EMBEDDED WAVELET PACKETS–BASED ALGORITHM FOR ECG COMPRESSION Manuel Blanco–Velasco † , Fernando Cruz–Rold´ an † , Juan I. Godino–Llorente ‡ and Kenneth E. Barner § † Dep. Teor´ ıa de la Se ˜ nal y Comunicaciones, Escuela Polit´ ecnica, Universidad de Alcal´ a Alcal´ a de Henares (Madrid), Spain phone: +34 91 885 67 08, fax: +34 91 885 66 99, email: manuel.blanco@uah.es web: http://msc.tsc.uah.es/ ‡ Dep. Ingenier´ ıa de Circuitos y Sistemas, Universidad Polit´ ecnica de Madrid Madrid, Spain § Dep. of Electrical and Computer Engineering, University of Delaware Newark, DE 19716 USA ABSTRACT The conventional Embedded Zerotree Wavelet (EZW) algo- rithm takes advantage of the hierarchical relationship among subband coefficients of the pyramidal wavelet decomposi- tion. Nevertheless, it performs worse when used with Wa- velet Packets as the hierarchy becomes more complex. In order to address this problem we propose a new technique that considers no relationship among coefficients, and is the- refore suitable for use with Wavelet Packets. So in this work, an embedded ECG compression scheme is presented using Wavelet Packets that shows better ECG compression perfor- mance than the conventional EZW. Keywords: Electrocardiogram (ECG), ECG compres- sion, Embedded Zerotree Wavelet, Wavelet Packets (WP), channel bank filter, filtering theory, filter bank. 1. INTRODUCTION The design of electrocardiogram (ECG) compression tech- niques has been widely studied in the last few years. An outline of the most common techniques can be seen in [1], where a classification in three categories was proposed: di- rect methods, transform methods and parameter extraction methods. Since the early 90s, there have been many contri- butions among the transform methods due to the use of the Wavelet Transform, which has allowed the improvement of the compression ratios reported by the prior transform met- hods. The Embedded Zerotree Wavelet (EZW) algorithm was specifically designed to use the Discrete Wavelet Transform (DWT) [2] in image coding applications. This method de- monstrated good performance and was quickly applied to ot- her types of signals, such as ECG [3] and myoelectric [4] signals. In the DWT decomposition algorithm, every coef- ficient at any scale is related with two other coefficients at the immediate lower scale. This correspondence is iterated through scale giving the temporal orientation tree. An exam- ple is illustrated in Fig. 1. The set of a coefficient and its descendents is called zerotree. In the encoding process, the whole set of coefficient of a zerotree can be pointed by its root which is the first coefficient of the temporal orientation tree at the lower scale. In the encoding–decoding process, a coefficient is called significant if its amplitude is greater than a given threshold value ε . Therefore, depending on the magnitude of a coefficient related to ε , i.e., its significance, it can be encoded as a symbol of a reduced alphabet to ob- tain a significance map. The EZW algorithm takes into ac- count the hierarchy of the DWT coefficients among different subbands to efficiently encode the significance map and use an alphabet of four symbols [2]:{POS, NEG, IZ, ZTR}. Symbols {POS} and {NEG} indicate the sign of a significant coefficient. A non significant coefficient is encoded with the symbol {ZTR} if it is the root of a zerotree, i.e., if all the coefficients of the zerotree are also non significant. Conver- sely, the non significant coefficient is encode as an isolate zero with the symbol {IZ}. In the ECG compression case, a modified version of the EZW algorithm is reported in [3] that uses Wavelet Packets (WP), but the resulting algorithm performed worse than the DWT–based algorithm. The reason for the poor performance in the WP case is that the best basis decomposition often splits the signal into a number of smaller hierarchies that can- not be efficiently encoded by zerotrees. The motivation of this work has been the development of an EZW-based algorithm to be used with WP. To do so, the hierarchical relationships among coefficients has not been ta- ken into consideration. In this sense, the {ZTR} [2] symbol that identifies the root of a zerotree is withdrawn from the alphabet so that only three symbols ({POS, NEG, IZ}) encode the significance map. In this paper we present a versatile embedded encoding scheme to be used with WP —Embedded Wavelet Packets (EWP) algorithm. Simulations results are provided demons- trating the improvement in performance of the proposed en- coder over the original EZW DWT–based algorithm. Finally, we want to emphasize that although this work focus on ECG, other kinds of signals such as myoelectric signals or images (processed using linear–phase filter banks) can be also com- pressed with the proposed algorithm. 2. WAVELETS PACKETS The Discrete Wavelet Transform (DWT) decomposes a sig- nal f (t ) as a successive approximation in several scales as follows [5] f (t )= ∑ k c j 0 (k)2 j/2 ϕ ( 2 j t − k ) + ∑ k ∞ ∑ j= j 0 d j (k)2 j/2 ψ ( 2 j t − k ) , (1)