Progressive Data Hiding in Integer Wavelet Transform of Electrocardiogram by Using Simple Decision Rule and Coefficient Calibration

Progressive Data Hiding in Integer Wavelet Transform of Electrocardiogram by Using Simple Decision Rule and Coefficient Calibration

Chingyu Yang* Wenfong Wang

National Penghu University of Science and Technology, 300, Liu-Ho Rd., Magong, Penghu 880, Taiwan

National Yunlin University of Science and Technology, 123 University Rd., Section 3, Douliou, Yunlin 64002, Taiwan

Corresponding Author Email: 
chingyu@gms.npu.edu.tw
Page: 
11-20
|
DOI: 
https://doi.org/10.18280/ria.340102
Received: 
3 November 2019
|
Accepted: 
14 January 2020
|
Published: 
29 February 2020
| Citation

OPEN ACCESS

Abstract: 

Based on one dimensional (1D) integer wavelet transform (IWT) domain, patient’s data can be effectively embedded in electrocardiogram (ECG) via the proposed criterion and coefficient alignment. Multiple data bits can be sequentially hidden in host bundles (with different lengths) of the low and high subbands of IWT coefficients. Simulations indicated that the average signal-to-noise ratio (SNR) and the payload of the proposed method are superior to those of existing techniques. Additionally, the proposed method exhibited a robustness that has rarely been observed in conventional ECG steganography. Our method is capable of resisting attacks such as cropping, inversion, scaling, translation, truncation, and Gaussian noise addition. Because bit embedding and extraction procedures are quite simple, our method can be applied in portable biometric devices.

Keywords: 

data hiding, ECG steganography, 1D IWT progressive bit embedding/extraction, coefficient alignment

1. Introduction

Due to the rapid evolution and growth of networking technology, the ubiquitous deployment of intelligent computing and automated devices, and various applications with user-friendly interfaces, people have become able to surf the Internet economically by using computing (or smart portable) devices. However, sensitive messages (or private data) are vulnerable to interception, copying, and tampering during transmission between a sender and an intended receiver. Encryption/decryption systems are commonly used to solve these problems. However, to reduce the cost and functional limitations of portable devices, various researchers have reported data hiding techniques as a solution. Recently, data hiding has played a crucial role in protecting secret data in multimedia files, such as documents, images, and videos [1-5]. In addition, several researchers have presented data hiding for biomedical signals such as an electrocardiogram (ECG) to secure personal sensitive information, including patients’ diagnoses [6-16].

In the context of the Fourier transform and spread spectrum approaches, Kozat et al. [6] proposed robust watermarking and fragile watermarking techniques for electrocardiograms (ECGs) to protect private data and the ownership of metadata. Simulations indicated that the robust watermarking technique exhibited effectiveness against manipulation, whereas the fragile watermarking technique effectively detected alteration. However, the payload size was <60 bits, and the resultant SNR was approximately 40 dB. To protect patients’ confidential information in point-of-care systems, Ibaida and Khalil [7] presented an efficient ECG steganography method that used encryption, scrambling, and wavelet packets. Simulations revealed that the perceived quality of marked ECGs was favorable with a low distortion rate of 1%. Chen et al. [8] reported three different kinds of ECG watermarking techniques to hide patients’ data in discrete wavelet transforms (DWTs), discrete cosine transforms, and discrete Fourier transforms. The average execution time was approximately 1.60 s and the size of the payload was only 32 bits; both of these problems may limit the usage of the method. On the basis of DWT and singular value decomposition, Jero et al. [9] proposed a noteworthy ECG steganography method to secure information about patients. Experimental results indicated that the bit error rate (BER) of their method was <0.6% because the high-high subband of DWT was used for hiding the secret information. However, their proposed method provided a payload size of 4,489 bits. By using curvet transform and quantization techniques, Jero and Ramu [10] developed a simple ECG steganography for data security. Simulations indicated that the percentage residual difference (PRD) and BER of the method were 0.110 and 31.84%, respectively; the size of the payload was 4,016 bits.

