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EP-based wavelet coefficient quantization for linear distortion ECG data compression King-Chu Hung a , Tsung-Ching Wu a,b,∗ , Hsieh-Wei Lee a , Tung-Kuan Liu a a b

Department of Computer and Communication Engineering, National Kaohsiung First University of Science and Technology, Taiwan Department of Electronics and Computer Science, Tung Fang Design Institute, Taiwan

a r t i c l e

i n f o

Article history: Received 13 July 2012 Received in revised form 16 September 2013 Accepted 26 January 2014 Keywords: ECG data compression Evolution program (EP) Wavelet transform Error control

a b s t r a c t Reconstruction quality maintenance is of the essence for ECG data compression due to the desire for diagnosis use. Quantization schemes with non-linear distortion characteristics usually result in timeconsuming quality control that blocks real-time application. In this paper, a new wavelet coefficient quantization scheme based on an evolution program (EP) is proposed for wavelet-based ECG data compression. The EP search can create a stationary relationship among the quantization scales of multiresolution levels. The stationary property implies that multi-level quantization scales can be controlled with a single variable. This hypothesis can lead to a simple design of linear distortion control with 3-D curve fitting technology. In addition, a competitive strategy is applied for alleviating data dependency effect. By using the ECG signals saved in MIT and PTB databases, many experiments were undertaken for the evaluation of compression performance, quality control efficiency, data dependency influence. The experimental results show that the new EP-based quantization scheme can obtain high compression performance and keep linear distortion behavior efficiency. This characteristic guarantees fast quality control even for the prediction model mismatching practical distortion curve. © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction Sensing the electrical depolarization and polarization action of the heart from the body’s surface, ECG is a non-invasive modality widely used for heart disease diagnosis [1]. Since the heart is a three-dimensional (3-D) organ, heart disease diagnosis usually needs multiple ECG signals derived from different positions around the heart. The standard examination process is a record of 12-lead ECG signals for 24 h. ECG data compression is crucially desired for efficient real-time transmission and storage of mass data [2,3]. Wavelet-based ECG data compression with excellent performance has attracted much attention from researchers recently [4–6]. The Wavelet-based approaches executing in lossy ECG data compression need to optimize a compromise between high compression ratio (CR) and distortion. The compromise should be based on two prerequisites, i.e., preserving clinical information and guaranteeing reconstruction quality. The former concerns capability of preserving significant features of ECG signal, e.g., P and T waves,

∗ Corresponding author at: Department of Computer and Communication Engineering, National Kaohsiung First University of Science and Technology, Taiwan. Tel.: +886 988669556. E-mail address: [email protected] (T.-C. Wu).

QRS complex, and ST segment. These features are dominantly distributed below 40 Hz [4]. The later concerns maintaining the compression result with stable reconstruction quality. Data compression methods based on fixed bit rate or fixed quantization scale cannot satisfy this requirement due to the non-stationary property of ECG signal. There are many indices proposed for distortion measurement, e.g., percentage root mean square difference (PRD) [2], weighted diagnostic distortion (WDD) [6], and wavelet-based diagnostic measure (WWPRD) [4], where PRD with simplicity and indications is commonly used as the index of reconstruction quality maintenance [2]. Reconstruction quality maintenance is generally performed with a closed-loop error control process that limits reconstruction error within an acceptable small region [2,6,7,4]. Closed-loop error control process needs a quantization scale prediction function to generate a new set of multi-level quantization scales. Traditional wavelet-based data compression achieves bit allocation with multi-level quantization scales [8–11]. The adjusting of multi-level quantization scales is time-consuming and usually results in a nonlinear distortion compression result. With uniform quantization scheme, Chen and Itoh [8] determined the quantization scale by using a close-loop error control process to limit distortion. Benzid et al. [9] determined threshold value by keeping fixed percentages of wavelet coefficients at zeros (FPWCZ). By using the distortion measure percentage root mean square difference (PRD), FPWCZ

1350-4533/$ – see front matter © 2014 IPEM. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.medengphy.2014.01.007

Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

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criterion was replaced by a target PRD for threshold determination [10]. Lu et al. [11] presented a set partitioning in hierarchical trees (SPIHT) algorithm which embedded quantization process by using bit plane coding and ended the coding by desired bit rate. The ending process of SPIHT algorithm was then modified with Newton–Raphson prediction process for fitting desired PRD [12]. Based on distortion curve tracking, bisection algorithm was also applied for determining the quantization scale of DCT and DWT coefficients [13,14]. Ku et al. [2] utilized linear prediction to achieve an efficient quantization scale determination. For real-time application, linear prediction can be desirable due to simplicity. However, linear prediction function is only suitable for a compression performance with a linear distortion characteristic. In this paper, a new wavelet domain quantization scheme based on the combination of EP search [15] and linear distortion programming is presented. The EP search is first applied for optimizing some sets of quantization scales that will be used as the seeds of linear distortion planning. By using PRD as the distortion measure, an EP search using minimum PRD/CR as the criterion can induce a stationary relationship among the quantization scales of multiple levels. This property implies the feasibility of using a single variable to control multi-level quantization scales. Conducted by this hypothesis, a 3-D polynomial curve fitting technique is then applied for linear distortion programming with respect to a quantization factor (QF). The design process is based on the reversible round-off nonrecursive discrete periodized wavelet transform (RRO-NRDPWT) [16]. The data dependence effect of the EP-based quantization scheme is minimized with a cross validation strategy that uses MIT-BIH arrhythmia and ST change databases [17] due to different diversifications. The data dependence effect is further studied by using the Physikalisch-Technische Bundesanstalt (PTB) database [18,19] that involves 12-lead untrained ECG signals. Experimental results show that the EP-based quantization scheme can keep high compression performance and obtain fast quality control based on the data-independent linear distortion characteristic. In comparison with the SPIHT scheme [11], the average compression performance can be improved by 18.52%.

sj = sJ Hj−J and dj = sj Hj−J−1 G,

(2) j−J−1

where the column vectors of Hj−J and H G are called the non-recursive low-pass and high-pass filters of the jth level, respectively. Both Hj−J and Hj−J−1 G contain 2j–J cycles of non-recursive filters. In each cycle, the filter coefficients of two adjacent columns have 2j–J relationship in vertical direction. Using Eq. (2), the wavelet coefficients of each level can be derived directly from the original sampled data. This can resist error propagation. For overall stages decomposition, let Aj denote the N×2−j matrix consisting of the 2−j column vectors in one cycle of Hj−J−1 G and let B0 be a column vector of H−J . By introducing a N × N non-recursive filter matrix A = [B0 , A0 , A−1 , . . ., Aj+1 ], called the 1-D NRDPWT matrix, the overall stages decomposition can be obtained from d = [s0 , d0 , d−1 , . . ., dj+! ] = sJ A.

