Data compression for arterial pulse waveform

Wen-Shiung Chen

Abstract: The arterial pulse possesses important clinical information in traditional Chinese medicine. It is usually recorded for a long period of time in the applications of telemedicine and PACS systems. Due to the huge amount of data, by recognizing the strong correlation between successive beat patterns in arterial pulse waveform sequences, a novel and efficient data compression scheme based mainly on pattern matching is introduced. The simulation results show that our coding scheme can achieve a very high compression ratio and low distortion for arterial pulse waveform.

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In traditional Chinese medicine, arterial pulse (or pulse) waveform, a kind of biomedical signal measured from the human wrist, always provides essential clinical information to traditional Chinese physicians and is usually employed to detect the health of patients. Since the arterial pulse is generated in the artery, it suggests that changes in physical condition must be reflected in the shape of the blood pressure wave. Normally, a long duration recording is desirable for the traditional practitioner to detect a human body’s abnormalities, and this will be required in clinical applications such as picture archiving and communication systems (PACS), and telemedicine video-conferencing systems. Data compression (or waveform coding) for arterial pulse waveform data (Tompkins, 1993) is thus desired and important mainly for decreasing the requirement for archival storage space and transmission bandwidth.

A significant amount of work has been done on compression of ECG data (Abenstein and Tompkins, 1982; Bolis and Barr, 1988; Cox et al., 1968; Hamilton and Tompkins, 1991; Hamilton and Tompkins, 1991; Ishijima et al., 1983; Jalaleddine, Hutchens, and Strattan, 1990; Mammen and Ramamurthi, 1990; Muller, 1978; Ruttimann and Pipberger, 1979; Wang and Yuan, 1997). However, to the best of our knowledge, there is no literature in arterial pulse waveform compression. It is interesting that arterial pulse waveforms are oscillatory in nature, so that they may be viewed as periodic from an engineering viewpoint, although not periodic in a strictly mathematical sense. Hence, typical arterial pulse signals can be decomposed into a sequence of successive beats (or pitches) with similar patterns; that is, they exhibit little variation from one beat to another. Accordingly, it is worthy to develop a data compression algorithm operating in real time to reduce the amount of data without losing any critical clinical information content through fully utilizing pattern similarity characteristics of waveform beats.

The fact that arterial pulse data have not only temporal intrabeat correlations between successive samples but also strong temporal interbeat similarities or correlations between successive beats is extremely valuable. To achieve low bit rate or high compression ratio coding, interbeat correlation in addition to intrabeat correlation must be as well utilized. In this paper, we develop an efficient data compression scheme for biomedical arterial pulse waveforms, based upon the conception of interbeat correlation using pattern matching techniques, which can achieve a high compression ratio, but produce, upon reconstruction, a clinically acceptable signal quality.

This paper is organized as follows. In Section II, the proposed approach is presented based on the conception of pattern matching technique following beat segmentation and beat normalization followed by adaptive vector quantization (AVQ) residual coding. Compression and decompression procedures are given in Section III. Section IV is dedicated to the evaluation of compression results and comparison. Finally we draw our conclusion in Section V.

Data Compression for Arterial Pulse Waveforms

The Proposed Method

The sampled waveform of a typical arterial pulse wave, as shown in Figure 1(a), demonstrates the fact that it is intrinsically composed of a sequence of beats with similar pattern. This characteristic motivates us to apply it to data compression. Figure 1(b) shows the variation of beat lengths while Figure 1(c) shows the variation of variances of waveform differences between consecutive beats, in which a small variation of shapes of successive waveform beats is observed. It instinctively exhibits that beats of arterial pulse waveforms in an original data file have a very strong interbeat similarity and correlation. Consequently, in order to achieve a higher compression ratio, the interbeat feature of arterial pulse signals should be employed. Accordingly, the feature motivates to design a novel data compression scheme for biomedical arterial pulse waveforms, in which it employs AVQ coding technique for intrabeat correlation and, most importantly, a pattern matching technique for interbeat similarity and correlation.