Based on the integer wavelet transform (IWT) domain and a coefficient adjustment technique, Yang and Lin [11] embedded data bits in the low and high subbands of IWT coefficients. Simulations confirmed that the average SNR introduced using the proposed method was approximately 42 dB with the payload of size 15,000 bits and a certain degree of robustness. Yang and Wang [12] employed a smart coefficient alignment technique and designed an effective ECG steganography for hiding patients’ information. The technique has two approaches: method A and method B. Experimental demonstrations indicated that method A created a high SNR value of approximately 55 dB with a payload size of 7,500 bits, whereas method B generated an SNR value of 44 dB with a large payload size of approximately 15,000 bits. By using DWT, singular value decomposition (SVD), and continuous ant colony optimization techniques, Jero et al. [13] embedded patient data in an ECG host. First, DWT decomposed a two dimensional ECG matrix into frequency subbands; and then, data bits were effectively hidden in the selected subbands by using SVD and quantization techniques. Experiments indicated that the resultant PRD was 0.015; the payload size was approximately 18,000 bits.

To obtain efficient wireless transmission, Pandey et al. [14] embedded sensitive data regarding patients in ECG signals by combining orthogonal frequency division multiplexing, chaotic map, and sample value difference methods. The average SNR of their method was 52 dB (or PRD = 0.260) with a payload size of 21,504 bits. To obtain a high-capacity ECG steganography, Yang and Wang [15] concealed patients’ diagnoses in biometric signals by embedding two data bits in a host bundle of the ECG. The payload size was 20,000 bits when the size of the host bundle was 3. Additionally, the average SNR of their method was approximately 45 dB. Instead of using auxiliary information, Yang and Wang [16] used the absolute-value-decision policy effectively promoting the SNR performance of the study [15]. Furthermore, the number of input bits can be designed on-demand by using host bundles of various sizes. Experimental results indicated that the average SNR of their method was larger than that of the study [15] by approximately 3.54 dB.

In the aforementioned studies, the SNR, PRD, or resultant payload was not sufficiently favorable. In this study, we proposed an efficient ECG steganography method with the merits of high hiding capacity and perceived quality. Additionally, our method provided robust performance, which has rarely been observed in conventional ECG steganography methods. The remainder of this paper is organized as follows. Sec. 2 presents the procedures of bit embedding and bit extraction of our proposed method. Sec. 3 provides the simulation results. Sec. 4 presents conclusion of this study.

2. Proposed Method

To obtain a high hiding capacity with low computation time, and favorable perceived quality with robust performance, we embedded data bits in the IWT domain [17]. First, an input ECG host was decomposed into low subband coefficients (IL) and high subband coefficients (IH) by using level 1 (L1) one dimensional (1D) IWT. Then, predetermined criteria for bit embedding and bit extraction were employed to conceal secret information in the IL and IH subbands, respectively. However, to obtain high perceived quality, data bits can be embedded only in the IH subband of IWT coefficients with host bundle sizes of <4. Although a multilevel IWT decomposition can be employed in our method to further promote robustness with approximate payload capability and similar perceptual quality, the cost of computation time might be an issue for real-time applications. As stated earlier, we focus on hiding secret data in L1 IWT domain. Without loss of generality, let $H_{j}=\left\{s_{j i}\right\}_{i=0}^{\mathrm{n}-1}$ be the jth host bundle of size n, as illustrated in Figure 1. The decision criterion Θ is defined as follows:

$\Theta=\left|\frac{\sum_{i=0}^{n-2} s_{j i}}{n-1}-s_{j n-1}\right| \leq \tau$     (1)

where, t is the control integer. For example, a data bit 1 or 0 can be virtually hidden in a host bundle of size 2 if $-\tau \leq\left|s_{j 0}-s_{j 1}\right|<0$ or $0 \leq\left|s_{j 0}-s_{j 1}\right| \leq \tau$ is satisfied. Then, the subsequent input data bit 1 or 0 can be embedded in the (enlarged) bundle of size 3 along with the preceding sub bundle, if either $-\tau \leq\left|\frac{s_{j 0}+s_{j 1}}{2}-s_{j 2}\right|<0 \quad$ or $\quad 0 \leq\left|\frac{s_{j 0}+s_{j 1}}{2}-s_{j 2}\right| \leq \tau$ is satisfied, and so on. Theoretically, if no violation occurs, then data bits (of length n−1) can be completely concealed in a host bundle of size n. Notably, a large value of n, large payload size, and low SNR were obtained using the proposed method.

Figure 1. jth host bundle of size n

In our method, it is crucial to determine the values of n and $\tau$. Coefficient adjustment must be conducted if violation occurs during bit embedding. Furthermore, if the bundle (or subbundle) carries no data bit, it is considered a skipped bundle. Because the skipped bundles (or subbundles) can be easily detected at the receiver site according to the decision criterion $\Theta$ extra information is not required to recode the position of skipped bundles. The major steps of bit embedding and bit extraction for our proposed method are summarized in the following sections.