(3)

In Eq. (3), s0 denotes the scaling coefficient in the termination level being the mean of input sequence. The vectors dj , 0≥j≥J + 1, contain 2−j points of the wavelet coefficients in the jth level, respectively. For performing the 1-D NRDPWT with minimum word length computation and perfect reconstruction guaranteed, the RROLT theorem is applied. The reversibility of RROLT is suitable for arbitrary transformation functions and independent of input data. Let d∗ =  d where  d denotes to round each element of d to the nearest integer. From Eq. (3), the fixed-point 1-D NRDPWT can be defined with ∗

d∗ =  d =  c  sJ A and s J =  sJ = 

1 ∗ −1 d A . c

(4)

where c is a constant. The rounding processes in Eq. (4) will produce two error vectors ˛ = d − d∗ and r = sJ s ∗J . The absolute value of each element of ␣ and r is less than or equal to 0.5, i.e., |˛i | ≤ 0.5 and |ri | ≤ 0.5 for i = 0, 1, . . ., N − 1. The RROLT theorem guarantees s ∗J

2. Review of the reversible round-off non-recursive discrete periodized wavelet transformation

= sJ if and only if c  = max

 N−1 



|akl | l = 0, 1, . . ., N − 1

≡

k=0

RRO-NRDPWT [20], associating the non-recursive discrete periodized wavelet transform (NRDPWT) and the reversible roundoff linear transformation theorem, was developed for resisting truncation error propagation and minimum word length implementation. This improvement facilitates the reconstruction error control of finite precision discrete wavelet transformation. In this section, the RRO-NRDPWT-based ECG data compression is briefly reviewed. Let Sj denote a row vector involving N-point sampled ECG data with N = 2−J where J < 0 is referred to as the decomposition level. The low-pass and high-pass filters can be represented with the t column vectors h = [h0 , h1 , . . ., hN−1 ] and g = [g0 , g1 , . . ., gN−1 ]t , t respectively, where X denotes the transpose of X. The elements of h will satisfy the Daubechies’ constrain, while g is given by a homeomorphous high-pass filter   [21]. By introducing an N × N 0 1 matrix T such as T = where IN−1 is the (N − 1) × IN−1 0 (N − 1) identity matrix, we can define the low-pass filter matrix H = [T0 h, T2 h, . . ., TN−2 h, T0 h, T2 h, . . ., TN−2 h] and high-pass filter matrix G = [T0 g, T2 g, . . ., TN−2 g, T0 g, T2 g, . . ., TN−2 g] for the 1-D recursive DPWT process. For J < j ≤ 0, let sj and dj denote the scaling and wavelet coefficient vectors of the jth level, respectively. The 1-D recursive DPWT process can be represented with sj = sj−1 H and dj = sj−1 G,

where both H and G contain 2 cycles of column filters. By substituting sJ for sj−1 , Eq. (1) becomes

(1)

 cmax where akl denotes the kth row and lth column element of the inverse matrix A−1 . Based on the RRO-NRDPWT (i.e., Eq. (4) with the specified cmax ), a quantization scheme with single control variable QF can be defined with

∗ = d j



d∗j



cj (QF)





and s¯ 0∗

Sj∗ cDC (QF)



,

(5)

where X denotes to truncate the elements of vector X into integers and cj (QF) is the normalized quantization scale of the jth level. The cj (QF) can be defined with cj (QF) =

cpj (QF) SNFj

and cDC (QF) =

cpDC (QF) , SNFDC

(6)

where cpj (QF) is an adjustable parameter and SNFj is the significance normalization factor defined with SNFj =

⎧ ⎫ ⎨2−j+1 ⎬ −1   a  , l = 0, 1, . . ., N − 1 . For inverse quantimax kl ⎩ ⎭ −j k=2

zation, each retrieved datum will be compensated by half of the quantization scale, namely, ˆ j = cj (QF) ∗ (d¯ ∗ + 0.5sign(d¯ ∗ )) d j j

(7)

ˆ j is the jth sub-band vector of dˆ and sign(X) denotes the where d sign vector of X.

Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

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number axes. For simplicity, the generation function is approximated with cpj (QF) = aj QF2 + bj QF + cj where QF defined with

3. EP-based quantization scheme design for linear quality control scheme



EP is a global searching method commonly used for finding optimal solutions of multi-variable non-linear system. The method achieves global searching based on a uniformly distributed population [15,22] of training data and finds solutions by three stratagems, i.e., selection, crossover, and mutation. Selection defines the criterion of candidate selection, crossover acts as a filter with clustering effect, and mutation is used to prevent from a trap of local sink. For diminishing data dependency effect, it is desirable to use diversified data for EP search. For this purpose, 11 arrhythmia ECG signals (i.e., record number 100, 101, 102, 103, 107, 109, 111, 115, 117, 118, and 119) saved in the MIT-BIH database are selected to build a training dataset. Each signal with 360 sampling rate and 11 bits resolution involves 10-min length sampled data. The quantization scheme design process consists of two stages. In the first stage, EP process is applied for finding four sets of optimal quantization scales where each set involves 11 level quantization scales, i.e., {cpDC ( ) and cpj ( ), j = 0, −1, . . ., −9}. Each set of multi-level quantization scales acts as a seed that will result in each signal having a PRD value within the range [0.5%, 7%]. The PRD is defined with



PRD = 100 ×

N−1 2 (s [n] − sˆJ [n]) n=0 J %, (s [n] − 1024)2 n=0 J

N−1

Fitness function: Initialization: Evolution rules: Selection: Crossover:

Mutation:

Termination:

QF = PRD2 + CR2 is the control variable. For dealing with low PRD region, the curve fitting process also involves two new sets  of low CR cases. One is a constant cpj ( ) = napj ∗ cmax , this case will introduce 11 CR values with PRD = 0 for the 11 training ECG signals. The other case is cpj ( ) = napj . Combining the two cases, the training dataset will provide 66 3-D points for the curve fitting of each cpj (QF). By using the least square error (LSE) method, the 10-level coefficients aj , bj , and cj for j = 0, . . ., −9 can be found as follows: cpDC (QF) = 0.001974 × QF2 + 0.01451 × QF + 0.008015, cp0 (QF) = 0.001974 × QF2 + 0.0198 × QF + 0.01412, cp−1 (QF) = 0.002712 × QF2 + 0.03241 × QF + 0.01997, cp−2 (QF) = 0.005194 × QF2 + 0.0637 × QF + 0.0374, cp−3 (QF) = 0.009606 × QF2 + 0.09847 × QF + 0.05275, cp−4 (QF) = 0.01613 × QF2 + 0.1544 × QF + 0.07405,

