevat. I this example, we chose to ecode the upper ramificatios with bit ad the lower oes with bit 1. However, the opposite represetatio could have bee used as well. Ay decisio criteria may be used i ramificatios with equal probabilities. Huffma codig has the disadvatage of assigig a iteger umber of bits to each symbol. This is a suboptimal strategy, because the optimal umber of bits per symbol depeds o the iformatio cotet, ad is geerally a ratioal umber. Arithmetic codig is a more sophisticated compressio techique, based o Huffma codig cocepts. It results i compressio gais closer to the theoretical limits. I this codig, character sequeces are represeted by idividual codes depedig o their probability of occurrece. Huffma ad Arithmetic codes are ofte used i combiatio with Ru-Legth codig, for further compressig biomedical sigals that were first compressed usig orthogoal trasforms. Delta Codig Delta codig refers to sigal compressio techiques that store a digital sigal as the differece betwee successive samples. Figure 3 shows a example of how this is performed. The first sample i the ecoded sigal is equal to the first sample of the origial sigal. Subsequet ecoded samples are equal to the differece betwee the curret sample ad the previous sample of the origial sigal. Usig this techique, the ecoded sigal has a smaller amplitude dyamic rage tha the origial sigal. Therefore, it takes fewer bits to store or trasmit the ecoded sigal. Delta codig is a particular case of Differetial Pulse Code Modulatio (DPCM). DPCM is used i combiatio with Huffma coders i several biomedical sigal compressio algorithms. Figure 1. Ru-legth codig example

5 Figure 2. Huffma code costructio example B Figure 3. Delta codig example lossy compressio There are two major categories of lossy compressio techiques used with biomedical sigals: direct methods, ad trasform compressio. Direct Methods Direct methods ecode sigals i time domai. These algorithms deped o the morphology of the iput sigal. I most cases, these methods are complex, ad provide lower compressio efficiecy tha trasform coders (discussed i the ext sectio). Direct compressio methods use sophisticated processes ad itelliget sigal decimatio ad iterpolatio. I other words, these methods extract K sigificat samples of the origial sigal x(), such that: (,x ()), =,..., N-1 (,x( )), k =,...,K-1, k k (1) where k<n. The recostructio of values betwee sigificat samples is performed by iterpolatio, usig the geeric expressio (Sörmo & Lagua, 26): x(), =,...,k 1; f, 1,...,1 1;, () = + 1 x()= ˆ f K-2 1,..., 1 1; K-2, () = + K K-1 (2) The process of selectig sigificat samples is based o the characteristics of the sigal, ad o a tolerace iterval criterio for the recostructio error. The iterpolatio fuctio f, () is geerally a low k-1 k order polyomial, of either zero or first order. These polyomials approximate the origial sigal with a series of lies coectig the K sigificat samples. The geometric parameters of these lies (legth ad icliatio) are stored istead of the discarded sample values, resultig i a reductio i the amout of stored or trasmitted data.

6 Trasform Compressio Amog the several methods for sigal compressio, the techiques based o trasforms yield the best performace i terms of compressio gai ad fidelity of the waveform of the recostructed sigal. Give a vector of data x=[x(1) x(2)... x(n)], we ca defie a orthogoal trasform as a liear operatio give by a liear trasformatio T, such that: y = Tx, (3) where y=[y(1) y(2)... y(n)] represets a vector of trasformed coefficiets, ad T satisfies the orthogoality coditio: T t = T -1 (4) Trasform compressio is based o a simple premise: whe the sigal is processed by a trasform, the sigal eergy (iformatio) that was distributed amog all the samples i the time domai ca be represeted with a small umber of trasformed coefficiets. This ca be observed i Figure 4, where a ECG sigal is show alog with the correspodet coefficiets i trasformed domai. I this example, we use the discrete cosie trasform (DCT). The DCT is used i the most popular stadard for image compressio, the Joit Picture Expert Group (JPEG). Note that, i the trasformed domai, the eergy of the sigal is cocetrated i a small umber of coefficiets with high amplitude. Thus, if we store the highamplitude coefficiets, ad discard the low-amplitude coefficiets, the sigal may be represeted accurately eough, ad ca be recovered by iverse trasformatio. Figure 5 shows the same ECG sigal i Figure 4, ad the recostructed sigal after discardig 8% of the DCT coefficiets. Note that, by storig oly 2% of the DCT coefficiets it is