A COMPARATIVE STUDY OF SOME NOVEL ECG DATA COMPRESSION TECHNIQUES
Sven Ole Aase, Ranveig Nygaard, and John H kon Hus y
H gskolen i Stavanger Department of Electrical and Computer Engineering 2557 Ullandhaug, 4004 Stavanger Norway
This paper presents a comparison of modern time and frequency domain coding of ElectroCardioGram (ECG) signals. A set of di erent subband decompositions are compared for coding purposes. These results are then compared with a time domain linear interpolation technique which is optimal with respect to reconstruction error given the number of retained samples. Comparing the optimized time domain solution to the subband coders, we observe better performance for the latter class of coders in terms the percentage root mean square di erence (PRD) performance measure. The observations referred to above is con rmed and complemented by visual inspection of the reconstructed signals.
coding capabilities of dedicated time domain ECG coders with a range of subband based frequency domain coders. The comparison is not straightforward, since the dedicated methods typically refer to the sample reduction ratio , i.e. the fraction of the total number of signal samples, divided by the number of original signal samples kept. In contrast, general compression techniques refer to the number of bits used for representation.
2. DEDICATED TIME-DOMAIN METHODS
Coding by time-domain methods is based on the idea of extracting a subset of signi cant signal samples to represent the signal. The key to a successful algorithm is a good rule to determine the most signi cant samples. Decoding is based upon interpolation in this set. We distinguish between traditional heuristic methods, of which several variants have been available for some time, and recently developed optimization approaches.
Electrocardiogram (ECG) signals are recorded from patients for both monitoring and diagnostic purposes. If the signals are to be stored or transmitted in digital form, an e cient algorithm for data compression is appropriate. Many data compression techniques for ECG waveforms have been presented. Roughly, they can be classi ed into two categories: 1. Dedicated techniques: These are mainly time domain techniques dedicated to compression of ECG signals, including the AZTEC 1], FAN 2], CORTES 3] and Turning Point 4] algorithms. The more recent CCSP technique 5], based on a rigorous mathematical model of the problem and guaranteeing a minimum distortion for a given sample reduction ratio, also ts into this framework. 2. General techniques: Techniques, which historically were developed for the compression of speech and image/video compression, having a sound mathematical foundation. They include Di erential Pulse Code Modulation (DPCM), Subband- and Transform Coding, and Vector Quantization (VQ). Recently there has been some activity using methods from the second category to compress ECG signals: Transform coding and vector quantization 6, 7], and subband coding 8, 9, 10]. Our goal in this paper is to present some new results relating to both the dedicated time domain technique, CCSP, as well as to transform/subband coding. Perhaps equally important, we present a fair comparison of the
Heuristic time-domain algorithms are usually fast generators of compressed code satisfying certain reconstruction requirements. Typically, the absolute error of the decoded signal is guaranteed to be below a prescribed bound. A frequently cited heuristic is the FAN algorithm 2]. The basic idea of this algorithm is to identify signal segments where a straight line serves as a close approximation, and to discard all but the terminal points along this line. When signi cant deviations from linearity are detected, the corresponding samples are included in the extracted signal samples. Despite the incorporation of intelligent selection rules, all heuristics su er from lack of ability to yield the most condense among all codes satisfying the error bound. However, by a rigorous mathematical model of the compression problem, and by a corresponding solution algorithm, the minimum set of samples may be achieved. In the CCSP algorithm presented in 5] the samples are considered as nodes in a directed graph. Any pair of nodes are connected by one arc, the direction of which is consistent with the sample order. Each arc signi es the option to include the samples corresponding to its end nodes as consecutive samples in the extracted subset. The
2.2. Optimization methods
goal is to minimize the reconstruction error given a bound on the number of extracted samples. It is shown that this is identical to solving the cardinality constrained shortest path problem de ned on the graph. This problem refers to nding the shortest path from the rst to the last sample, and is solved by a dynamic programming algorithm thoroughly described in 5]. The length of the path is given as the sum of arc lengths along the path. The length of the arc connecting nodes i and j is de ned as the contribution to the reconstruction error introduced by eliminating all samples recorded between i and j .
