Myoelectric signal compression using zero-trees of wavelet coefficients

Medical Engineering & Physics 25 (2003) 739–746 www.elsevier.com/locate/medengphy

Myoelectric signal compression using zero-trees of wavelet coefficients Jason A. Norris, Kevin B. Englehart ∗, Dennis F. Lovely Institute of Biomedical Engineering, University of New Brunswick, 25 Dineen Drive, Fredericton, NB, Canada E3B 5A3 Received 21 August 2002; received in revised form 9 April 2003; accepted 24 June 2003

Abstract Recent progress in the diagnostic use of the myoelectric signal for neuromuscular diseases, coupled with increasing interests in telemedicine applications, mandate the need for an effective compression technique. The efficacy of the embedded zero-tree wavelet compression algorithm is examined with respect to some important analysis parameters (the length of the analysis segment and wavelet type) and measurement conditions (muscle type and contraction type). It is shown that compression performance improves with segment length, and that good choices of wavelet type include the Meyer wavelet and the fifth order biorthogonal wavelet. The effects of different muscle sites and contraction types on compression performance are less conclusive. A comparison of a number of lossy compression techniques has revealed that the EZW algorithm exhibits superior performance to a hard thresholding wavelet approach, but falls short of adaptive differential pulse code modulation. The bit prioritization capability of the EZW algorithm allows one to specify the compression factor online, making it an appealing technique for streaming data applications, as often encountered in telemedicine.  2003 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Myoelectric; Data compression; Wavelet transform

1. Introduction The myoelectric signal (MES) has many important clinical uses, including the diagnosis and assessment of neuromuscular disorders [1–3], the assessment of muscle fatigue [4,5], and the control of powered assistive devices [6,7]. Telemedicine offers the potential of greater accessibility to diagnostic and assessment procedures, and reduced costs to the healthcare system. In the context of telemedicine, there is a motivation to transmit the myoelectric signal as efficiently as possible, without degrading the signal’s diagnostic characteristics. This is the motivation for developing a means of compressing the myoelectric signal that performs well under a variety of experimental conditions. Biomedical signal compression research has been directed almost exclusively toward medical images, elec-

Corresponding author. Tel.: +1-506-453-4966; fax: +1-506-4534827. E-mail address: [email protected] (K.B. Englehart). ∗

trocardiograms, and electroencephalograms. An extrapolation of the successes and failures regarding compression of other biological signals cannot be made, due to the unique nature of the myoelectric signal. Whereas most images and the electrocardiogram are highly structured, the myoelectric signal is not, in general. The MES originates from a complex spatial and temporal superposition of motor unit action potentials, which may or may not be correlated in their firing behavior [8]. As a result, the MES has a strong stochastic1 component, which presents a challenge to a compression scheme. There has been very little literature on the compression of the myoelectric signal; the few investigations addressing MES compression have considered techniques that have shown success in speech and electrocardiography. Norris and Lovely [9] investigated lossy

1 Although the MES is often assumed to be completely random this is, in general, an oversimplification. Some degree of structure is evident in ballistic or cyclic contractions [6,8], and is the basis for schemes of pattern-recognition based control of prostheses [7].

1350-4533/$30.00  2003 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1350-4533(03)00118-8

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compression of static2 surface recorded MES using a hardware-based implementation of adaptive differential pulse code modulation (ADPCM), a popular standard for voice compression. As a follow up to this work, Chan et al. [10] extended the scope of the investigation to include both static and dynamic3 surface MES data. These results suggest that ADPCM is a promising method of MES compression. Guerrero and Mailhes [11] compared the performance of three common predictive compression techniques to the performance of two transform-based techniques. They observed that the transform-based compression methods, which were based on either the discrete cosine transform or the discrete wavelet transform (WT), produced reconstructed signals with less distortion than predictive techniques, which included differential pulse code modulation, multi-pulse coding, and code excited linear prediction. Unfortunately, very little detail about the compression methods or the nature of the MES data is given in this work. Wellig et al. [12] investigated static intramuscular MES compression using a modified version of the embedded zero-tree wavelet (EZW) compression, developed by Shapiro [13]. The performance of the EZW shows promise in Wellig’s investigation, but the work considers only a narrow range of analytical and experimental parameters, and no comparison is provided to other compression methods. The purpose of this investigation is to gain greater insight into the capabilities of the EZW method as applied to compression of the surface myoelectric signal. To this end, various experimental conditions and analysis parameters are considered, to determine their effect upon compression performance. Important experimental conditions include: 1. The nature of the contraction; static and dynamic activity are compared. 2. The muscle group involved; differences between the myoelectric signal produced by the biceps brachialis and triceps brachialis4 are compared. The main analysis parameters which affect the performance of the EZW algorithm are: 1. The length, in samples, of the MES data segments, and 2. The type of wavelet used in the WT. To provide a frame of reference, the performance of 2 The use of “static” in this context implies an isometric, constant force contraction. 3 The use of “dynamic” in this context implies an anisometric, anisotonic contraction. 4 For brevity of notation, the biceps brachialis and triceps brachialis will be referred to as biceps and triceps, respectively.

