Wavelet-based Compression of Ecg Signals

An example of application of the wavelet transform to electrocardiography is described in the paper. The transform is exploited as a first stage of an ECG signal compression algorithm. The signal is decomposed into particular timefrequency components. Some of the components are removed because of their low influence to signal shape due to nonstationary character of ECG. Resulted components are quantized, composed into one block and compressed by a classical entropic Huffman coder. The wavelet transform with the threshold detector, the quantizer, and the Huffman coder can compress data with average compression ratio CR=9.2 and percentual root mean square difference PRD=3.0%. The lossy compression algorithm was tested on CSE library of rest ECG signals. Introduction Efficiency of lossless algorithms that are usually based on Huffman coding with prediction is limited. The best CR=3 for common ECG data is obtained [1]. Entropic coding of the predictor residuals can be lossless, i.e. the compressed signals can be fully reconstructed. Algorithms of lossy compression are significantly more efficient. Recommended sampling frequency fs=500 Hz is derived from "high frequency" spectral content of QRS-complexes. However, the QRS-complexes duration is only about 10% of a heart cycle. This fact can be exploited to design a compression algorithm based on timefrequency signal processing. Time-frequency wavelet transform can be used and be considered as a special case of subband signal processing [2, 3, 4]. The use of orthonormal base of functions can sufficiently meet the requirement of exact reconstruction. Discrete Time Wavelet Transform of Finite Sequences The dyadic discrete time wavelet transform (DTWT) of a finite sequence {x(i) | i=0,1,...,N-1}, where N=2, can be evaluated as cyclic convolution ( ) ( ) ( ) [ ] y m n DFT X k H k N m m , , = − 2 1 (1) where m=1,2,...,M; n=0,1,...,N/2-1; k=0,1,...,N-1; X(k)=DFT[x(i)] and ( ) ( ) H k G k m m m = 2 2 * is a sampled frequency characteristic of m-th filter that corresponds to a proper expanded mother wavelet. N,2 index means N-point inverse discrete Fourier transform where every 2-th sample of output signal y(m,n) is chosen. Use of orthogonal set of wavelets is necessary to transform the signal without any error. We used Meyer’s wavelets that are originally defined in frequency domain as described in [5]. Method The dyadic DTWT can decompose a signal into timefrequency octave bands with their band widths B f m m s = − 2 2 / (2) where m is a band number, fs is sampling frequency. Let us note that N samples of the signal is decomposed into M = log2(N) bands that contain N−1 samples. Number of samples in particular bands is