possible to recostruct the origial sigal without visible distortios. Curretly, the most widely used trasform for ecodig biomedical sigals is the discrete wavelet trasform (Daubechies, 1988; Mallat, 1989). The wavelet trasform is used for image compressio such as i the JPEG 2 compressio stadard ad i more recet studies o biomedical sigal compressio. I this trasform, a sigal cotaiig N samples is filtered by a pair of filters that decompose the sigal ito low- (L) ad a high- (H) frequecy bads. Each bad is udersampled by a factor of two; that is, each bad cotais N/2 samples. With the appropriate filter desig, this actio is reversible. This procedure ca be exteded for two-dimesioal sigals, such as images. I Figure 6, we show a example of wavelet decompositio for a gray-scale image with 256 x 256 pixels. Similarly to what was observed usig the DCT, may of the coefficiets i the high-frequecy subbads have amplitudes close to zero (very dark pixels), ad it is possible to compress the image by discardig them. Wavelet trasform compressio is evolvig with respect to the way i which the coefficiets are ecoded. Whe a coefficiet i a low-frequecy subbad is ozero, there is a high probability that, at positios that correspod to high frequecies, the coefficiets are also ozero. Thus, the ozero coefficiets ca be represeted i a tree, begiig with a low frequecy root. Figure 7 illustrates this cocept. A sigle coefficiet i the LL bad of layer 1 has a correspodet coefficiet i the other bads. The positios of the coefficiets i layer 1 are mapped ito four daughter-positios i each subbad of layer 2. A efficiet way of codig the coefficiets that are o-zero is to code each tree of coefficiets, begiig with the root decompositio level. The coefficiets at the lower layers are ecoded, ad followed by their childre coefficiets i the higher layer, util a ull coefficiet is foud. The ext coefficiets of the tree have great probability of also beig ull, ad they are replaced by a code that idetifies a tree of zeros (zerotree code). This method is called Embedded Zerotree Wavelet (EZW). Aother method, similar to the EZW, ad commoly used i the wavelet coefficiets ecodig, is the Set Partitioig I Hierarchical Tree (SPIHT) (Said & Pearlma, 1996). commets o curret ad Future research The compressio of biomedical sigals has bee extesively studied by the scietific commuity. I this article, we discuss more thoroughly the compressio of electrocardiographic (ECG) ad electromyographic (EMG) sigals. I geeral, we ca group the techiques for compressio of ECG sigals i two mai groups:

7 Figure 4. (a) ECG sigal (top); (b) trasformed coefficiets (bottom) 1 B mv s Dedicated techiques: a. Direct Methods: Amplitude Zoe Time Epoch Codig (AZTEC) (Cox, Noelle, Fozzard, & Oliver, 1968), Turig Poit (TP) (Mueller, 1978), Coordiate Reductio Time Ecodig System (Abestei & Tompkis, 1982), FAN algorithm (Dipersio & Barr, 1985) ad modified time domai codig algorithms, such as SLOPE (Tai, 1991) ad Sca Alog Polygoal Approximatio (SAPA) (Shahei & Abbas, 1994). b. Optimizatio algorithms: Log-Term Predictio (LTP) (Nave & Cohe, 1993), algorithms based o aalysis by sythesis (ASEC) (Jalaleddie, 199), ad the Cardiality Costraied techique (Nygaard & Haugla, 1998). 2. Geeric techiques: These techiques ca be used with a great variety of sigals, icludig voice, image, ad video. This icludes Differetial Pulse Code Modulatio (DPCM), Subbad Codig (SC) ad trasform-based codig (Hilto, 1997; Istepaia, Hadjileotiadis, & Paas, 22; Lu, Kim, & Pearlma, 2; Rajoub, 22).

8 Figure 5. (a) origial ECG sigal (top); (b) recostructed ECG sigal after discardig 8% of the coefficiets (bottom) mv mv Curretly, the algorithms that provide the best ECG compressio results use trasform-based codig, ad the most widely used is the wavelet trasform. These algorithms ca be grouped, with respect to coefficiet ecodig, ito two mai groups: algorithms with coefficiet thresholdig, ad algorithms with tree-based coefficiet ecodig. Coefficiet thresholdig algorithms follow a methodology that was preseted i the previous sectio. The majority of these algorithms also apply lossless compressio techiques to ecode the wavelet coefficiets. Oe example of this techique is the work by Rajoub (22). Tree-based coefficiet ecodig algorithms use hierarchic structures for ecodig the wavelet coefficiets, by exploitig the redudacy i the scales of the wavelet decompositio. Such algorithms provide results superior to traditioal thresholdig algorithms. Amog recet works that use this paradigm, we ca metio the works of Istepaia et al. (22), Hilto (1997), ad Lu et al. (2).