EZW approach is compared to ADPCM and hard thresholding wavelet compression techniques.

2. Background 2.1. Data compression Data compression minimizes the number of bits required to represent information by reducing the redundancy present in the original data. This results in a reduced storage requirement or, in the context of data transmission, a more efficient use of available bandwidth. The degree of compression is usually expressed as a percentage using a figure of merit called the compression factor (CF): CF(%) ⫽

US⫺CS ⫻ 100, US

(1)

where a high CF corresponds to a large degree of compression. In Eq. (1), US is the original data size and CS is the compressed data size. Lossless compression techniques attain low CFs and produce decompressed signals that are identical to the original data. Conversely, lossy compression techniques attain significantly higher CFs but produce decompressed signals that differ from the original data. In lossy compression, the reconstruction error is often expressed using a distortion metric called the percent residual difference (PRD):

冪冘 K

PRD(%) ⫽

冒冘 K

(xi⫺xˆi)2

i⫽1

x2i ⫻ 100.

(2)

i⫽1

In Eq. (2), x is the original signal, xˆ is the reconstructed signal, and K is the signal length in samples. The capability of a compression algorithm can be described by its PRD vs. CF characteristics. In the context of telemedicine, there is an interplay between bandwidth usage, transmission time, and signal distortion. Given a specified level of acceptable distortion, compression ameliorates the tradeoff between bandwidth usage and transmission time. 2.2. The EZW algorithm In the past decade, researchers in applied mathematics and signal processing have developed wavelet methods, a powerful new framework for analyzing transient phenomena in signals [14,15]. It is not the intention to reproduce wavelet theory here; many excellent papers [16,17] and texts [1819] now exist as an introduction and reference. The efficiency of representation offered by orthogonal wavelet transforms has made them an attractive choice in data compression and noise removal [20,21]. The traditional approach to wavelet-based com-

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pression is achieved by modifying or discarding certain wavelet coefficients that are insignificant [22]. The EZW algorithm was originally developed for lossy compression of two-dimensional wavelet coefficients [13]. This algorithm has been applied to medical images [23] and the electrocardiogram [2425] with good success. Two distinct properties of the EZW algorithm make it an effective means of compression, as compared to traditional approaches. First, the EZW algorithm exploits the hierarchy of the wavelet coefficients, and establishes a connection between coefficients from different subbands, allowing multiple coefficients to be encoded simultaneously. Second, coefficients are encoded in order of importance using bit prioritization. The embedded coding scheme places the most important bits at the beginning of the bit-stream; therefore, the encoding or decoding process can terminate at any moment and allow a target bit-rate or distortion metric to be met exactly. In addition to producing a fully embedded bit stream, EZW consistently produces compression results that are competitive with virtually all known compression algorithms. For a detailed discussion of the EZW algorithm, the reader is referred to [13].

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The same subject pool was used for the dynamic MES acquisition as was employed for the static MES acquisition. Dynamic MES data were acquired from the biceps of the right arm for a series of cyclic contractions. The subjects were seated with the upper-arm parallel to the torso, the elbow-joint angle at 90°, and a 2.27 kg dumbbell in hand. Subjects were instructed to cyclically contract and relax their biceps at a frequency of 0.5 Hz (2 s/cycle) by raising and lowering their forearm and hand, using the elbow as the pivot point. A single cycle is defined as a reduction in the elbow-joint angle to approximately 40°, followed by a return to the 90° starting position. The cycle time was regulated using an electronic metronome. The sampling began when the elbowjoint angle was at 90°; however, to prevent involuntary variations in the contractile motion, the subjects were not informed of the time when sampling was started. Each subject was given the opportunity to practice the cyclical movement to adjust to the contraction cycle time prior to acquisition. The cyclic dynamic MES was acquired for 20 s, or approximately 10 cycles.