2.1 Bit embedding

The main procedure of bit embedding is described in the following algorithm.

Algorithm 1. Hiding secret bit in the ECG host.

Input: Host ECG data $\Psi=\left\{s_{k}\right\}_{k=0}^{|\Psi-1|},$ the desired size of a host bundle $n,$ a control integer $\tau,$ and a secret message $W$.

Output: Marked ECG data $\widehat{\Psi}$.

Method:

Step 0. Perform 1 D forward IWT from $\Psi$ to obtain two sets of host bundles $I_{L}=\left\{H_{j}|j=1,2, \ldots,| I_{L} |\right\}$ and $I_{H}=\left\{H_{j} | j=1,2, \ldots,\left|I_{H}\right|\right\}$.

Step 1. Input a bundle, for example $H_{j}=\left\{s_{j i}\right\}_{i=0}^{n-1}$ from $I_{L}$ (and $I_{H}$). If the end of input is encountered, then go to Step 12.

Step 2. Compute the offset $\emptyset=s_{j 0}-s_{j 1},$ if the condition $|\emptyset|>\tau$ is satisfied, then go to Step $5,$ otherwise, input a data bit $b_{p}$ from $W$.

Step 3. If both conditions of $b_{p}=1$ and $-\tau \leq \emptyset<0$ are satisfied, the sub-bundle carries data bit "1," then go to Step 5. Otherwise, if the condition $b_{p}=1$ is satisfied, then repeatedly adjust the value of $\phi$ by increasing $s_{j 1}$ by 1 and decreasing $s_{j 0}$ from 1 simultaneously until $-\tau \leq \emptyset<0$ is achieved, go to Step 5。

Step 4. If both conditions of $b_{p}=0$ and $0 \leq \varnothing \leq \tau$ are satisfied, the sub-bundle carries data bit "0," then go to Step 5. If the condition $b_{p}=0$ is satisfied, then repeatedly adjust the value of $\phi$ by increasing $s_{j 0}$ by 1 and decreasing $s_{j 1}$ from 1 simultaneously until the condition $0 \leq \varnothing \leq \tau$ is satisfied.

Step 5. Compute the offset $\gamma=\frac{s_{j 0}+s_{j 1}}{2}-s_{j 2},$ if the condition $|\gamma|>\tau$ is satisfied, then go to Step $8,$ otherwise, input next input bit $b_{q}$ from $W$。

Step 6. If both conditions of $b_{q}=1$ and $-\tau \leq \gamma<0$ are satisfied, indicating the subbundle carries data bit " 1 ," then go to Step $8 .$ Otherwise, if the condition $b_{q}=1$ is satisfied, then repeatedly adjust the value of $\gamma$ by increasing $s_{j 2}$ by 1 and decreasing both $s_{j 0}$ and $s_{j 1}$ from 1 simultaneously until the condition $-\tau \leq \gamma<0$ is satisfied, go to Step 8。

Step 7. If both conditions of $b_{q}=0$ and $0 \leq \gamma \leq \tau$ are satisfied, indicating the subbundle carries data bit "0," then go to next step. Otherwise, if the condition $b_{q}=0$ is satisfied, then repeatedly adjust the value of $\gamma$ by increasing both $s_{j 0}$ and $s_{j 1}$ by 1 and decreasing $s_{j 2}$ from 1 simultaneously, until the condition $0 \leq \gamma \leq \tau$ is met.

Step 8. If $n>3,$ then set parameter $m=4$, otherwise go to Step 1.

Step 9. Compute the offset $\beta=\frac{\sum_{i=0}^{m-2} s_{j i}}{m-1}-s_{j m-1}$ if both conditions of $|\beta|>\tau$ and $m \leq n$ are satisfied, then set $m=m+1$ and repeat this step. Otherwise, if the condition $m>n$ is satisfied, then go to Step 1.

Step 10. Input next bit $b_{s}$ from $W .$ If both conditions of $b_{s}=$ 1 and $-\tau \leq \beta<0$ are satisfied, then set $m=m+1$ and go to Step $9 .$ Otherwise, if the condition $b_{q}=1$ is satisfied, then change the value of $s_{j m-1}$ to $s_{j m-1}=s_{j m-1}+|\beta|+1,$ set $m=m+1$ and go to Step 9.