number of signal samples in the critically sampled subbands are the same as in the input signal. Since the importance of the various subbands is unequal, compression is obtained by representing (quantizing) the less important subbands with a small number of bits. Normally, the signal energy is concentrated in the lower frequency subbands, implying that the higher frequency subbands can be represented with a small number of bits. Figure 2 shows the main components in the subband coder system. analysis lter bank
2.3. Coding scheme
The performance of time domain compression methods are often evaluated as a chosen distortion measure as a function of sample reduction ratio, de ned as the number of samples in the original signal per retained sample. When it comes to other techniques, such as subband- and transform coding, the performance is often evaluated as a chosen distortion measure as a function of bit rate, i.e. the average number of bits necessary to represent one sample of the signal. In order to be able to compare the results from time domain methods to other methods in a fully justi ed way, encoding of the extracted samples will have to take place. Reconstruction of a signal encoded by a linear interpolation time domain method requires one sample amplitude and the distance from the previous sample, referred to as run, for each segment of the signal to be reconstructed. In this context we choose to encode the runs and the amplitudes by two separate entropy coders. This is done to keep the number of possible di erent symbols low, and thus reduce the necessary side information. The structure of the encoding system is as illustrated in Figure 1.
Extraction of x(n) samples by CCSP algorithm amplitude Entropy coder 2 run Entropy coder 1 MUX channel
synthesis lter bank
Figure 2: Building blocks in a subband coder system. After the signal has been split into subbands it is in a form well suited for quantization and coding. In the system described in this paper a uniform quantizer is used together with run-length and entropy coding. As for the time-domain coder, a record adaptive coding scheme is used. In our subband coder we explore the use of lter banks based on Johnston's almost perfect reconstruction FIR lters 11], the 2-channel, 16 tap F16B, and the perfect reconstruction IIR lters described in 12], the 2-channel F_2_2_smpl. In each case a full 4-stage decomposition tree is used, giving a 16-band uniform frequency splitting. In addition to these traditional lter banks we also apply the following short-kernel lter banks: The Discrete Cosine Transform (DCT), a Lapped Orthogonal Transform 13], and the ECG-optimized lter bank designed in 14]. The latter is a parallel, nonunitary FIR lter bank optimized with respect to coding gain, as well as visual criteria 14]. The channel lter length is 32 taps in the case of the LOT and the ECG-optimized lter bank, and 16 taps for the DCT. Again, a 16-band uniform frequency partitioning is used.
Figure 1: Structure of time-domain encoding system. We choose to use a record adaptive entropy coders1 , and account for the overhead necessary due to side information. The results from the complete coding system are presented and discussed in Section 4.
4. CODING EXPERIMENTS
For evaluation of the reconstructed signals a commonly used performance measure is the percentage root mean square di erence (PRD) 15]. Although useful for testing the relative performance of coding techniques within a narrow family, the PRD hardly quali es as an authoritative judge for intermethod comparisons. Each compression method has it's own distortion characteristics, and visual inspection of the reconstructed waveforms is the only way of judging their merit as diagnostic tools. In this paper we will use both criteria for coding evaluation. All records used in this article are taken from the MIT/BIH Arrhythmia CD-ROM database, second edition 16]. The sampling frequency is 360 Hz with 12 bits per sample. In order to test the robustness of the coding systems presented earlier, a set of 6 test signals is used, similar to 10].
3. SUBBAND AND TRANSFORM CODING
A subband coder splits the input signal into a collection of approximately disjoint frequency bands. If the resulting subbands have the same extent in the frequency domain, the subband decomposition is said to be uniform. Since the bandwidth of each subband is reduced by an amount corresponding to the number of subbands, - say N , each subband, can be subsampled by a factor of N . Thus, the
1 In our case one record corresponds to 10 minutes of a single channel ECG recording.
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Figure 3: Coding performance for varying input signals. The lter banks used are: Johnston's F16B 11] (..), IIR lter bank F_2_2_smpl 10] (-.), DCT (- -), 32-tap LOT (solid line with circles), and the ECG-optimized 32-tap FIR lter bank (solid line). The time domain algorithm are: CCSP (solid line with x-marks), and FAN (solid line with diamonds).