9 Figure 6. Two-dimesioal wavelet decompositio Lx B L /2 LL L /2 H /2 LH L /2 HL H /2 H /2 HH Ly Figure 7. Wavelet coefficiets tree The mai techiques described i the literature for EMG sigal compressio ca be foud i (Berger, Nascimeto, Carmo, & Rocha, 26; Guerrero & Maihes, 1997; Norris, 21; Norris, Eglehart, & Lovely, 21; Wellig, Zhela, Semlig, & Moschytz, 1998). Norris et al. (1995) ivestigates the compressio of EMG sigals usig Adaptive Differetial Pulse Code Modulatio (ADPCM). Guerrero ad Maihes (1997) compared differet methods for lossless compressio with methods based o orthogoal trasforms. The orthogoal trasform based showed better performace, with respect to compressio ratio. Recetly, the use of wavelet trasform for compressio of EMG sigals was studied by Wellig et al. (1998), Norris et al. (21), ad Berger et al. (26). Wellig et al. (1998) ad Norris et al. (21) ecoded the trasformed coefficiet usig the EZW algorithm ad compared their results with the traditioal wavelet trasform. Berger et al. (26) used a scheme for adaptive dyamic bit allocatio for ecodig the coefficiets. These methods provide performace equivalet or better tha previously described methods. Comparig differet algorithms for EMG sigal compressio is difficult, because there is o stadard

10 database, such as the MIT-BIH Arrhythmia Database, which is used i most studies o compressio of ECG sigals. The studies o EMG sigal compressio usually use differet test sigals, ivolvig differet muscles, volume coductors, coductio velocities, loads, samplig rates ad duratio. Therefore, the compariso betwee differet algorithms should always be aalyzed with cautio. The algorithms metioed i this article have the goal of guarateeig the fidelity of the recostructed sigal after decodig. I this sese, the wavelet trasform ad the EZW ad SPIHT algorithms are cosidered by the specialized public as the most promisig lies of work, ad future research ted to emphasize improvemets i these algorithms. However, reachig a good quality represetatio of sigals with low bit rates comes with the cost of icreasig the complexity of the compressio algorithms. Few studies o low-cost real-time compressio of biomedical sigals have bee published, eve though the iterest o telemedicie applicatios is growig. This is a importat issue, which should be addressed i the future. The works by Alesaco, Olmos, Istepaia, ad García (23) ad Kim, Yoo, ad Lee (26) proposed the first solutios for real-time ECG compressio, ad Carotti, De Marti, Merletti, ad Faria (26) a lossy codig techique for surface EMG sigals that is based o the algebraic code excited liear predictio (ACELP) paradigm, widely used for speech sigal codig. The algorithm was adapted to the EMG characteristics ad tested o both simulated ad experimetal sigals. This method is characterized by moderate complexity (approximately 2 millio istructios/s) ad a algorithmic delay smaller tha 16 samples ( 16 ms). coclusio This article preseted a review of techiques for compressio of biomedical sigals. Amog the differet techiques that were preseted, the oes based o wavelet trasforms had the best performace with respect to compressio gai ad recostructed waveform fidelity. Whe the wavelet trasform is used, a great challege is to fid effective alteratives for efficietly ecodig the trasformed coefficiets. The most efficiet methods for this are the EZW ad SPIHT algorithms. A importat lie of future work is the search for real-time, low-cosumptio algorithms, which would be suitable for telemedicie applicatios. refereces Abestei, J., & Tompkis, W. (1982). New data-reductio algorithm for real-time ECG aalysis. IEEE Tras. Biomed. Egieerig. 29, Alesaco, A., Olmos, S., Istepaia, R., & Garcia, J. (23). A ovel real-time ultilead ECG compressio ad de-oisig method based o the wavelet trasform. Computers i Cardiology, 3, Alesaco, A., Olmos, S., Istepaia, R.S.H., & García, J. (26) Ehaced real-time ECG coder for packetized telecardiology applicatios. IEEE Trasactios o Iformatio Techology i Biomedicie, 1(2), Berger, P.A., Nascimeto, F.A.O., Carmo, J.C., & Rocha, A.F. (26) Compressio of EMG sigals with wavelet trasform ad artificial eural etworks. Physiological Measuremet, 27, Carotti, E., De Marti, J.C., Merletti, R., & Faria, D. (26). Compressio of surface EMG sigals with algebraic code excited liear predictio. Medical Egieerig & Physic, 29 (2), Cox, J., Noelle, F., Fozzard, H., & Oliver, G. (1968). AZTEC: A preprocessig program for real-time ECG rhythm aalysis. IEEE Tras. Biomed. Egieerig. 15, Daubechies, I. (1988). Orthogoal bases of compactly supported wavelets. Comm. Pur. Appl. Math. 41, Dipersio, D.A., & Barr, R.C. (1985). Evaluatio of the FAN method of adaptive samplig o huma eletrocardiograms. Med. Biomed. Eg. Computig, Guerrero, A., & Maihes, C. (1997). O the choice of a electromyogram data compressio method. I Proceedigs of the 19th aual Iteratioal Coferece of the IEEE Egieerig i Medicie Biology Society (pp ). Gersho, A., & Gray, R. (1992). Vector quatizatio ad sigal compressio. Kluwer Acad. Publicatio.