[FIGURE 1 OMITTED]

Figure 2 shows the functional block diagram of the proposed arterial pulse compression scheme in that it consists mainly of four modules: beat segmentation, beat normalization, pattern-matching, and residual coding. The pattern-matching module is actually the kernel of the proposed system, which contains a template pattern library having a template pattern.

[FIGURE 2 OMITTED]

The proposed corripression algorithm is briefly described as follows. Since the waveform data file has a strong similarity and correlation between beat and beat, initially we suitably select a waveform beat pattern from the data sequence, store it into the waveform template pattern library, and make its length, [T.sub.s], as the standard beat period. As encoding procedure begins, a process called beat segmentation (or pitch segmentation) is performed to segment the sequence of the sampled waveform data into a sequence of patterns of isolated waveform beats. By noting that the data sizes of waveform beats may be variable from each other, a beat normalization (or pitch normalization) process is then performed to ensure that the size of each pattern is adjusted to be the standard period [T.sub.s] before the pattern-matching process is performed. This assures that the following pattern-matching process can be conformable with proceeding. The matching that produces the best match is deemed to be the recognized pattern if the match error (or residual beat error) is smaller than a preset threshold of similarity.

The entropy H of a signal X is defined as

H(X) = [summation over x] p(x) [log.sub.2] 1 / p(x),

Where p(x) represents the probability of signal value x. Signal entropy is the natural measure of compression performance since it represents the minimum average number of bits needed to losslessly code a sample from a given signal (Berger, 1971; Gersho and Gray, 1992). Measuring data rate as a function of distortion allows us to estimate the optimal rate-distortion function for a biomedical data compression algorithm. The rate-distortion theory (Berger, 1971) shows us that this optimal rate-distortion function indicates the theoretical minimum data rates required to store biomedical data over a range of distortions, regardless of compression technique. Figure 3 shows the histograms of occurrence frequency versus variance computed and accumulated beat by beat. According to the rate-distortion theory, coding residual waveform is superior to coding original waveform. Therefore, a pattern-matching mechanism is introduced in order for obtaining a smoother residual waveform with a smaller variance than the original waveform pattern. Finally, the residual waveform beat is coded using AVQ coding technique. In the following, the detailed description of each process is stated.

[FIGURE 3 OMITTED]

Beat Segmentation

In order to fully utilize the similarity and correlation between beat and beat in addition to inter-sample correlation, a subsequence of sampled data, called beat or pitch as shown in Figure 4 and extracted from the original waveform data file, must be recognized first and declared as a pattern. Therefore, the encoding procedure is firstly to segment a sequence of waveform samples to be coded into beats. The beat segmentation method can be simply performed by searching two points, namely [P.sub.1] and [P.sub.2], both with the minimum amplitude from a series of consecutive samples. Being found the two points, the first point [P.sub.1] is referred as the starting point and the previous point of the next point [P.sub.2] as the ending point of a beat, and all together with those points between them form the so-called beat. The length of a beat (i.e., the number of sample data in a beat) is defined as the period of the beat or the standard period, [T.sub.s]. Generally speaking, the lengths of isolated beats extracted from a data file are often inconstant (see Figure 1(b)), hence, before proceeding pattern matching stage a beat-length normalization process is necessary for each isolated beat to guarantee that every beat has the same length. The standard period, say [T.sub.s], can be suitably selected from some initial cycles of the data file being coded, and must be sent to the decoder at the beginning.

[FIGURE 4 OMITTED]

Beat Normalization

A simple beat normalization criterion is described as follows. If the length L of the current beat is larger than the standard period [T.sub.s] (i.e., L < [T.sub.s]), then the beat must be contracted or shrunk by a simple decimation (or deletion) operation. On the other hand, if the length L is smaller than [T.sub.s] (i.e., L< [T.sub.s]), then the beat must be expanded or stretched by a simple interpolation (or insertion) operation. This process converts the beats of variable lengths into beats of constant period. A number of extra bits indicating how many points are inserted or deleted and where they are inserted into or deleted from are also sent to the decoder. A beat normalization algorithm for arterial pulse is proposed and the pseudo code is given as follows.