(9)

2

cp−5 (QF) = 0.02507 × QF + 0.2209 × QF + 0.1033, cp−6 (QF) = 0.04367 × QF2 + 0.241 × QF + 0.1422,

(8)

where sJ [n] and sˆJ [n] denote original and reconstruction sampled data. The four seeds corresponding to four specified cp−9 () (i.e., cp−9 ( ) = 16, 8, 4, and 2) will be found with minimum PRD/CR as the selection criterion. The EP searching process is described in the following: Objective:

3

Find the values of cpDC (QF) and cpj ( ), −8 ≤ j ≤ 0, for cp−9 ( ) = 2, 4, 8, and 16, respectively. Minimizing the ratio of PRD/CR. Generate 100 data sets randomly with each set defined as {cpDC ( ), cp0 ( ), cp−1 ( ), . . ., cp−8 ( )}. Eighty sets with smallest PRD/CR are selected for crossover in each iteration. (1) For the best 80 sets, the choice of two cpj ( ) for crossover is random where the value of j is also randomly chosen and the choosing probability is defined by 0.5. (2) Crossover processing number for each iteration is defined by 40. (1) Mutation process is defined as exchanging the values of cpi ( ) and cpj ( ) when they are selected. (2) The mutation probability is defined by 0.3. I. Recursive search should exceed 100 times. II. The same result should be maintained for 20 times.

In this algorithm, a large mutation probability (i.e., 0.3) is used for the desire of fast convergence. The set {cpDC ( ), cp0 ( ), cp−1 ( ), . . ., cp−8 ( )} with maximum cp−8 ( ) is selected as the desired solution. A cpj ( ) solution for ECG signal 101 is shown in Fig. 1(a) where a trend of cpi ( ) < cpj ( ) for i > j is obvious. In fact, this trend is also true for all ECG signals. This trend implies that for a fixed cp−9 ( ), EP search can always end at a globally optimal solution that selects one set of multi-level quantization scales (cpj ( ), −8 ≤ j ≤ 0) with minimum PRD/CR. This result will not be influenced by mutation probability. For the 11 training signals, there are 44 cpj ( ) values found for each j. Fig. 1(b) shows the 44 values of cp−7 ( ). The uniqueness solution of EP searching also implies that the criterion minimum PRD/CR can induce a stationary relationship among multi-level quantization scales. This property rationalizes the control of all cpj ( ) with a single variable. Based on the hypothesis, the second stage is to create a cpj ( ) generation function by applying a 3-D curve fitting technique. The 3-D coordinate system is defined by using PRD, CR, and cpj ( ) as the three real

cp−7 (QF) = 0.05839 × QF2 + 0.322 × QF + 0.1897, cp−8 (QF) = 0.0661 × QF2 + 0.4167 × QF + 0.2384, cp−9 (QF) = 0.0661 × QF2 + 0.5122 × QF + 0.2506. Fig. 1(b) illustrates the curve fitting result of cp−7 (QF) (i.e., the solid line). The quantization scales of cp−j (QF) for j = 0∼ − 9 and QF = 1∼15 are depicted in Fig. 1(c). This result shows that the proposed quantization scheme design method can effectively prevent from obtaining an exponential cpj (QF) growth in high CR region. For convenience, the EP-based quantization scheme of Fig. 1(c) is referred to as the NRDPWT-EPar where the 6-tap Daubechies’ wavelet is used. By using the 48 arrhythmia ECG signals saved in MIT arrhythmia database, each signal involves 10-min length sampled data, Fig. 1(d) shows the average PRD-QF and CR-QF curves of NRDPWT-EPar. For the evaluation of CR, the compressed data file consists of a QF value and quantized ECG data. The former was encoded with the DPCM method and the latter was encoded with lossless SPIHT scheme. Note that the encoding process will be also applied for all the experiments in this paper, Fig. 1(d) shows that both curves are approximately linear. The linearity of PRD–QF relation permits using linear QF prediction model for quality control without the cost of precision and convergence speed in a low bit rate situation. The error control process is described as follows. Definition:

Step 1: Step 2:

Step 3: Step 4: Step 5:

PRDT \\ target PRD, ε\\tolerable error bound, loop\\ iteration number, and QFdefault \\ default QF value used for the first segment. Set the parameters and let loop = 0, QF0 = QFdefault . Refine QF value with a linear prediction algorithm defined as follows: (2.1) If loop = 1, set QFloop = 2.4166 × (PRDT − PRDloop−1 ) + QFloop−1 . (2.2) If loop > 1, set QFloop = QFloop−1 + a(QFloop−1 − QFloop−2 ) where a = (PRDT − PRDloop−1 )/(PRDloop−1 − PRDloop−2 ). Quantize wavelet coefficients d* with QFloop . Take inverse quantization and inverse 1-D RRONRDPWT. Compute PRD with PRD% =

Step 6:

N−1 n=0

2

N−1

(sJ [n] − sˆJ [n]) /

n=0

sJ [n]2 × 100%.

Reconstruction quality maintenance with a specific criterion: If (|PRD − PRDT |/PRDT ) > ε, then loop = loop + 1; go to Step 2 for a refinement of QF; else QF0 = QFloop \\assign the initial QF for the next segment; loop = 0; go to Step 3.

Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

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18 16 14 12 10 8 6 4 2 0

cp-9()=2 cp-9()=4 cp-9()=8 cp-9()=16 cp-7

value of cpj()

4

DC 0

16 14 12 10 8 6 4 2 0 0

-1 -2 -3 -4 -5 -6 -7 -8 -9

5

10

level (j)

(a) The EP-based 101 for fixed

of ECG signal values.

25 QF=1 QF=3 QF=5 QF=7 QF=9 QF=11 QF=13 QF=15

15 10 5

(b) Curve fitting result of using the training dataset.

by

25

7 QF-CR

20

6

QF-PRD

5

15

4

10

3

CR

value of cpj()

20

15

QF

2 5

0

1

0 DC

0

-1

-2

PRD(%

-3

-4

-5

-6

-7

-8

-9

level (j)

values of the (c) The NRDPWT-EPar quantization scheme.

0 1

6

11

16

QF

(d) Compression performance of the NRDPWT-EPar quantization scheme using 48 arrhythmia ECG signals.

Fig. 1. EP-based quantization scheme design for linear quality control scheme.