Step 11. If both conditions of $b_{s}=0$ and $0 \leq \beta \leq \tau$ are satisfied, then set $m=m+1$ and go to Step $9 .$ Otherwise, if the condition $b_{s}=0$ is satisfied, then change the value of $s_{j m-1}$ to $s_{j m-1}=s_{j m-1}-|\beta|-1,$ set $m=m+1,$ and go to Step 9.

Step 12. Perform $1 \mathrm{D}$ inverse IWT for $I_{L}\left(\text { and } I_{H}\right)$ to obtain mark ECG data $\widehat{\Psi}$.

Step 13. Stop.

2.2 Bit extraction

In the proposed method, the bit extraction is considerably simpler than bit embedding. The major steps of bit extraction are listed in the following algorithm.

Algorithm 2. Extracting hidden message from marked ECG.

Input: Marked ECG data $\widehat{\Psi}$, the desired size of a host bundle $n,$ and an integer $\tau$.

Output: Secret message W.

Method:

Step 0. Perform $1 \mathrm{D}$ forward IWT by using $\hat{\Psi}$ to obtain two sets of marked bundles $\hat{I}_{L}=\left\{\widehat{H}_{j}|j=1,2, \ldots,| \hat{I}_{L} |\right\}$ and $\hat{I}_{H}=\left\{\hat{H}_{j}|j=1,2, \ldots,| I_{H} |\right\}$, respectively.

Step 1. Input a bundle $\widehat{H}_{j}=\left\{\hat{s}_{j i}\right\}_{i=0}^{n-1}$ from $\hat{l}_{L}\left(\text { and } \hat{I}_{H}\right) .$ If the end of input is encountered, then go to Step 9.

Step 2. Compute the offset $\emptyset=\hat{s}_{j 0}-\hat{s}_{j 1},$ if the condition $|\emptyset|>\tau$ is satisfied, then go to Step 4.

Step 3. If the condition $-\tau \leq \emptyset<0$ is satisfied, then data bit " 1 " is recognized, otherwise, data bit "0" is identified.

Step 4. Compute the offset $\gamma=\frac{\hat{s}_{j 0}+\hat{s}_{j 1}}{2}-\hat{s}_{j 2},$ if the condition $|\gamma|>\tau$ is satisfied, then go to Step 6.

Step 5. If the condition $-\tau \leq \gamma<0$ is satisfied, then data bit " 1 " is recognized, otherwise, data bit "0" is identified.

Step 6  If $n>3,$ then set parameter $m=4,$ otherwise, go to Step 1.

Step 7. Compute the offset $\beta=\frac{\sum_{i=0}^{m-1} \hat{s}_{j i}}{m-1}-\hat{s}_{j m-1},$ if both conditions of $|\beta|>\tau$ and $m \leq n$ are satisfied, then set $m=m+1$ and repeat this step. Otherwise, if the condition $m>$ $n$ is satisfied, then go to Step 1.

Step 8. If the condition $-\tau \leq \beta<0$ is satisfied, then data bit "1" is recognized, otherwise, data bit "0" is identified. Set $m=m+1$ and go to Step 7.

Step 9. Assemble all extracted bits and rebuild the secret message.

Step 10. Stop.

Figure 2. Scenarios of embedding two data bits 11 in the host bundle of size 3. (a) Initial (host) bundle, (b) the transit bundle, which carried bit 1 (without adjustment), and (c) the final form of the bundle (marked bundle), which carried the second bit 1 (after adjustment)

Figure 3. Scenarios of embedding three data bits 111 in a host bundle of size 4

Figure 4. Scenarios of embedding four data bits 1111 in the host bundle of size 5

Figures 2-4 present the examples of bit embedding in the host bundles with the size of 3-5, respectively, that was performed using our proposed method with t = 9. Figure 2(a) illustrates the initial (host) bundle, Figure 2(b) presents the transit bundle, which carried data bit “1” without adjustment (according to Steps 2 and 3 of Algorithm 1), and Figure 2(c) presents the final form of the bundle (marked bundle), which carried another data bit “1” after adjustment. The figure displays the aligned values as three numbers surrounded by squares. Similarly, according to Steps 8–10 of Algorithm 1, Figures 3 and 4 illustrate the scenarios of embedding data bits in a host bundle of size 4 and 5. Furthermore, the mean absolute error (MAE) computed from Figures 2(a) and 2(c), Figures 3(a) and 3(d), and Figures 4(a) and 4(e) were 1, 1, and 1.8, respectively. We assumed that no error (or data corruption) occurred during transmission at the receiver site. According to Steps 2–5 of Algorithm 2, data bits “11” could be extracted using the marked bundle illustrated in Figure 2(c). Similarly, both the hidden bits “111” and “1111” could be extracted using the marked bundles illustrated in Figures 3(d) and 4(e), respectively, which is in accordance with Steps 6–8 of Algorithm 2.