11 Hilto, M.L. (1997). Wavelet ad wavelet packet compressio of electrocardiograms. IEEE Tras. Biomed. Egieerig, 44, Huffma, D.A. (1952). A method for the costructio of miimum redudacy codes. I Proceedigs of IRE (Vol. 4, No. 1, pp ). Istepaia, R.S.H., Hadjileotiadis, L., & Paas, S. (21). ECG data compressio usig wavelets ad higher order statistics methods for telemedical applicatios. IEEE Trasactios o Iformatio Techology i Biomedicie, 5(2), Jalaleddie, S.M., Hutches, C.G., Satratta, R.D., & Coberly, W.A. (199). ECG data compressio techiques The uified approach. IEEE Tras. Biomed. Egieerig, 37(4), Jayat, N.S., & Noll, P. (1982). Digital codig of waveforms priciples ad applicatio to speech ad video. Pretice Hall. Ke, C. P. (1985). Priciples of digital audio. Sams/ Pretice-Hall Computer Publishig. Kim, S.B., Yoo, S.K., & Lee, M.H. (26). Waveletbased low-delay ECG compressio algorithm for cotiuous ECG trasmissio. IEEE Trasactios o Iformatio Techology i Biomedicie, 1(1), Lu, Z., Kim, D.Y., & Pearlma, W.A. (2). Wavelet compressio of ECG sigals by the set partitioig i hierarchical trees (SPIHT) algorithm. IEEE Tras. Sigal Processig, 47, Mallat, S. (1989). A theory for multiresolutio sigal decompositio: The wavelet represetatio. I Proceedigs of IEEE Tras o Patter Aal. ad Math. itel. (Vol. 11, No. 7). Mueller, W. (1978). Arrhythmia detectio program for a ambulatory ECG moitor. IEEE Tras. Biomed. Egieerig, 14, Nave, G., & Cohe, A. (1993). ECG compressio usig log-term predictio. IEEE Tras. Biomed. Egieerig, 4, Norris, J.A., Eglehart, K., & Lovely, D. (21). Steadystate ad dyamic myoelectric sigal compressio usig embedded zero-tree wavelets. I Proceedigs of the 23th aual Iteratioal Coferece of the IEEE Egieerig i Medicie Biology Society (pp ). Nygaard, R., & Hauglad, D. (1998). Compressig ECG sigals by piecewise polyomial approximatio. I Proceedigs of the It. Cof. Acoust. Speech Sigal Processig (pp ). Seattle, WA. Rajoub, B.A. (22). A efficiet codig algorithm for the compressio of ECG sigals usig the wavelet trasform. IEEE Tras. Biomed. Eg., 49(4), Said, A., & Pearlma, W.A. (1996). A ew fast ad efficiet image codec based o set partitioig i hierarchical Trees. IEEE Trasactios o Circuits ad Systems for Video Techology, 6, Sayood, K. (1996). Itroductio to data compressio. I C.F. Shahei, & H.M. Abbas (Eds.), ECG Data-Compressio via Cubic-Splies ad Sca Alog Polygoal Approximatio. Sigal Processig, 35(3), Morga Kaufma. Shahei, C.F., & Abbas, H.M. (1994). ECG data-compressio via cubic-splies ad sca alog polygoal approximatio. Sigal Processig, 35(3), Shao, C.E. (1948). A mathematical theory of commuicatio. Bell System Tech. Joural, 27, Sörmo, L., & Lagua, P. (26). Electrocardiogram (ECG) sigal processig. I M. Akay (Ed.), Wiley Ecyclopedia of Biomedical Egieerig (Vol. 2, pp ). Wiley. Tai, S.C. (1991). Slope a real-time ECG data compressor. L Biomed. Eg. Computig, 29, Wellig, P., Zhela, C., Semlig, M., & Moschytz, G.S. (1998). Electromyogram data compressio usig sigle-tree ad modified zero-tree wavelet ecodig. I Proceedigs of Egieerig i Medicie ad Biology Society 23rd Aual Iteratioal Coferece of the IEEE (pp ). Witte, I., Neal, R., & Cleary, J. (1987). Arithmetic codig for data compressio. Commuicatios of the ACM, 3(6). B