4. Results and discussion 3. Methodology A standard bipolar electrode configuration was used for MES acquisition. Two Ag–AgCl electrodes (0.5 cm in diameter), spaced 2.4 cm apart, were placed on the skin’s surface longitudinal to the muscle fibers of the biceps and triceps. The signals were optically isolated, amplified, and bandlimited 0.1 Hz–1 kHz. The amplifier gains were adjusted to ensure maximum use of the dynamic range of the A/D without exceeding the maximum and minimum voltage levels, or overranging the amplifiers.5 The signals were sampled at 2000 samples/s, and stored in 16-bit integer format. Five subjects, four males and one female, ranging from 24 to 35 years in age, with no history of neuromuscular disorders, were recruited for this investigation. For the static MES, acquisition data were recorded on two channels, one for each of the biceps and triceps muscles, from the right arm. Subjects were placed in a chair and electrode pairs were placed over the belly of the biceps and triceps muscles. Each subject was then required to sustain a constant force co-contraction of the biceps and triceps while 20 s of MES data were acquired. The level of force was not of interest here; subjects were merely instructed to produce a constant force contraction of moderate strength.

5

The amplifiers were equipped with overrange LEDs, which were monitored during a validation session before actual acquisition was performed.

All MES data were compressed and subsequently decompressed using the EZW algorithm. The results were assessed to determine whether compression performance is affected by analysis parameters, such as segment length and wavelet type, and experimental factors, such as contraction type and muscle type. 4.1. Analysis parameters 4.1.1. Record length Data segmentation are essential when using transform-based compression methods, such as the EZW algorithm. The segment size will determine the resolution in time and in frequency of the WT. Computational complexity is also affected by segment size; the complexity of the WT and the EZW algorithm is proportional to the segment length M. This is important in realtime applications. The data were segmented into dyadic record lengths ranging from 64 to 4096 samples. A typical analysis scenario was chosen, in which the MES epochs were compressed to 75% using wavelet coefficients computed using the Meyer wavelet.6 A 75% CF was chosen to ensure that the results could be compared to the fourbit compression results, i.e. CF of 75%, obtained from ADPCM. The wavelet type was kept constant to ensure 6 It should be noted that wavelet decomposition was carried out to one-half of the full decomposition depth. A full decomposition was not performed, as no improvement in compression performance was observed (empirically) beyond the midpoint.

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that record length was the only factor contributing to the variability of each set of results. Fig. 1 shows the variation in PRD with record length, averaged across subjects, for the static biceps MES. The PRD values were calculated using the overall reconstructed signal, not the individually reconstructed epochs. To accommodate the dyadic nature of the record lengths, the x-axis is normalized using a base-2 log conversion. It is clear from this figure that compression performance improves with increasing record length; however, the degree of improvement diminishes with longer record lengths. Recall that computational effort for the EZW algorithm is O[M]. This implies that, for a K-sample record of data, with K/M non-overlapping segments of M samples, the total computational effort does not change with M. The implication, therefore, is that for best offline compression performance, the segment size should be as large as possible. This is consistent with the expectation that compression efficiency will increase with segment length, if accompanied by increasing entropy [26]. A practical constraint exists regarding segment size in the context of transmission of data, in that data must be segmented, encoded, and transmitted in real time. For a given processing capacity, an upper bound on segment size must be determined. For the remainder of this discussion, it will be assumed that a segment size of M = 1024 samples represents a reasonable tradeoff between performance and computational complexity. As is evident in Fig. 1, the best possible PRD performance with large M is within 1% of that when using M = 1024. 4.1.2. Wavelet type There does not exist a single prescription for the selection of a wavelet type for a given application. One can consider mathematic properties of the wavelet basis,

Fig. 1. Variation in PRD with MES segment length for static biceps MES.

such as the vanishing moments and the regularity, which affect the wavelet’s ability to model the smooth parts of a signal [15]. For compression, it is also intuitive to select a wavelet basis that “looks like” the elemental components of a signal under consideration [3]. For the myoelectric signal, there are a number of wavelet types that look like motor unit action potentials. For a given wavelet, it is reasonable to expect that the small scales would capture isolated motor unit activity, while larger scales would model longer-duration trends in the signal. Inevitably, the selection of a wavelet type is problem specific, and is best served by empirical comparison of an ensemble of candidate basis functions. An empirical assessment of wavelet types was performed here, considering one discrete Meyer wavelet, four Coiflet wavelets, five Daubechies wavelets, six Symlet wavelets, seven biorthogonal wavelets, and seven reverse biorthogonal wavelets. The order, N, was varied within these families to accommodate a wide range of wavelet regularity. This list was not meant to be exhaustive, but rather to demonstrate how the “best” wavelet can be chosen from a given ensemble of candidate wavelet types. Static and dynamic surface MES data were segmented into 1024-sample epochs, transformed to the wavelet domain using the wavelets in the wavelet test set, and compressed to a CF of 75% using the EZW algorithm. Again, the 75% CF was chosen to ensure that the results could be compared to those obtained using ADPCM. The compressed data were subsequently decompressed, and the PRD between the original and overall reconstructed MES was computed for each wavelet type. Fig. 2 shows the average variation in PRD with wavelet type, computed across subjects, for each type of MES. The well-defined peaks and troughs in this figure indicate that compression performance is affected by the choice of wavelet used in the WT, and is reasonably consistent for the different contraction types and muscle types. In Fig. 2, the dashed vertical hairlines indicate the wavelets for which minimal distortion occurred: the discrete Meyer wavelets, and the fifth order biorthogonal wavelet. The reduction in PRD with increasing order N observed for the Coiflet, Daubechies, and Symlet wave-