The QF determination of Step 2 is actually a linear tracking process. The original value (i.e., QF0 ) is set to be QFdefault defined with QFdefault = PRDT /0.4138 for the begin of new signal or the last value of previous segment where the default error prediction model PRD = 0.417QF − 0.07717 ∼ = 0.4138QF is derived from Fig. 1(d) by applying LSE method. The second value (QF1 ) is determined by the gradient of default error prediction model and QF0 . For loop > 1, the values are found with the practical distortion curve of signal. The linearity of practical distortion curve will influence convergence speed. For encoding, QF value is represented in integer. With this aim, all the ECG signals in MIT-BIH arrhythmia database are investigated. It is sufficient to range QF value from 0 to 32. This range will be uniformly quantized into 512 levels with quantization steps equal to 0.0625. The computed QFloop value will be assigned to the nearest quantization level. Here, we note that the QFdefault value will be used for all the experiments including MIT-BIH and PTB databases (discussed in Section 5). The finite precision QF can always guarantee a convergence for ε = |PRD − PRDT |/PRDT × 100% = 5% and 10%. 4. Experimental results Data dependency is an intrinsic property of GA-based approaches. Diversified training data can only diminishing the bias effect of data dependency, mismatching the optimal solution is unavoidable for practical application. Studying the adaptability for general data can be more meaningful. For this purpose, the MIT-BIH ST change database with lower diversity is used for a comparison.

By using the PTB database that involves 12-lead ECG signals, the influence of data dependency effect on quality control is discussed in Section 5. All experiments were performed on an IBM PC with Microsoft Windows 7, Intel Core i7 2.8 GHz CPU and 8 GB RAM. In the use of MIT-BIH ST change database, 8 ECG signals, records 301, 305, 310, 314, 315, 317, 325 and 326, were selected. Each signal involves 10-min length sampled data. The same EP algorithm and 3-D curve fitting process described in Section 3 were applied to obtain a second EP-based quantization scheme referred to as the NRDPWT-EPst and shown in Fig. 2(a) where the exponential growth in high CR region is also resisted. For a comparison, these two EPbased quantization schemes were applied for compressing all the signals saved in arrhythmia database and ST change database. The former and later comprise 48 and 28 ECG signals, respectively. Each signal involves 15-min length sampled data. The evaluation results were shown in Fig. 2(b) and (c) where both the two schemes can obtain approximately linear distortion results with very minor difference. This result implies that the data dependency effect is unconscious in compression performance. With slightly better, NRDPWT-EPar scheme was applied for a comparison by using untrained noisy signals (i.e., records 104, 107, 111, 112, 115, 116, 117, 118, 119, 201, 207, 208, 209, 212, 213, 214, 228, 231, and 232). Each signal contains about 1-min length sampled data. The evaluation results of three quantization schemes were shown in Fig. 2(d) where the NRDPWT-EPar scheme has the best compression performance, especially for high CR region due to linear distortion characteristic. In comparing with SPIHT scheme, the compression performance can be improved by 6.19(%) and 27.85% for the two

Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

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25

15 10

quanzaon scheme #2

4 3 2

5

1 0

0 DC

0

-1

-2

-3 -4 -5 level (j)

-6

-7

-8

4

-9

(a) The values of the second EP-based quantization scheme.

6

8

10

12 CR

14

16

18

20

(b) Compression performances of two EP-based quantization schemes for MIT-BIH arrhythmia database. 8

13 11

quanzaon scheme #1

7

quanzaon scheme #2

6

9

PRD(%)

PRD(%)

quanzaon scheme #1

5 PRD(%)

value of cp (j )

6

QF=1 QF=3 QF=5 QF=7 QF=9 QF=11 QF=13 QF=15

20

5

7

NRDPWT-EP NRDPWT-6t SPIHT

5 4

5

3

3

2 1

1 4

6

8

10

12

14

16

18

20

4

8

12

16

20

CR

CR

(c) Compression performances of two EP-based quantization schemes for MIT-BIH ST change database.

(d) Compression performance comparison of three wavelet-based schemes by using untrained noisy ECG signals.

Fig. 2. The experimental results.

ranges 4 ≤ CR ≤ and 14 ≤ CR ≤ 20, respectively. A comparison with the DCT-based approach [23] was also taken where three distortion measures PRDN, SNR, and RMS are used. The three indices are defined with

 PRDN = 100 ×

2 N−1 (x(n) − x∗ (n)) n=0 %, N−1 2  n=0 (x(n) − )  N−1 2

SNR = 10 × log

 RMS =

N−1 n=0

n=0

N−1 n=0

(x(n) − )

(x(n) − x∗ (n))

(x(n) − x∗ (n)) N−1

2

, and

2

,

where x(n) and x∗ (n) denote the originally sampled data and reconN−1 structed data, respectively, and  = x(n)/N is the mean of a n=0 segment x(n). The measurement result was shown in Table 1. Note that the PRD index could not be properly calculated in [23] because the offset value (1024) saved in each datum of MIT database was not removed. The influence was detailed studied in [24]. Table 1 clearly shows that NRDPWT-EPar scheme can be much superior to DCT-based approach for ECG data compression. Based on the error control process described in Section 3, the quality maintenance performance of NRDPWT-GAar scheme is evaluated by using all the 48 and 28 ECG signals saved in arrhythmia and ST change databases, respectively. The signals in the former and later involve 30- and 13-min length sampled data, respectively. The

convergence speed of quality control is represented by the iteration times (ITs) required for the error control process. Tolerable bound ε = 5% was considered for all cases of quality control. The analysis results with PRDT = 3%, 5%, and 7% were shown in Fig. 3(a)–(c) where each signal of arrhythmia database was recorded by a normal channel CH1 and a noisy channel CH2. The average ITs for the three databases mostly lies in the range [1.5, 2.5]. The ITs variation respecting to different PRDs is undistinguishable, especially for the ST change database. This implies that for all test signals, the PRD-QF curves can be approximately linear. In general, CH2 slightly requires more iterations than CH1 and CH2 has less CR than CH1 because noisy abounding in high frequency components is also regarded as signal. For PRDT = 3%, 5%, and 7%, the average iterations of (CH1, CH2) are (1.85, 2.00), (1.98, 2.05), and (2.09, 2.13), respectively. This phenomenon shows that noisy can degrade quality control performance. The experimental results also reveal that linear QF prediction model is suitable for all test ECG signals due to stability. By using the 48 arrhythmia signals (CH1) with each involving 15-min length sampled data, Table 2 shows that both the mean and standard deviation of NRDPWT-EPar scheme are smaller than that of NRDPWT-6t scheme. These experimental results implies that the influence of data dependent effect is almost invisible in the evaluation of compression performance and quality control, even for untrained ECG signals. In Figs. 4–6, we demonstrate the data compression results of NRDPWT-EPar scheme for the three ECG signals records 109, 117, and 232, respectively, where the first 316 segments are shown. Record 109 has a waveform with baseline wandering and slightly

Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

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Average ITs

4

PRDT=3%

3.5

PRDT=5%

3

PRDT=7%

2.5 2 1.5 1 100 102 104 106 108 111 113 115 117 119 122 124 201 203 207 209 212 214 217 220 222 228 231 233

ECG Signals

(a) Using the 48 ECG signals in MIT arrhythmia database Ch1. 4

Average ITs

3.5 3

PRDT=3% PRDT=5% PRDT=7%

2.5 2 1.5 1 100 102 104 106 108 111 113 115 117 119 122 124 201 203 207 209 212 214 217 220 222 228 231 233

ECG Signals

(b) Using the 48 ECG signals in MIT arrhythmia database Ch2. 4

Average ITs

3.5

PRDT=3% PRDT=5%

3

PRDT=7%

2.5 2 1.5 1 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327

ECG Signals

(c) Using the 28 ECG signals in MIT ST change database. Fig. 3. Quality control performance of NRDPWT-EPar scheme.

noise coupling. Fig. 4 shows that a stable low bit rate (CR ≈ 20 from Table 1) can be achieved. The desired QF can be also stable and convergence speed is very fast, even for a suddenly violent rate change. The dynamic range of ITs is [1,3]. The two segment demonstrations of Fig. 4(e) and (f) shows that the clinical information including the amplitude and duration can be preserved well. Record 117 is a nice waveform ECG signal. Fig. 5 shows that for violent QF changes, the convergence speed can be still fast. The dynamic range of ITs is [1,4]. The reconstructed signal with very low rate (CR ≈ 24) has slightly distortion at the boundary of segments. This can be overcome by reducing PRDT . As shown in Fig. 6, record 232 is a distorted and noisy waveform ECG signal. Though both rate and QF are violently changed, the dynamic range of ITs can be maintained in [1,4]. This signal has poor PRD due to the smoothing effect of quantization process, but the reconstruction error is almost unobservable. 5. Discussion The data dependency problem in EP search is a latent risk for real-time application due to the bias effect. For alleviating this

influence, it is desirable to use diversified training data, i.e., involving all types of available ECG signals. However, the influence on data compression performance is absolutely unnoticed in a large percentage of data tests covered in Figs. 2(b)–3(c). For this EP-based design scheme, quality control performance can be influenced by three factors, i.e., curve fitting function, QF prediction model, and practical distortion curve (PRD–QF curve). Curve fitting is to derive the control functions cpj ( ), j = −9, −8, . . ., 0, with a single variable (QF) and keep the three parameters QF, PRD, and CR in linear relationship for high compression performance. In practice, this aim is not easily achieved due to the requirement of the conditions. Investigating the distributions of PRD and CR with respect to cp−7 ( ) in the training phase of NRDPWT-GAar GA search shown in Figs. 7 and 8, respectively, it is seen that both indices have quadratic curve distributions for each ECG signal. This feature motivates the use of quadratic curve fitting for cpj ( ) generation with a single control variable defined in Eq. (9). The Quality control efficiency of NRDPWT-GAar quantization scheme (i.e., cpj ( ) generation function) can be analyzed by a comparison of the prediction model (i.e., Step 2 in error control process) and the practical PRD–QF curve. For

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MIT-BIH Record 109

7 6 5 4 3

PRD(%)

7

51

1

101

151 segments

201

251

301

251

301

201

251

301

201

251

301

rate(bps)

(a) 800 600 400 200 0 1

51

101

151 segments

201

(b) QF

30 20 10 0 1

51

101

151 segments

iteraon

(c) 4 3 2 1 0 1

51

101

151 segments

amplitude

(d) O a Orignal ECG signal

1200

700 0

1024

2048

(e) CR=17.85 PRD=4.96

Reco nstructed ECG siignal

CR=19.90 PRD=5.00

amplitude

1200

700 0

1024

2048

(f) error

30 0 -30 0

1024

2048

(g) Fig. 4. Compression performance of NRDPWT-EPar scheme for the ECG signal of record 109 with PRDT = 5% and ε = 5%.

neglecting the data dependency effect in the analysis, two files of PTB database were used. Each file involves 12-lead ECG signals and each lead, involves 40-s length sampled data. The performances of data compression and quality control are shown in Table 3 where the quality control for leads avr and i needs the most iteration times. From Table 3, some segments of the ECG signal are selected for

investigating the difference between the prediction model and the practical PRD curve where the PRD is ranged from PRDT = 3 to 7. As shown in Fig. 9, it reveals that a closer relation can obtain a faster convergence result for quality control. On the other hand, in a case of being farther away, the value of QFi for i≥2 will be predicted by the gradient of the practical PRD curve due to the adaptive

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MIT T-BIH Record 117

PRD(%)

5 4 3 2 1 1

51

101

151 segments

201

251

301

201

251

301

201

251

301

251

301

(a) Rate(bps)

600 400 200 0 1

51

101

151 segments

(b)

QF

30 20 10 0 1

51

101

151 segments

(c) iteraon

6 4 2 0 51

1

101

151 segments

201

amplitude

(d) O a Orignal ECG signal

1100

600 1024

0

2048

amplitude

(e) CR=22.71 PRD=2.88

1100

Recoonstructed ECG siignal

CR=25.95 PRD=3.05

600 0

1024

2048

(f)

error

30 0 -30 0

1024

2048

(g) Fig. 5. Compression performance of NRDPWT-EPar scheme for the ECG signal of record 117 with PRDT = 3% and ε = 5%.

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MI T-BIH Record 232

9 8 7 6 5

PRD(%)

9

1

51

101

151 segments

201

251

301

201

251

301

201

251

301

201

251

301

R t (b ) Rate(bps)

(a) 600 400 200 0 1

51

101

151 segments

(b) QF

30 20 10 0 51

1

101

151 segments

iteraon

(c) 5 4 3 2 1 0 1

51

101

151 segments

(d) O Orignal ECG signal a

amplitude

1200

800 1024

0

2048

(e) CR=9.06 PRD=7.00

Reconnstructed ECG signal

CR=9.82 PRD=7.09

amplitude

1200

800 0

1024

2048

1024

2048

(f) error

30 0 -30 0

(g) Fig. 6. Compression performance of NRDPWT-EPar scheme for the ECG signal of record 232 with PRDT = 7% and ε = 5%.