From the above two algorithms we can see that the computation complexity of the proposed decision rule and coefficient adjustment is quite simple. For example, a host bundle whose size is larger than 2, it requires the computation of (n-2) ´ (n-1) ´ addition, (n-2) ´ division, subtraction, and absolute value; if the size of a host bundle is 2, it only needs the computation of subtraction and absolute value. Furthermore, the process of coefficient calibration just uses increment and decrement to achieve the goal within a finite number of times. That is, the adjustment values would be limited between -t and t. It may take a little computation time at the Steps 3-4 and Steps 7-8 of Algorithm 1 during coefficient adjustment procedure. A possible way of reducing computation time is not use iterative adjustment, that is, we could directly force and chane the values of the target coefficients to be satisfied with decision criteria. It would result in a lower SNR value obtained by our method. That is the reason why we employ simple decision and (iterative) coefficient calibration in our proposed method. To obtain extreme hiding storage (and if one neglects perceived quality), the optimal payload of the proposed method with host bundleof size $n$ and without violation was $\frac{n-1}{n} \times|\Psi| .$ By contrast, to obtain high perceived quality, data bits can only be embedded in the $I_{H}$ sub-band of IWT coefficients. Because the distortion caused by the proposed method by embedding secret bits in $I_{H}$ was considerably less than that caused by the proposed method by embedding secret bits in $I_{L} .$ However, in this case, the payload without violation would be at most $\frac{2}{3} \times\left|I_{L}\right|$ when the size of a host bundle was $3 .$ In addition, the value of $\tau$ was not necessarily constant. When $\tau$ value was small, SNR increased and vice versa. Moreover, when the size of host bundles was large, a large payload was obtained using the proposed method. Furthermore, for a given constant value of $\tau$, the maximum payload of the proposed method with a certain size of host bundle can be observed in the ECG host. The proposed method with a large $\tau$ provides more robust performance than it provides with any smaller $\tau$. Figure 5 presents the block diagram of the proposed method.

Figure 5. Block diagram of the proposed method

3. Experimental Results

Demonstrations of the proposed method by using an Intel(R) Core(TM) i5 1.7 GHz Laptop with 4 GB RAM. The average central processing unit (CPU) time for our method was approximately 0.0310 s. Several ECG host signals obtained from the MIT-BIH arrhythmia database [18] were used as test data, and each ECG host consisted of 30,000 samples. Both the control integer t and size of a host bundle were not constant during simulations. Three objective measurements, namely, SNR, MAE, and PRD were used for performance evaluation. They are defined as follows:

$S N R=10 \log _{10} \frac{\sum_{i} s_{i}^{2}}{\sum_{i}\left(s_{i}-\hat{s}_{i}\right)^{2}}$     (2)

$M A E=\frac{1}{N} \sum_{i=1}^{N}\left|s_{i}-\hat{s}_{i}\right|$     (3)

and

$P R D=\sqrt{\frac{\sum\left(s_{i}-\hat{s}_{i}\right)^{2}}{\sum_{i} s_{i}^{2}}}$    (4)