Algorithm BN_PULSE (Beat normalization for arterial pulse waveform)

[T.sub.s]=standard period; [D.sub.s]=length of U-P range of waveformtemplate; L=input beat’s period; D=length of U-P range of input

beat;

begin

if L [less than or equal to] [T.sub.s] then {* interpolation or

insertion process * }

if D [less than or equal to] [D.sub.s] and L+ ([D.sub.s]-D) [less

than or equal to] [T.sub.s] then insert ([T.sub.s]-L) points into

U-P region and tail of waveform beat;

elseif D [less than or equal to] [D.sub.s] and L+ ([D.sub.s]-D)

> [T.sub.s] then insert ([T.sub.s]-L) points into U-P region;

else D>[D.sub.s] then insert ([T.sub.s]-L) points into the tail

of waveform beat;

else L>[T.sub.s] then {* decimation or deletion process *)

if D>[D.sub.s] and L- (D-[D.sub.s]) [less than or equal to]

[T.sub.s] then delete (L-[T.sub.s]) points from U-P region and

tail of waveform beat;

elseif D>[D.sub.s] and L- (D-[D.sub.s]) <[T.sub.s] then

delete (L-[T.sub.s]) points from U-P region;

else D [less than or equal to] [D.sub.s] then delete (L-[T.sub.s])

points from the tail of waveform beat;

end

Pattern -Matching Process

After performing the beat normalization to each isolated beat, a pattern-matching process is then performed to obtain a residual beat with smaller variance. In this process, a waveform template pattern library containing only one pre-selected waveform template pattern (or standard beat) is designed. The waveform template pattern is an appropriately selected pattern searched from the waveform data file to be coded and needs to be transmitted to the decoder so that the waveform template pattern library in the decoder has the same waveform template pattern as that in the encoder. As the shape of input beat varies drastically and becomes very different from the waveform template pattern during the encoding session, the waveform template pattern is then replaced by the input beat.

The pattern-matching process is summarized as follows. For each isolated beat, a simple pattern matching process is performed. Since the waveform template pattern library has only one standard waveform template pattern, no bit transmission is necessary. The residual beat is thus obtained from the difference between the input beat and the waveform template pattern. The residual beat is then fed into the AVQ residual coding module. The simple updating criterion of the waveform template pattern is that if the variance of the residual beat is greater than a threshold, the template pattern is replaced by the following beat pattern as the new one.

GW-based A VQ Coding for Residual Beat

Recently, vector quantization (VQ) (Gersho and Gray, 1992) has attracted considerable attention since it can nearly achieve asymptotically optimal rate-distortion performance in principle by coding vectors instead of scalars, which was proven by Shannon’s rate-distortion theory, and has broad applications to image and speech coding. A vector quantizer may be defined by a codebook C which is composed of a set of [N.sub.c] [T.sub.s]-dimensional vectors, called codewords, and a search criterion which tries to seek the best matched codeword most resemble to the input vector in a minimum mean square error (MSE) sense. The generalized Lloyd clustering algorithm, also referred as Linde, Buzo, and Gray (LBG) algorithm (Gersho and Gray, 1992), is usually used for codebook design.

In order to fully utilize the intrabeat correlation between sample and sample within the residual beat pattern, VQ is employed to encode the residual beat pattern. In VQ coding scheme, each residual beat is viewed as a vector X, which is treated as one single entity and encoded with a binary word. Using this binary word, the decoder may easily reconstruct an approximation to the original residual beat. The binary word is an index, I, to the entries of a codebook of [N.sub.c] codewords.