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cp-7

12 10 8 6 4 2 0 0

2

4 PRD

14

100 101 102 103 107 109 111 115 117 118 119

6

12 cp-7

10

4 2 0 0

10

Fig. 8. Distribution of cp−7 ( ) vs. CR in NRDPWT-GAar training phase.

Lead aVR - segment 8 praccal PRD

predicve PRD 7.7

6.9

6.7

5.9

5.7

PRD

7.9

4.9

4.7 2.7

2.9 15

20

25

24.2

14.2

30

QF

praccal PRD

34.2

QF

Lead aVL - segment 7

Lead aVF - segment 8 praccal PRD

predicve PRD

8

7.4

7

6.4

6

5.4

PRD

PRD

predicve PRD

3.7

3.9

5

predicve PRD

4.4 3.4

4

2.4

3 18

13

23

16

28

26

36 QF

QF

Lead

56

Lead aVR - segment 1

- segment 1

praccal PRD

46

(d) Average iteration times = 2.4

(c) Average iteration times = 1.8

praccal PRD

predicve PRD

predicve PRD

7

6.9

6 PRD

5.9 PRD

20

CR

Lead Ι - segment 5

PRD

8 6

Fig. 7. Distribution of cp−7 ( ) vs. PRD in NRDPWT-GAar training phase.

praccal PRD

10

100 101 102 103 107 109 111 115 117 118 119

4.9

5 4

3.9 2.9

3 7

17

27 QF

(e) Average iteration times = 3.0

37

7

27

47

67

QF

(f) Average iteration times = 3.6

Fig. 9. Influence study of the relationship between linear PRD prediction model and practical PRD curve on quality control performance by using variant leads of Patient001-s0010.

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Table 1 A compression performance comparison with the DCT-based scheme [23] based on the three indices PRDN, RMS and SNR. Compression Schemes

Signals (CR)

PRDN

RMS

SNR

Signals (CR)

PRDN

RMS

SNR

Signals (CR)

PRDN

RMS

SNR

[7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar [7] NRDPWT-EPar

100 (22.94) 101 (23.86) 102 (25.91) 103 (20.33) 104 (22.94) 105 (20.96) 106 (19.55) 107 (18.55) 108 (23.11) 109 (19.89) 111 (22.99) 112 (23.82) 113 (19.96) 114 (25.58) 115 (19.88) 116 (17.75)

48.88 14.73 38.34 11.38 35.70 15.65 37.74 10.05 32.54 13.32 14.19 10.21 24.00 8.29 22.88 6.26 13.61 12.99 8.05 7.18 19.60 12.71 19.08 14.83 34.85 8.30 34.52 16.87 38.00 9.37 29.48 8.32

18.78 5.50 20.20 5.32 13.61 5.76 24.52 6.11 16.38 6.26 11.45 7.09 17.57 5.74 38.98 10.43 7.59 5.16 7.51 6.83 10.18 5.32 8.65 5.62 28.81 6.57 10.70 4.48 27.76 5.98 40.43 8.36

6.22 16.71 8.33 19.00 8.95 16.18 8.46 20.01 9.75 17.60 16.96 19.89 12.40 21.69 12.81 24.09 17.33 18.09 21.88 22.90 14.15 18.14 14.39 16.71 9.16 21.66 9.24 15.80 8.41 20.78 10.61 22.02

117 (24.43) 118 (19.83) 119 (19.31) 121 (25.84) 122 (21.30) 123 (20.80) 124 (21.23) 200 (19.97) 201 (23.35) 202 (21.66) 203 (19.53) 205 (23.12) 207 (24.45) 208 (19.28) 209 (20.15) 210 (22.12)

20.80 11.38 20.52 12.03 16.30 7.13 7.73 10.01 12.27 10.09 33.30 8.66 13.62 6.40 29.33 10.01 18.56 8.90 15.30 8.40 12.12 9.11 44.59 16.84 8.43 7.54 29.20 8.87 43.11 16.24 14.65 10.54

10.03 4.58 17.48 9.53 17.63 6.73 4.63 3.78 8.97 7.22 19.33 4.79 12.74 4.97 22.56 7.13 7.19 3.15 9.05 4.56 12.11 7.92 17.65 6.03 6.02 4.71 28.28 7.84 23.02 8.12 7.67 5.10

13.64 19.01 13.76 18.51 15.76 23.20 22.23 20.34 18.22 19.96 9.55 21.31 17.32 24.12 10.65 20.02 14.63 21.12 16.30 21.60 18.33 20.90 7.02 15.60 21.48 22.55 10.69 21.15 7.31 15.89 16.68 19.63

212 (19.86) 213 (17.20) 214 (19.97) 215 (20.27) 217 (20.02) 219 (19.06) 220 (20.06) 221 (20.40) 222 (23.33) 223 (19.46) 228 (22.33) 230 (19.55) 231 (21.79) 232 (24.12) 233 (18.90) 234 (21.54)

37.43 15.28 23.24 9.21 12.09 6.80 25.18 16.11 13.12 6.77 11.66 6.78 40.71 10.09 22.55 9.02 45.96 15.06 14.31 8.07 13.13 10.82 26.90 9.80 45.46 9.35 31.01 14.25 14.45 8.48 28.12 12.34

24.59 9.44 31.15 11.64 11.48 6.20 14.16 8.73 16.13 7.99 12.87 6.34 25.82 6.29 13.73 5.19 16.92 4.78 11.68 6.10 9.22 5.89 18.83 6.59 24.44 4.74 10.27 3.79 15.72 8.77 18.81 7.39

8.53 16.40 12.67 20.76 18.35 23.37 11.98 15.90 17.64 23.42 18.66 23.67 7.81 19.96 12.94 20.95 6.75 16.70 16.89 22.01 17.63 19.51 11.40 20.22 6.85 20.69 10.17 17.33 16.80 21.48 11.02 18.28

algorithm (Step 2.2 in the error control process). The small average iteration value of Fig. 9 implies that the compression results of untrained data can be also inherent with an approximately linear distortion characteristic. Another advantage of the EP-based design scheme is worth mentioning here. In the comparison between NRDPWT-EPar and NRDPWT-6t [2] schemes, the EP-based design method can effectively suppress cpj (QF) curve exponentially growing in the high CR

region. As shown in Fig. 1(d), this smoothing effect can obtain a more linear relationship between PRD and QF. Also, the smoothing effect can improve the compression performance for both low and high CR regions. The average execution time of NRDPWT, an iteration of error control process and SPIHT coding is 1.782 ms, 4.578 ms, and 30.278 ms, respectively. For 360 Hz sampling rate, the sampling period is 2.78 ms. This implies that for real-time application, a buffer able to save at least 20 sampled data is required