Fig. 2. Average variation in PRD with wavelet type (dmey = discrete Meyer, db = Daubechies, sym = Symlet, bior = biorthogonal, rbio = reverse biorthogonal).

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lets, may be attributed to the regularity of these wavelets. Since the smoothness of the wavelet improves as N increases, an improved approximation of the low frequency portion of the MES may be obtained. Apart from some scaling differences, the shape of the Meyer and biorthogonal wavelet functions resemble the triphasic shape of the motor unit action potential. For the analysis of the physiological factors that may effect compression performance, the Meyer wavelet is used in the WT. 4.2. Experimental factors The contraction type analysis examines biceps signals acquired for static, and cyclic dynamic contractions, while the muscle type analysis examines static MES acquired from the biceps and triceps muscles. For these analyses, the segmented MES was compressed to CFs ranging from 60% to 95% using the Meyer wavelet and a five-level decomposition. The encoded signals were subsequently decompressed, and the compression performance was evaluated by examining the variation of PRD with CF. 4.2.1. Contraction type: static vs. dynamic Figs. 3 and 4 illustrate the change in compression performance with CF for the static and cyclic dynamic MES, respectively. The upward trend of the PRD vs. CF curves was expected, since the consequence of higher CFs is an increase in reconstructed signal distortion. With the exception of the static MES of subject 1, the compression performance of the static MES was consistently better (indicated by lower PRDs) than dynamic MES.

Fig. 3.

Variation in PRD with CF for static biceps MES.

Fig. 4.

Variation in PRD with CF for cyclic dynamic biceps MES.

4.2.2. Muscle type: biceps vs. triceps Fig. 5 illustrates the change in compression performance with CF for the triceps MES. A comparison of these results to the static biceps MES results shown in Fig. 3 indicates that the biceps MES compresses consistently better than the triceps MES. The compression results shown in Figs. 3–5 are best explained by examining the manner in which the EZW algorithm processes wavelet coefficients, and the frequency content of the MES. Wavelet coefficients vary in magnitude according to how much they contribute to the signal from which they were derived. In the MES, it appears that the larger wavelet coefficients approximate the overall shape of the signal (low frequency), while smaller wavelet coefficients are the details (high frequency). Since the EZW algorithm uses a decreasing threshold approach to compression, the majority of the

Fig. 5.

Variation in PRD with CF for static triceps MES.

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high frequency content is removed by zeroing the smaller coefficients. For signals with a considerable amount of low and high frequency content, this translates into greater reconstructed signal distortion at high CFs. Fig. 6 shows the power spectral densities of the static biceps, dynamic biceps, and static triceps data of subject 2. Consider first the power spectral density for the static biceps and dynamic biceps MESs. A visual inspection of the spectral content of these signals clearly shows that the bandwidth of the static MES is narrower than that of the dynamic MES. A comparison of the compression results shown in Figs. 3 and 4 to the power spectral densities shown in Fig. 6 suggests a possible correlation between compression and bandwidth. The PRD vs. CF curve produced by the static MES was consistently lower than the same curve produced by the dynamic MES, indicating that better compression performance may be obtained from MES of narrower bandwidth since there is less high frequency information to lose when smaller coefficients are zeroed. With the exception of subject 1, similar results were also observed for the other subjects. Since the contractile force was not regulated during static MES acquisition, it is hypothesized that subject 1 may have exerted more effort than the other four subjects, resulting in a signal with a more evenly spread spectrum. The loss of the additional high frequency information during compression may explain why the static biceps MES of subject 1 suffered more loss than the other subjects, as indicated in Fig. 3. Consider now the PSD curves for the static biceps and static triceps data. A visual inspection of these curves clearly shows that the bandwidth of the biceps MES is narrower than that of the triceps MES. Since the EZW algorithm rejects much of the high frequency content of a signal, the triceps MES is more easily distorted than the biceps MES during compression. This is supported