The encoder compresses X in the MSE distortion measure, (1 / L) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] between the input X and each codeword [c.sub.i], i = 1, 2 …, [N.sub.c], from the codebook. The data, I, transmitted is the index of the codeword yielding the least distortion. The decoder merely looks up the I-th codeword from its copy of the codebook and forms the reconstructed beat pattern X. Obviously, we need [log.sub.2]([N.sub.c]) bits to transmit the index if a fixed-length code is employed. The quantity [log.sub.2]([N.sub.c])/L gives the bit rate in bits per sample. A compression technique based on pattern matching mechanism and basic VQ for coding residual beat has been developed by Chen, et al. (Chen, Liao, Yuan and Wu, 1998).

In typical VQ applications, source vectors are sequentially extracted from a real signal and are individually coded by a basic vector quantizer. To improve the performance of a basic VQ, the statistical and structural redundancy between the neighboring blocks must be sufficiently used. Rather than coding each vector independently, one examines the context or local environment of a vector and modifies the quantizer to suit one’s awareness of the big picture of how other vectors in the sequence are behaving in order to more efficiently code this particular vector. Recently, Zhang and Wei (Zhang and Wei, 1996) developed a basic Gold-Washing (GW) codebook adapting mechanism and proved that for memoryless (or i.i.d.) sources the rate distortion function can be asymptotically achieved. Chen, Zhang and Yang (Chen, Zhang and Yang, 1995) applied it successfully to image compression. In this paper, an efficient AVQ coding based on the GW mechanism is introduced to coding residual beat patterns to achieve higher compression ratio.

This new adaptive technique uses the GW mechanism to keep good codewords in the codebook and discard bad codewords. Through the carefully designed GW mechanism, good codewords and only good codewords are kept with high probability. The initial codebook is totally random and has a very simple structure. The codebook is generated on the fly and refined after each source vector is coded, as well as eventually achieves an optimal state. It has very good adaptability in the sense that its convergence rate is reasonably fast.

Basically, the GW codebook refining mechanism consists simply of a GW dynamic codebook and a GW algorithm that performs coding and codebook refining. The GW dynamic codebook is composed of two sub-codebooks, sub-codebook-1 [B.sub.1] with size [N.sub.b1] and sub-codebook-2 [B.sub.2] with size [N.sub.b2], (where the total size of the GW dynamic codebook [N.sub.GW] = [N.sub.b1] + [N.sub.b2]) and a frequency counter associated with each codeword or [B.sub.2] in the GW codebook. The sub-codebook-1 [B.sub.1] is also referred as “main codebook” while the sub-codebook-2 “candidate codebook.”

The GW codebook refining algorithm and the GW-based AVQ coding scheme are described as follows. For each source vector X to be coded, the best matched codeword is identified by computing the distortion measure for the source vector with respect to each of the codewords [c.sub.j] in the GW codebook and finding that one with the minimum distortion. If the minimum distortion measure [d.sub.min]= min d(X, [c.sub.i] [less than or equal to] i [less than or equal to] [N.sub.GW], where [d.sub.th,GW] is a preset threshold, then the best-matched codeword, [c.sub.I], exists and the associated index is I. Two possible cases are to be considered:

i) If [c.sub.I] [member of] [B.sub.1], then the GW dynamic codebook is refined by the Move-To-Front (MTF) algorithm.

ii) If [c.sub.I] [member of] [B.sub.2], then the frequency counter [f.sub.I] associated with [c.sub.I] is increased by 1. Otherwise, a new codeword is generated by a basic VQ codec with the codebook size [N.sub.UM] and pushed into the GW dynamic codebook. The GW dynamic codebook is then refined via the Promotion (PMT) algorithm.