4.1. Comparison based on the PRD measure
The test signals presented above are coded using in total 7 di erent compression algorithms: The time domain algorithms CCSP and FAN, and subband coding using 5 di erent signal decompositions as described in Section 3.: The F16B FIR lter bank, the F_2_2_smpl IIR lter bank, the DCT, the 32-tap LOT, and the ECG-optimized FIR lter bank. All decompositions use uniform frequency band splitting, with 16 channels. Figure 3 presents obtained PRDs for all combinations of coders and test signals for bit rates between 0.2 and 1.4 bits per sample (bps). We start the discussion by looking at the frequency domain coders. Due to the sharp peaks in the rst signal, mit100_1000 (a regular heartbeat signal), the relatively short kernel of the DCT, the LOT, and the ECG-optimized lter bank results in a better performance than that of the more traditional lter banks. Especially the IIR lter bank has inferior performance in this case. For the 5 remaining test signals the DCT is outperformed by the other decompositions. This is due to the smoother nature of the test signals, thus rendering them more suitable for approximations by larger lter kernels. For all test signals the ECG-optimized FIR lter bank outperforms the other decompositions. The optimality of the CSSP algorithm is clearly demonstrated when compared to the heuristic FAN algorithm. For all test signals the CCSP outperforms the FAN algorithm with a large margin over the range of bit rates shown. The performance of the time domain algorithms suffers at low bit rates due to the fact that when few sam-
ples are extracted, the number of possible runs increases. The block size of the encoding process should therefore be tuned together with the increase in the number of runs. Here a xed block size of 500 samples is used. In spite of being optimal, in the sense outlined in Section 2, the CCSP coder cannot compete, in terms of obtained PRD, with the majority of the subband coders. Only the IIR lter bank, as well as the DCT, do in some cases give rise to a PRD that is marginally larger.
4.2. Comparison based on visual inspection
As mentioned in the beginning of this section, inter-method comparisons should also include visual inspection of the reconstructed signals. The scope of this investigation is to show coding artifacts as they appear using the presented compression methods for a typical ECG signal. We have chosen a short segment taken from mit100_1000 representing a regular heartbeat. Figure 4 shows the reconstructed signal segment at 1.0 bits per sample (bps), when coding the whole 10 minute record. The original signal segment is also included. At 1.0 bps all coders smooth out some of the details in the original signal. This is particularly evident for the time domain coders, and for the DCT coder. The latter also produces some blocking artifacts. In contrast to the short-kernel LOT and ECG-optimized lter banks, the traditional F16B and F_2_2_smpl lter banks produce some ringing noise. This is evident near the R-wave of the QRS complex in both cases.
Figure 4: Reconstructed signal segment (taken from mit100_1000) at 1.0 bit per sample.
We have presented an overview of current time- and frequency domain methods for compression of ECG signals. In time domain coding the compressed signal is represented by retained signal samples, whereas in frequency domain coding the compressed signal is represented by quantized subband samples. For both categories entropy coding was used for bit-e cient representation. Coding experiments demonstrate that time domain methods based on linear interpolation of retained samples cannot compete, in terms of PRD, with subband coders at low bit rates, i.e., around 1.0 bps and below. This was also veri ed by visual inspection of the reconstructed waveforms. The loss of detail was more prevalent in the time domain coding cases. However, the optimal time domain algorithm performed dramatically better than the well known FAN algorithm. A collection of lter bank decompositions were tested in a complete subband coding setup. The short kernel lter banks, the parallel, nonunitary, ECG-optimized lter bank and the LOT, had the best overall coding performance, both with respect to obtained PRD and visual evaluation, with the ECG-optimized lter bank being the better of the two.
5] 6] 7] 8] 9] 10] 11] 12] 13] 14] 15] 16]
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