Table 2 A comparison of reconstruction quality maintenance performance using the 48 signals in MIT arrhythmia database Ch1. Target PRD (PRDT )

ε = 5%

ε = 10%

ITs ±  3% 4% 5% 6% 7% 8% 9%

NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP NRDPWT-6t NRDPWT-EP

1.96 1.86 1.97 1.92 2.04 2.00 2.10 2.05 2.17 2.11 2.21 2.16 2.26 2.18

± ± ± ± ± ± ± ± ± ± ± ± ± ±

PRD ±  0.83 0.64 0.80 0.69 0.84 0.74 0.90 0.77 0.95 0.82 0.98 0.85 1.00 0.87

2.99 3.00 3.99 4.00 4.98 4.99 5.98 5.99 6.98 6.99 7.97 7.98 8.97 8.98

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.08 0.07 0.10 0.10 0.13 0.13 0.16 0.16 0.18 0.18 0.21 0.21 0.24 0.24

CR ±  11.10 11.19 14.47 14.60 17.57 17.75 20.47 20.70 23.23 23.51 25.86 26.20 28.47 28.95

ITs ±  ± ± ± ± ± ± ± ± ± ± ± ± ± ±

6.34 2.16 7.96 3.07 9.40 3.80 10.92 4.53 12.48 5.28 14.10 5.96 15.76 6.73

1.56 1.53 1.58 1.56 1.62 1.60 1.66 1.63 1.71 1.68 1.74 1.72 1.77 1.74

± ± ± ± ± ± ± ± ± ± ± ± ± ±

PRD ±  0.69 0.54 0.66 0.58 0.68 0.62 0.72 0.65 0.77 0.69 0.81 0.73 0.81 0.74

2.99 2.99 3.98 3.99 4.97 4.98 5.97 5.97 6.96 6.97 7.96 7.97 8.95 8.96

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.15 0.14 0.20 0.20 0.26 0.25 0.31 0.30 0.36 0.36 0.41 0.41 0.47 0.47

CR ±  11.08 11.17 14.42 14.56 17.53 17.73 20.41 20.65 23.15 23.43 25.81 26.17 28.44 28.94

± ± ± ± ± ± ± ± ± ± ± ± ± ±

6.34 2.15 7.90 3.04 9.37 3.81 10.79 4.54 12.39 5.29 14.05 6.04 15.84 6.90

Distinguish between NRDPWT-6t and NRDPWT-EP.

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Error bounds: ε = 5%

Error bounds: ε = 10%

PRDT = 3% Leads avf avl avr i

V1 V2 V3 V4 V5 V6 Leads avf avl avr i ii iii V1 V2 V3 V4 V5 V6

CR

2.99 ± 0.07

10.36 ± 3.74

2.98 ± 0.06

5.27 ± 0.52

2.99 ± 0.07

5.46 ± 2.1

3 ± 0.05

4.49 ± 0.67

3 ± 0.07

9.25 ± 6.01

3 ± 0.06

7.82 ± 1.4

3.01 ± 0.08

20.41 ± 2.68

3.01 ± 0.07

19.57 ± 2.02

3.01 ± 0.07

22.55 ± 2.58

2.99 ± 0.07

16.62 ± 3.88

2.98 ± 0.05

8.89 ± 2.57

2.99 ± 0.09

7.33 ± 3.1

File Name: patient147-s0211 2.98 ± 0.06 1.91 ± 0.64 3 1.86 ± 0.67 2.99 ± 0.07 3 3 ± 0.08 1.78 ± 0.67 3 1.97 ± 0.76 2.98 ± 0.08 3 1.7 ± 0.57 3 ± 0.06 3 2.48 ± 0.69 3 ± 0.07 3 1.72 ± 0.6 3.01 ± 0.08 3 1.45 ± 0.6 2.99 ± 0.07 3 1.89 ± 0.65 2.99 ± 0.07 3 2.99 ± 0.09 1.54 ± 0.69 3 1.64 ± 0.67 2.98 ± 0.08 3 3 ± 0.07 1.75 ± 0.72

9.37 ± 1.36 10.79 ± 4.72 27.13 ± 4.33 25.77 ± 6.17 17.47 ± 2.53 4.73 ± 1.66 29.93 ± 2.09 21.59 ± 2.11 26.49 ± 2.12 31.48 ± 2 33.59 ± 2.26 31.59 ± 2.23

Loops MAX 1.97 ± 0.68 4 2.08 ± 0.49 3 2.43 ± 0.92 5 2.32 ± 0.85 4 2.13 ± 0.53 4 1.94 ± 0.52 3 2.4 ± 0.79 4 2.08 ± 1.01 4 2.16 ± 1.04 4 2.02 ± 1.01 5 1.89 ± 0.61 3 2.02 ± 0.64 3 1.78 ± 0.58 3 1.91 ± 0.75 3 1.94 ± 1.07 6 2.43 ± 1.09 5 1.78 ± 0.97 6 2.37 ± 0.63 3 2.45 ± 1.28 5 1.94 ± 0.81 4 2.27 ± 1.3 5 2.37 ± 1.08 5 1.86 ± 0.94 4 2.21 ± 1.29

PRDT = 3% PRDN

CR

5.99 ± 0.16

30.25 ± 9.52

5.96 ± 0.15

12.46 ± 2.37

6 ± 0.14

17.03 ± 14.91

5.97 ± 0.13

9.44 ± 3.15

5.98 ± 0.16

26.98 ± 16.73

5.98 ± 0.13

21.73 ± 5.41

5.96 ± 0.17

35.22 ± 5.11

5.98 ± 0.18

33.58 ± 4.14

6.01 ± 0.15

36.4 ± 5.55

5.96 ± 0.13

36.03 ± 7.16

5.99 ± 0.16

25.18 ± 5.3

5.97 ± 0.17

21.61 ± 8.11

6 ± 0.14

23.09 ± 3.79

5.97 ± 0.13

30.76 ± 13.75

6 ± 0.16

51.51 ± 4.61

5.98 ± 0.16

52.06 ± 5.75

6 ± 0.16

44.11 ± 4.15

5.98 ± 0.13

9.82 ± 5.34

6.04 ± 0.17

49.92 ± 4.2

5.96 ± 0.14

41.26 ± 3.33

6.01 ± 0.15

43.8 ± 2.91

5.98 ± 0.17

48.54 ± 2.14

6.05 ± 0.18

53.07 ± 2.64

6.01 ± 0.17

53.27 ± 2.67

Loops MAX 1.86 ± 0.63 4 2.43 ± 0.83 3 2.21 ± 0.94 4 2.21 ± 0.88 3 2.05 ± 0.81 3 2.18 ± 0.7 3 1.67 ± 0.47 2 1.32 ± 0.47 2 1.45 ± 0.55 3 1.64 ± 0.53 3 1.81 ± 0.46 3 1.89 ± 0.65 3 1.27 ± 0.5 3 1.62 ± 0.63 3 1.4 ± 0.49 2 1.62 ± 0.59 3 1.35 ± 0.58 3 2.29 ± 0.81 3 1.37 ± 0.54 3 1.29 ± 0.46 2 1.18 ± 0.39 2 1.27 ± 0.5 3 1.16 ± 0.44 3 1.32 ± 0.47