where, $s_{i}$ and $\hat{s}_{i}$ are the coefficients in original ECG and marked ECG, respectively. The resultant SNR, MAE, and payload for the proposed method with three distinct values of $\tau$ are listed in Tables 1-3, respectively. In our method, the smaller value of $\tau$ caused the value of SNR to become larger, and a low payload was obtained. The average SNRs, MAEs, and payloads of the proposed method with $\tau=9 / 22 / 55$ were 49.90/45.14/40.31 dB, 1.9335/3.0780/4.7157, and 21,704/24,313/25,806 bits, respectively. In addition, the relationship between payload and SNR of the proposed method that was obtained using host bundles of various sizes is presented in Figure 6. Of the six ECG signals that were tested as host bundles, ECG 100 exhibited the most efficient performance, followed by ECG 102, ECG 101, ECG 232, and ECG213. The performance of ECG 116 ranked the last place, which means ECG116 providing less SNR and hiding-capacity than other five tests. This can be confirmed from Tables 1-3. The resultant SNR of ECG116 always below the average SNR value with 1-2 dB. The average SNRs of these six tests were 70, 60, and 50 dB when their payload sizes were 3.1, 9.7, and 21.2 kb, respectively. Figure 7 presents the trade-off between payload, SNR, and the size of host bundle for the proposed method. The larger the bundle size is, the larger the payload is, and the lower the SNR is, and vice versa. Similar performance, as shown in Figure 8, was demonstrated when the z-axis was replaced by various values of $\tau$. As specified in the last paragraph of Sec. 2.2, the larger values of $\tau$, the better robustness performance obtained by the proposed method. Furthermore, close observations obtained (within the first 3 s with $\tau$=9) from the marked ECGs are presented in Figure 9. The marked signal introduced by our methods (red line) was approximately similar to the original one (blue line). This implies that the distortion caused by our method was not significant. namely, the resultant perceived quality is not bad. The performance comparison between various methods is presented in Table 4. Both the average SNR and payload of the proposed method are the best among the compared methods. A difference image generated from Figure 9 is illustrated in Figure 10. The disturbances in the lines that appeared in Figures 10(a)-10(e) were not so drastic, indicating they exhibited more favorable performance than the Figure 10(f) did. Moreover, Figure 11 indicates that both the SNR and payload performance of the proposed method were superior to those of Pandey et al. [14] and Yang and Wang [16]. Especially, both the SNR and hiding capacity of our method is significant better than other two techniques as payload size being increased to 20 kb.