The MTF algorithm moves the best-matched codeword [c.sub.I] to the top entry of [B.sub.1] and shifts down the first I-1 codewords of [B.sub.1] by one notch. The PMT algorithm is described as follows. After the new codeword [c.sub.new] generated by VQ was pushed onto the top entry or [B.sub.2] and its associated frequency counter was initialized to be zero, then all of the codewords of [B.sub.2] are shifted down by one notch. If the content of the frequency counter for the last codeword of [B.sub.2] is smaller than a preset frequency threshold [f.sub.th,GW], the last codeword of [B.sub.2] is discarded. Otherwise, this codeword is promoted to the top entry of [B.sub.1] and all of the codewords of [B.sub.1] are then shifted down by one notch and finally the last codeword in [B.sub.1] is discarded.

Compression and Decompression Procedures

Compression Procedure

In this paper, we take account of the variation on the beat periods and fully exploit both intrabeat and interbeat correlations to design compression and decompression algorithms. The functional block diagram of the compressor is shown in Figure 2. The compression procedure is depicted as follows.

E1 Appropriately select an initial pulse waveform template pattern using the beat segmentation process and calculate the standard beat period [T.sub.s]; Store the waveform template pattern into the waveform template pattern library; Encode it and [T.sub.s] using VLC coding and transmit to the decoder; Compression procedure begins:

E2) Perform beat segmentation to slice a beat (i.e., a cycle); Compute the length L of the input beat;

E3) Perform beat normalization using Algorithm BN_PULSE for the input beat;

Transmit the overhead bits of the beat normalization process;

E4) Perform the pattern-matching process by comparing the input beat with the waveform template pattern in the waveform template pattern library to obtain the residual beat;

E5) encode and transmit the residual beat by using the GW-based AVQ coding scheme;

if the variance of the residual beat > the preset threshold

then encode and transmit the residual beat by using VLC coding and replace the waveform template pattern by the input beat;

E6) if end of input data file then stop.

else goto step E2);

B. Decompression Procedure

The decompression procedure is depicted as follows.

D1) Decode the standard beat period [T.sub.s];

D2) Decode the initial waveform template pattern and put it into the waveform template pattern library; Decompression procedure begins:

D3) Decode the residual beat by using the GW-based AVQ decoder;

D4) if the variance of the residual beat > the preset threshold

then decode the residual beat by VLC decoder; reconstruct the normalized waveform beat and replace the waveform template pattern by the newly reconstructed one;

else Add the residual beat into the waveform template pattern to reconstruct the normalized waveform beat;

D5) Decode the received overhead bits and perform the inverse beat normalization process to obtain the reconstructed waveform beat;

D6) if end of input data file then stop.

else goto step D3)

Result and Discussion

This section presents the experimental results for arterial pulse waveforms obtained from a hospital. We will examine the coding efficiency of the proposed pattern matching mechanism followed by AVQ coding method by comparing with other compression techniques applied to arterial pulse waveforms. Several sequence of arterial pulse data sampled at 85 samples/sec and quantized at 16 bits/sample were tested. An arterial pulse compression algorithm is judged by its ability of maximizing the compression ratio and minimizing the distortion while retaining all significantly clinical features of the waveforms. A commonly used error measure is the percent root-mean-square difference (PRD) defined as

PRD = [{[[summation of].sub.n][[x(n)-x(n)].sup.2] / [[summation of].sub.n][[x(n)].sup.2}.sup.1/2] x 100%,

where x(n) and xn), respectively, are the original and reconstructed signals.

For arterial pulse waveform, the simulation result obtained by using the GW-based AVQ coding is shown in Figure 5. It is seen from the figure that coding performances of very high compression ratio greater than 35 at small distortion PRD (about 4.4%-7%) may be achieved. It is also seen from the result shown in Figure 5 that the GW-based AVQ is superior to basic VQ for arterial pulse data. For the different codebook sizes, the GW-based AVQ used for coding residual can improve compression ratio up to about 20% higher at almost the same distortion than basic VQ.