PRDT = 6% PRDN

CR

3.02 ± 0.15

10.55 ± 3.96

3.02 ± 0.12

5.33 ± 0.59

2.95 ± 0.12

5.37 ± 1.99

2.98 ± 0.15

4.48 ± 0.73

3.03 ± 0.13

9.34 ± 6.05

2.98 ± 0.15

7.81 ± 1.48

3.02 ± 0.17

20.77 ± 2.96

2.98 ± 0.16

19.33 ± 2.26

3 ± 0.14

22.44 ± 2.87

3 ± 0.12

16.73 ± 3.76

3.03 ± 0.17

9.15 ± 2.78

3 ± 0.15

7.32 ± 2.98

3.05 ± 0.15

9.62 ± 1.33

2.97 ± 0.14

10.68 ± 4.64

2.99 ± 0.16

27.03 ± 3.86

2.94 ± 0.15

25.35 ± 5.62

3.02 ± 0.14

17.62 ± 2.51

2.99 ± 0.12

4.73 ± 1.67

3.01 ± 0.15

29.94 ± 1.97

2.94 ± 0.13

21.17 ± 2.24

2.99 ± 0.15

26.53 ± 1.83

3.01 ± 0.15

31.69 ± 1.94

3.02 ± 0.13

33.95 ± 2.3

2.94 ± 0.15

31.06 ± 2.38

Loops MAX 1.62 ± 0.54 3 1.86 ± 0.48 3 1.86 ± 0.78 3 1.89 ± 0.77 3 1.72 ± 0.65 4 1.67 ± 0.47 2 1.72 ± 0.73 3 1.62 ± 0.86 3 1.7 ± 0.77 4 1.45 ± 0.6 3 1.59 ± 0.49 2 1.62 ± 0.54 3 1.37 ± 0.49 2 1.59 ± 0.59 3 1.27 ± 0.5 3 1.78 ± 0.71 3 1.43 ± 0.55 3 2 ± 0.62 3 1.75 ± 0.92 4 1.45 ± 0.64 3 1.7 ± 0.9 4 1.81 ± 0.93 4 1.43 ± 0.68 3 1.59 ± 0.83

PRDN

CR

6.02 ± 0.29

30.49 ± 9.05

5.96 ± 0.25

12.53 ± 2.53

6 ± 0.3

16.43 ± 13.19

6.02 ± 0.27

9.69 ± 3.66

5.99 ± 0.31

27.21 ± 17.08

6.02 ± 0.23

21.91 ± 5.4

6.07 ± 0.32

35.69 ± 5.56

5.97 ± 0.27

33.7 ± 4.25

5.97 ± 0.36

36.06 ± 5.65

5.93 ± 0.3

35.74 ± 6.8

5.93 ± 0.26

24.88 ± 5.01

6.01 ± 0.29

21.87 ± 7.52

5.93 ± 0.28

22.82 ± 3.92

5.96 ± 0.27

30.32 ± 12.96

5.93 ± 0.32

51.04 ± 3.63

6.04 ± 0.31

52.87 ± 6.31

6.03 ± 0.28

44.83 ± 4.15

6.01 ± 0.28

9.93 ± 5.47

5.94 ± 0.33

49.32 ± 4.53

5.98 ± 0.36

41.19 ± 3.28

5.99 ± 0.34

43.76 ± 3.02

5.9 ± 0.3

48.66 ± 2.5

6.06 ± 0.25

52.81 ± 2.81

5.97 ± 0.29

53.06 ± 2.8

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Loops MAX 2.24 ± 0.76 4 2.59 ± 0.68 3 2.48 ± 0.86 4 2.51 ± 0.83 3 2.32 ± 0.83 3 2.51 ± 0.65 3 2.13 ± 0.71 3 1.91 ± 0.49 3 1.89 ± 0.51 3 2 ± 0.47 3 2.21 ± 0.67 3 2.21 ± 0.67 3

PRDT = 6%

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Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007

Table 3 Data compression and quality control performance evaluation of two ECG files in the PTB database.

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ARTICLE IN PRESS K.-C. Hung et al. / Medical Engineering & Physics xxx (2014) xxx–xxx

6. Conclusions For fast reconstruction quality control, an EP-based quantization scheme has been proposed for wavelet-based ECG data compression. The EP optimization with minimal PRD/CR criterion implies that multi-level quantization scales can be controlled with a single variable. This hypothesis leads to a simple design of linear distortion control with 3-D curve fitting technology. The inherent data independency property of linear distortion characteristic is also verified with many experiments by using the ECG signals saved in MIT and PTB databases. Linear distortion design can not only improve compression performance, but also facilitate reconstruction quality control. Funding None. Ethical approval Not required. Conflict of interest None declared. References [1] Vecht R, Gatzoulis MA, Peters N. ECG diagnosis in clinical practice. Springer: Martin Dunitz Ltd.; 2001. [2] Ku CT, Hung KC, Wu TC, Wang HS. Wavelet-based ECG data compression system with linear quality control scheme. IEEE Trans Biomed Eng 2010;57:1399–409. [3] Brechet L, Lucas MF, Doncarli C, Farina D. Compression of biomedical signals with mother wavelet optimization and best-basis wavelet packet selection. IEEE Trans Biomed Eng 2007;54:2186–92. [4] Al-Fahoum AS. Quality assessment of ECG compression techniques using a wavelet-based diagnostic measure. IEEE Trans Inf Technol Biomed 2006;10:182–91. [5] Miaou SG, Lin CL. A quality-on-demand algorithm for wavelet-based compression of electrocardiogram signals. IEEE Trans Biomed Eng 2002;49:233–9.

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Please cite this article in press as: Hung K-C, et al. EP-based wavelet coefficient quantization for linear distortion ECG data compression. Med Eng Phys (2014), http://dx.doi.org/10.1016/j.medengphy.2014.01.007