Table 1. SNR/MAE/payload performance of the proposed method with $\tau$=9

ECG data

SNR/MAE/payload

Bundle size

100

50.18/1.9652/24,146

15

101

50.27/1.9028/22,427

9

102

50.04/1.9828/23,542

11

103

49.93/1.9648/21,473

10

104

49.95/1.9726/21,312

10

105

50.49/1.9001/21,195

9

106

50.14/1.9685/20,911

10

107

52.26/1.4144/16,637

11

108

49.35/2.1747/23,154

14

109

50.92/1.6808/19,532

10

111

50.28/1.9607/21,651

10

112

48.44/2.0797/22,119

10

113

50.95/1.8418/21,844

10

114

49.85/2.1248/24,335

12

115

49.57/1.9234/23,364

12

116

48.97/1.8189/19,044

9

117

48.87/2.0211/22,493

10

118

48.89/1.8517/18,195

9

119

49.51/1.7968/20,466

10

121

49.07/1.9788/24,427

10

122

48.36/2.0692/22,099

10

123

48.88/2.0263/22,734

11

124

49.08/1.9193/23,079

12

200

50.40/1.8750/20,474

9

201

50.40/1.9099/23,160

9

202

50.46/2.0106/23,599

12

203

50.36/1.8143/17,571

10

205

49.37/2.0682/23,488

10

207

51.08/1.7824/21,992

10

208

50.66/1.8318/18,876

8

209

50.33/1.9125/21,139

7

210

50.27/1.9896/23,208

10

232

49.08/2.2722/22,542

15

Average

49.90/1.9335/21,704

-

Table 2. SNR/MAE/payload performance of the proposed method with $\tau$=22

ECG data

SNR/MAE/payload

Bundle size

100

45.41/2.9671/26,029

15

101

45.04/3.0394/24,897

9

102

45.95/2.9163/25,577

11

103

44.89/3.2131/24,149

10

104

45.03/3.2777/24,099

10

105

45.83/2.9305/23,977

9

106

44.71/3.3543/24,099

10

107

45.87/2.7020/19,675

11

108

44.59/3.5170/26,027

14

109

45.70/2.8330/23,000

10

111

45.53/3.1057/24,749

10

112

43.80/3.3185/24,861

10

113

46.61/2.6667/23,961

10

114

46.28/2.9440/26,167

12

115

44.78/3.0021/25,208

12

116

43.52/3.2029/22,300

9

117

44.75/2.9114/24,801

10

118

42.95/3.4706/23,140

9

119

44.25/2.9620/23,055

10

121

45.62/2.7462/25,829

10

122

43.48/3.4689/23,740

10

123

44.71/2.9447/24,829

11

124

44.47/2.9404/25,151

12

200

45.44/3.1493/23,531

9

201

46.65/2.7663/24,927

9

202

46.21/2.9139/25,577

12

203

44.69/3.4782/21,941

10

205

45.60/3.0624/25,240

10

207

45.70/2.9746/24,655

10

208

44.64/3.4608/22,807

8

209

46.13/2.8485/23,450

7

210

46.81/2.7528/25,056

10

232

44.11/3.7972/25,813

11

Average

45.14/3.0780/24,313

-

Table 3. SNR/MAE/payload performance of the proposed method with $\tau$=55

ECG data

SNR/MAE/payload

Bundle size

100

40.89/4.2992/26,943

15

101

41.59/4.2326/25,809

9

102

40.60/4.3088/26,524

11

103

39.81/5.1745/25,678

10

104

39.25/5.2619/25,769

10

105

40.17/4.7398/25,475

9

106

39.59/5.3807/25,811

10

107

37.53/6.5479/23,297

11

108

39.36/5.4429/27,317

14

109

38.98/5.3496/25,305

10

111

40.29/4.8932/26,246

10

112

40.22/4.4310/26,213

10

113

40.86/4.1979/25,537

10

114

41.49/4.1508/27,243

12

115

41.05/4.1554/26,227

12

116

37.92/5.4749/24,436

9

117

39.52/4.4712/26,212

10

118

38.69/5.2909/25,001

9

119

37.77/5.5064/25,390

10

121

42.16/3.3453/26,324

10

122

38.54/5.5784/25,566

10

123

39.02/4.8692/26,201

11

124

40.37/4.2905/26,426

12

200

40.77/4.6289/25,327

9

201

43.32/3.3566/25,726

9

202

41.37/4.1713/26,661

12

203

38.91/6.1755/25,001

10

205

42.86/3.7525/25,968

10

207

40.60/4.4125/26,003

10

208

39.96/5.5244/24,702

8

209

43.13/3.6387/24,467

7

210

42.51/3.6497/25,978

10

232

40.99/4.9134/26,830

11

Average

40.31/4.7157/25,806

-

Table 4. SNR/net-payload (bits) performance comparison between various methods

ECG data set

Yang and  Lin [11]

Yang and  Wang [15]

Yang and  Wang [16]

Our method

100

42.37/15,000

44.15/20,000

48.19/19,604

50.18/24,146

101

42.54/15,000

44.09/20,000

47.39/19,610

50.27/22,427

102

44.44/15,000

45.44/20,000

51.60/19,602

50.04/23,542

103

38.96/15,000

40.86/20,000

44.92/19,600

49.93/21,473

104

42.06/15,000

42.74/20,000

46.84/19,602

49.95/21,312

105

44.05/15,000

45.71/20,000

47.66/19,602

50.49/21,195

111

46.76/15,000

48.22/20,000

49.43/19,630

50.28/21,651

112

44.86/15,000

46.59/20,000

48.32/19,658

48.44/22,119

113

38.49/15,000

40.31/20,000

46.23/19,602

50.95/21,844

114

48.05/15,000

49.09/20,000

51.59/19,604

49.85/24,335

115

37.99/15,000

39.77/20,000

44.51/19,608

49.57/23,364

121

48.40/15,000

49.91/20,000

51.97/19,602

49.07/24,427

122

40.53/15,000

42.30/20,000

44.69/19,602

48.36/22,099

123

39.13/15,000

40.79/20,000

46.49/19,602

48.88/22,734

124

41.93/15,000

43.54/20,000

46.36/19,602

49.08/23,079

200

42.18/15,000

43.98/20,000

47.36/19,608

50.40/20,474

201

46.14/15,000

47.62/20,000

50.13/19,612

50.40/23,160

202

46.33/15,000

47.82/20,000

50.16/19,632

50.46/23,599

203

40.64/15,000

42.13/20,000

43.27/19,622

50.36/17,571

232

46.96/15,000

48.65/20,000

51.58/19,620

49.08/22,542

Average

43.14/15,000

44.69/20,000

47.93/19,611

49.80/22,355

Figure 6. Trade-off between SNR and payload of the proposed method

Figure 7. Relationship between payload, SNR, and bundle size of the proposed method with $\tau$=9

Figure 8. Relationship between payload, SNR, and $\tau$ of the proposed method with the bundle of size 15

