# Improved ECG Watermarking Technique Using Curvelet Transform
## 6 Experimental Results
### Kullback-Leibler divergence (KL):  
\[\mathrm{D}\left(\mathrm{P_{\mathrm{c}^{\prime}}P_{w}}\right)=\int\mathrm{P_{ \mathrm{c}}}(\mathrm{x})\log\frac{\mathrm{P_{w}}(\mathrm{x})}{\mathrm{P_{ \mathrm{c}}}(\mathrm{x})}\mathrm{d}\mathrm{x} \tag{15}\]  
where D = KL divergence, P\({}_{w}\) = probability x event in the watermarked, P\({}_{\mathrm{c}}\)= probability of the host signal  
All other metrics are access information in time domain only KL divergence calculated in frequency domain it will advantageous when the signals are frequency domain [28]. **F. Structure similarity index measure (SSIM):** PSNR was the traditional error summation approach for evaluating the similarity, but PSNR matrix only shows the difference between the image intensity, it does not relate with the quality [29; 30]. Hence, a new approach was developed by [PERSON] [29] to measure the comparison among the host and disturbing image. \[\mathrm{SSIM}=\frac{\left(2\ \partial_{i}\partial_{j}+\omega_{1}\right)\left(2 \beta_{j}+\omega_{2}\right)}{\left(\partial_{i}^{2}+\partial_{j}^{2}+c_{1} \right)\left(\beta_{i}^{2}+\beta_{j}^{2}+\omega_{2}\right)} \tag{16}\]  
where \(\partial_{i}=\frac{1}{\mathrm{M}}\sum\limits_{\mathrm{i=1}}^{\mathrm{M}} \mathrm{i_{\mathrm{r}}}\), \(\partial_{j}=\frac{1}{\mathrm{M}}\sum\limits_{\mathrm{i=1}}^{\mathrm{M}} \mathrm{\hat{i}_{\mathrm{r}}}\), \(\beta_{i}=\sqrt{\left(\frac{1}{\mathrm{M}}\frac{\mathrm{M}}{\mathrm{\hat{i}}} \left(\mathrm{\hat{i}_{\mathrm{i}}-\partial_{\mathrm{xi}}}\right)^{2}\right)}\), \(\beta_{j}=\sqrt{\left(\frac{1}{\mathrm{M}}\frac{\mathrm{M}}{\mathrm{\hat{i}}} \left(\mathrm{\hat{i}_{\mathrm{i}}-\partial_{\mathrm{i}}}\right)^{2}\right)}\), \(\omega_{1}=\left(t_{1}\mathrm{P}\right)^{2}\),\(\omega_{2}=\left(t_{2}\mathrm{P}\right)^{2}\). \(t_{1}=0.01\), \(t_{2}=0.03\), \(\mathrm{P}=255\) (maximum value of host ECG). The MIT-BIH arrhythmia database was used to collect the ECG signals [19] sampled at 128 Hz. The original 1D-ECG signal is shown in Figure 1 whereas the 2D-ECG signal is shown in Figure 2. The QRS complex attributes form the original ECG are shown in Figures 4 and 5 show the resulting image of the proposed embedding procedure, i.e., watermarked ECG signal. The visual quality of the original 1D-ECG signal is the same as watermarked 1D-ECG. The experimental result also concludedthat the watermarked image preserved the attributes QRS complex. The original and information embedded ECG, i.e., watermarked ECG both show a higher level of similarity. The performance of the proposed technique is analyzed by different ECG signals. The same watermark as shown in Figure 3 is embedded into the curvelet coefficients of the ECG signal. The selected clusters are 0-7, so the size of the watermark that embedded is \(128\times 128\). Table 1 shows the performance of the proposed technique with different metrics. The Stego ECG does not affect the ability to diagnose and as well as the signal disturbance is minimum. The PSNR is greater than 65 for all ECG signals to verify the quality of the original and Stego ECG is very similar. The values of NC, BER, MSE and SSIM show the comparative analysis of both Stego as original ECG. Values of KL and PRD shows that the signal contains minimum disturbance. The projected watermarked ECG has confirmed besides the dissimilar size of information and the cluster size the experimental results are accessible in Table 2. The visual quality of the original signal may be degraded by the size of embedded information. The discussed algorithm does not reduce the visual quality it delivers a good imperceptibility to the hidden information. As well as the discussed algorithm also takes care the embedded information will not modify the QRS attribute as well as not affect the ability to diagnose the disease. The experimental results shown in Table 2 verified the performance of the technique. The technique was verified by embedding different sizes of the watermark in different cluster sizes.