12 key terms Arithmetic Codig: A more sophisticated compressio techique, based o Huffma codig cocepts. It results i compressio gais closer to the theoretical limits. I this codig, character sequeces are represeted by idividual codes depedig o their probability of occurrece. Biomedical Sigals: Refers to sigals that carry useful iformatio for probig, explorig, ad uderstadig the behavior of biomedical systems uder ivestigatio. Delta Codig: Refers to sigal compressio techiques that store a digital sigal as the differece betwee successive samples. The first sample i the ecoded sigal is equal to the first sample of the origial sigal. Subsequet ecoded samples are equal to the differece betwee the curret sample ad the previous sample of the origial sigal. Direct Methods: Ecode sigals i time domai. These algorithms deped o the morphology of the iput sigal. Direct compressio methods use sophisticated processes ad itelliget sigal decimatio ad iterpolatio. Discrete Cosie Trasform: A techique for expressig a waveform as a weighted sum of cosies. The DCT is cetral to may kids of sigal processig, especially video compressio. Embedded Zerotree Wavelet: A simple, yet remarkable effective, compressio algorithm witch exploits the self-similarity of the wavelet trasform coefficiets at differet scales, by structurig the data i hierarchical tree sets that are likely to be highly correlated, yieldig a fully embedded code. Huffma Codig: Refers to a compressio techique where the data are represeted as a set of variable legth biary words. The legths deped o the frequecy of occurrece of the symbols used for represetig each sigal value. Characters that are used ofte are represeted with fewer bits, ad those that are seldom used are represeted with more bits. Lossless Compressio: A sigal compressio techique where the origial sigal ca be perfectly recovered from the compressed sigal. The Morse code of telegraphy provides a classic example: by sedig short patters (dots ad dashes) for frequet letters, ad log patters for rare letters, fewer bits are eeded o the average tha with the stadard computer represetatio (ASCII), which assigs the same umber of bits to all letters. Lossy Compressio: Compressio is lossy if the origial sigal caot be perfectly recovered from the compressed file, as a cotrolled amout of distortio is allowed. Lossy sigal compressio techiques show higher compressio gais tha lossless oes. Ru-Legth Codig: A lossless compressio. A set of symbols is represeted as a sequece of RUN/ LEVEL. RUN beig the umber of cosecutive zeros ad LEVEL beig the value of the followig ozero coefficiet. Set Partitioig i Hierarchical Tree: A refiemet of the Embedded Zerotree Wavelet algorithm. SPIHT requires partitioig the wavelet coefficiets ito a umber of lists, with list membership chagig as the executio proceeds, ad i some cases ivolvig dual membership of a coefficiet i differet lists. Sigal Compressio: The reductio of the ecessary amout of bits to represet a sigal. I may cases, this must be accomplished while preservig the morphological characteristics of the waveform. I theory, sigal compressio is the process where the redudat iformatio cotaied i the sigal is detected ad discarded. Trasform Compressio: Compressio techique that is based o a simple premise: whe the sigal is processed by a trasform, the sigal eergy (iformatio) that was distributed amog all the samples i the time domai ca be represeted with a small umber of trasformed coefficiets. Wavelet Trasform: Refers to a trasformatio where a sigal cotaiig N samples is first filtered by a pair of filters that decompose the sigal ito low ad a high frequecy bads. Each bad is udersampled by a factor of two, that is, each bad cotais N/2 samples. With the appropriate filter desig, this actio is reversible.