by the results presented in Figs. 3 and 5. The PRD vs. CF curve for the biceps signal of subject 2 shows consistently less distortion than the PRD vs. CF curve obtained for the triceps signal of the same subject. Similar results were obtained for all other subjects. Although a difference in compression performance was observed between different types of contractions and different muscle sites, it would be erroneous to draw any formal conclusions from these results. The frequency content of the MES may indeed influence the compression performance for different type of contractions and muscles, but subject variability is undoubtedly a factor as well. A larger database, taking into account the subject dependent effect, must be acquired before concluding any significance of the effect of contraction type and muscle type on MES compression.

Fig. 6. Comparison of static and dynamic surface MES PSDs of subject 2.

7 The ADPCM software was developed by Sun Microsystems Incorporated.

4.2.3. Comparison with other methods To complete the assessment of MES compression using zero-tree encoding, the EZW results were compared to those obtained by two lossy techniques: a hard thresholding wavelet compression algorithm, and ADPCM.7 The hard thresholding algorithm is a simple, commonly used wavelet compression technique, compressing data by replacing all wavelet coefficients that fall below a pre-defined global threshold value with a 0. For wavelet threshold encoding, the static and dynamic surface MESs were compressed to CFs ranging from 60% to 95%, while ADPCM was limited to a CF of 75%. A comparison of the static biceps MES compression results, averaged across subjects, is shown in Fig. 7. Similar results were also obtained for the static triceps and cyclic dynamic MES. It is clear that the EZW algorithm outperforms the hard thresholding wavelet technique. Of the three lossy compression techniques, ADPCM consistently performed better than both of the wavelet-based encoding schemes at its pre-defined CF of 75%. As the segment size is increased from M = 1024 to M = 4096, the performance of the EZW algorithm improves marginally. The degradation in compression performance of the wavelet-based methods is attributed to the poor approximation of the smaller wavelet coefficients. The quality of the ADPCM-encoded data stems from the ability of the algorithm to efficiently adapt to highly variable signals. One problem with the EZW algorithm is that it performs poorly when errors are introduced into the coded data. This is because the embedded nature of the coding causes errors to propagate from the point that they are introduced to the end of the data [27]. However, for applications where a target distortion metric is to be used as the stopping criteria for encoding, the EZW

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Fig. 7. Performance comparison of three compression techniques applied to static biceps MES.

algorithm may be the suitable choice, as this property is not easily implemented with other compression algorithms.

5. Conclusions This work provides a better understanding of the factors that affect the performance of the EZW algorithm, as applied to myoelectric signal compression. It is shown that compression performance is affected by analysis parameters, such as the MES segment length and the wavelet type, and experimental factors, such as the contraction type and the muscle site. Regarding segment length, the distortion of the reconstructed signal reduces as the length of the MES segment increases. For online processing, the segment size must be chosen to meet real-time constraints, with a compromise in compression performance. The wavelet type suggests that higher order wavelets produce lower reconstructed signal distortion, and that the Meyer wavelet and the fifth order biorthogonal wavelet produce the lowest PRDs (on average). In general, triphasic wavelets with high regularity produce reconstructed signals with less distortion. It is also notable that these wavelets closely resemble the shape of the constituent motor unit action potentials in the recorded MES patterns. The investigation into the effects of contraction type and muscle type on compression suggests greater compressibility of the static MES over the dynamic MES, and better compression performance of the biceps MES as compared to the triceps MES. It is shown that the

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inability of the EZW algorithm to accurately approximate smaller wavelet coefficients results in increased signal distortion in MES segments with both low and high frequency content. This suggests a relationship between signal bandwidth and compression performance, but more data are needed to draw any definitive conclusions. The comparative analysis between the EZW algorithm, the wavelet thresholding algorithm, and ADPCM showed that the high CF, and low PRDs associated with ADPCM-compressed data, make it the best choice for applications for which a fixed CF is acceptable. Although the EZW algorithm is more versatile in terms of CF and PRD control, its inability to adapt to MES data with significant high frequency content is a distinct disadvantage of the method. The dependence of the EZW algorithm on the spectral characteristics of the signal suggests that the algorithm must be modified to accommodate signals with a broad distribution of high frequency content. As an alternative to global thresholding, individual thresholds defined for each level of refinement may be used to ensure that larger coefficients at each level are retained.

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