[FIGURE 5 OMITTED]

Two sequences of waveforms, respectively with regular beats and irregular beats, were tested. According to the results listed in Table 1, our method gains tremendous improvements on coding performance of compression ratio (CR) versus PRD distortion measure over the other methods including TP algorithm (Muller, 1978), Fan algorithm (Bohs and Barr, 1988), AZTEC algorithm (Cox et al., 1968) and CORTES algorithm (Abenstein and Tompkins, 1982) for arterial pulse data compression. In conclusion, the achievement of the significant improvement is mainly due to the employment of the interbeat correlation and similarity via the pattern matching technique in our method. The result shows that the proposed coding scheme is superior to other coding methods and suitable for designing a very high compression ratio codec system for arterial pulse compression. Note that the proposed coding scheme is especially suitable for coding the pulse waveform of normal patients to obtain a very high compression ratio. However, for the irregular pulse waveform of abnormal patients, especially such as drastically varying pattern shape, the compression ratio will be severely reduced, although still better than the other methods.

The original waveform and reconstructed waveform are shown in Figure 6(a). Figure 6(b) shows the part of the waveforms in (a). Objectively, the PRD value of the reconstructed waveform is claimed to be small. Meanwhile, it is also subjectively judged by a practitioner from a Chinese hospital that the coded arterial pulse waveform still preserves most of the clinically significant information. Finally, only three beats of the original waveform and reconstructed waveform, shown in Figure 6, are shown in Figure 7 again. Upper sequence demonstrates the original waveform (solid line) and the reconstructed waveform coded by the proposed method (dotted line). Lower sequence shows the error waveform between them. It is very clear that the reconstructed arterial pulse waveform looks like the original waveform and still preserve most of the clinically significant information.

[FIGURES 6-7 OMITTED]

Conclusion

Biomedical waveforms such as arterial pulses inherently have a strong correlation and similarity between successive beats which is unemployed by any other ECG coding method. In this paper, the coding technique proposed accounts for the variation in the beat periods and then exploits both the intrabeat and the interbeat correlations. Accordingly, a novel and efficient data compression scheme based on the notion of pattern matching and the GW-based AVQ for residual coding of biomedical arterial pulse waves is presented. Significantly higher compression ratio performances with smaller distortions can be achieved. As compared with the other methods, our technique is very efficient and the implementation is also simple. On the other hand, the disadvantage is that it is not very suitable for irregular waveforms, such as a drastically varying pattern shape. Therefore, to modify the proposed algorithm to effectively compress arterial pulse data with irregular waveforms will be our research in near future.

Table 1: Comparison of the Simulation Results for Arterial Pulse

Waveforms

Regular waveform

PM- Basic TP Fan AZTEC CORTES

AVQ VQ

CR 50.48 34.40 2 2.5 5 4.6

PRD 5.15 5.99 7.77 5.9 29.0 8.4

Irregular waveform

PM- Basic TP Fan AZTEC CORTES

AVQ VQ

CR 24.5 17.2 2 2.3 4 4.4

PRD 7.2 8.8 9.12 7.9 31.2 9.4

The proposed compression method is PM-AVQ. For regular waveform: the

codebook size of basic VQ: [N.sub.VQ] = 128, the codebook sizes of

PM-AVQ are [N.sub.GW] = 32 (5 bits) and [N.sub.UM] = 4096 (12 bits).

For irregular waveform: the codebook size of basic VQ: [N.sub.VQ] =

256, the codebook sizes of PM-AVQ are [N.sub.GW] = 64 (6 bits) and

[N.sub.UM] = 8192 (13 bits).Acknowledgment

The authors would like to thank to Dr. Chang of Chinese Medical College Hospital for his judgment and suggestion on our results.

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Wen-Shiung Chen (1), Shang-Yuan Yuan (2) and Ho-En Liao (2)

(1) Department of Electrical Engineering, National Chi Nan University, Pu-Li, Nan-Tou, Taiwan and

(2) Department of Electrical Engineering, Feng Chia University, Taichung, Taiwan

(Accepted for publication March 9, 2001)

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