Figure 9. Close observations of the marked ECG generated using the proposed method with t = 9

Figure 10. Difference images generated from the close observations of the marked ECG generated using the proposed method

Figure 11. Performance comparison between various methods

Two examples of survived watermarks after the marked ECG 100 (with $\tau$=22) was manipulated are presented in Tables 5 and 6. The size of a host bundle was 15. Two different input binary images of size $161 \times 161$ were used as an input watermark. The resultant SNR of the marked ECG 100 was approximately 45 dB. Notably, the value of PRD = 0 when the marked ECGs were not being manipulated. The 2nd and 3rd rows of the Table 5 indicate that the watermarks extracted from the mark ECG attacked using the additive white Gaussian noise (AWGN) with 0.1 and 1 dB were recognized. Similarly, the extracted watermark presented in the 4th row of Table 5 that survived the cropping attack (with 33% off) was identified. Additionally, the extracted watermark (in the 8th row of Table 5) was identified when the last three bits of the marked samples were truncated. Although the PRD value of survived watermarks that were manipulated using inversion was close to 1, it was recognized. Our method exhibited robust performance against translation (+1500, −1500) and scaling (*0.9, *1.2) attacks. Table 6 indicates similar robustness generated by our method. Furthermore, the PRD performance of the proposed method under various attacks such as AWGN, scaling, and translation with different factors is presented in Figure 12. Figure 12(a) indicates that the tolerance test factor of our method for AWGN attack was 0.1 dB. the higher the SNR is, the lower the PRD is; thus, increasing SNR results in a good perceived quality. Figure 12(b) indicates the range attacked by scaling was from 0.9 to 1.2. Figure 12(c) indicates that our method resisted translation attacks in the range from −2000 to +2000. Finally, from Tables 5-6 and Figure 12, we concluded that the proposed method is capable of resisting various types of attacks.

Table 5. Examples of survived watermarks from the manipulations of marked ECG 100

Attacks

Survived Watermarks

Null-attack PRD = 0.0000

AWGN (with SNR 0.1 dB) PRD = 0.6845

AWGN (with SNR 1 dB) PRD = 0.6564

Cropping (33% off) PRD = 0.8295

Inversion PRD = 0.9879

Scaling (*0.9) PRD = 0.6689

Scaling (*1.2) PRD = 0.6570

Truncation+ PRD = 0.8018

Translation (+1500) PRD = 0.0000

Translation (-1500) PRD = 0.6828

+The last three bits of the marked data were truncated.

Table 6. Another example of survived watermarks from the manipulations of marked ECG 100

Attacks

Survived Watermarks

Null-attack PRD = 0.0000

AWGN (with SNR 0.1 dB) PRD = 1.1523

AWGN (with SNR 1 dB) PRD = 1.1287

Cropping (33% off) PRD = 1.0905

Inversion PRD = 1.5630

Scaling (*0.9) PRD = 1.1797

Scaling (*1.2) PRD = 1.2158

Truncation+ PRD = 1.1671

Translation (+1500) PRD = 0.0000

Translation (-1500) PRD = 1.1131

+The last two bits of the marked data were truncated

Figure 12. PRD performance obtained using the proposed method against three types of attacks under various test factors

4. Conclusions

In this study, we established a cumulative data hiding approach in ECG signals based on a 1D IWT domain. According to the predetermined criterion with host bundles of various sizes, sensitive data can be successfully embedded in the IWT coefficients of ECG hosts. Experimental results confirmed that the average SNR and payload of our proposed method are superior to those of the conventional ECG steganography. Moreover, the proposed method exhibited robust performance, which has rarely been observed in existing ECG steganography techniques. The proposed method exhibited the merits of high hiding capacity and superior resultant perceived quality. Moreover, our method was resistant toward attacks such as cropping, inversion, scaling, translation, truncation, and Gaussian noise addition. Because the procedures of bit embedding and extraction are simple and the computation time is short, our method can be applied in mobile biometric devices.

Nomenclature

$I_{L}$

low subband coefficients of IWT

$I_{H}$

high subband coefficients of IWT

$\Theta$

$\Psi$

decision criterion

host ECG data

$\hat{\Psi}$

Marked ECG data

Greek symbols

$\tau$

control parameter

$S k$

the kth element of the host ECG data

$\phi$

offset

$\gamma$

offset

$\beta$

offset

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