ECG Sensor Design Assessment with Variational Autoencoder-Based Digital Watermarking

Abstract

Designing an ECG sensor circuit requires a comprehensive approach to detect, amplify, filter, and condition the weak electrical signals produced by the heart. To evaluate sensor performance under realistic conditions, diverse ECG signals with embedded watermarks are generated, enabling an assessment of how effectively the sensor and its signal-conditioning circuitry handle these modified signals. A Variational Autoencoder (VAE) framework is employed to generate the watermarked ECG signals, addressing critical concerns in the digital era, such as data security, authenticity, and copyright protection. Three watermarking strategies are examined in this study: embedding watermarks in the mean (μ) of the VAE's latent space, embedding them through the latent variable (z), and using post-reconstruction watermarking in the frequency domain. Experimental results demonstrate that watermarking applied through the mean (μ) and in the frequency domain achieves a low Mean Squared Error (MSE) while maintaining stable signal fidelity across varying watermark strengths (α), latent space dimensions, and noise levels. These findings indicate that the mean (μ) and frequency domain methods offer robust performance and are minimally affected by changes in these parameters, making them particularly suitable for preserving ECG signal quality. By contrasting these methods, this study provides insights into selecting the most appropriate watermarking technique for ECG sensor applications. Incorporating watermarking into sensor design not only strengthens data security and authenticity but also supports reliable signal acquisition in modern healthcare environments. Overall, the results underscore the effectiveness of combining VAEs with watermarking strategies to produce high-fidelity, resilient ECG signals for both sensor performance evaluation and the protection of digital content.

Keywords: Fourier-simulated ECG dataset; latent variable space; variational AutoEncoder; watermarking technology.

Figure 1

Functional Block Diagram of ECG signal processing.

Figure 2

The plots represent (a) the Bode magnitude and (b) the phase response of a system consisting of high-pass, band-pass, and low-pass filters.

Figure 3

The architecture of the VAE.

Figure 4

The simulated electrocardiogram (ECG) [27,28,29,30].

Figure 5

The simulated ECG (a) original signal with the noise factors (b) 0.00, (c) 0.01, and (d) 0.05.

Figure 6

The architecture of the implemented VAE in experiments.

Figure 7

(A) Embedding a watermark into the mean ($\mu$) of the VAE model: (a) the loss vs. epochs; (b) ECG training data; and (c) VAE model-generated ECG embedded with a watermark. (B) Embedding a watermark into the latent variable (z) of the VAE model: (a) the loss vs. epochs; (b) ECG training data; and (c) VAE model-generated ECG embedded with a watermark in the latent variable (z). (C) Embedding a watermark through the frequency domain: (a) the loss vs. epochs; (b) the reconstructed ECG with the VAE model; and (c) ECG embedded with a watermark.

Figure 7

(A) Embedding a watermark into the mean ($\mu$) of the VAE model: (a) the loss vs. epochs; (b) ECG training data; and (c) VAE model-generated ECG embedded with a watermark. (B) Embedding a watermark into the latent variable (z) of the VAE model: (a) the loss vs. epochs; (b) ECG training data; and (c) VAE model-generated ECG embedded with a watermark in the latent variable (z). (C) Embedding a watermark through the frequency domain: (a) the loss vs. epochs; (b) the reconstructed ECG with the VAE model; and (c) ECG embedded with a watermark.

Figure 8

The simulated ECG at (a) alpha 0.5 and (b) alpha 0.9 embedding the watermark in the mean ($\mu$); (c) alpha 0.5 and (d) embedding watermarks through the latent variable ($z$); (e) alpha 0.5 and (f) alpha 0.9 embedding watermarks through the frequency domain.

Figure 9

(A) Embedding the watermark in the mean ($\mu$) with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (B). Embedding the watermark in the mean ($\mu$) with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; and (c) VAE reconstructed signal with watermarking. (C) Embedding the watermark in the mean ($\mu$) with noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking.

Figure 9

(A) Embedding the watermark in the mean ($\mu$) with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (B). Embedding the watermark in the mean ($\mu$) with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; and (c) VAE reconstructed signal with watermarking. (C) Embedding the watermark in the mean ($\mu$) with noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking.

Figure 10

(A) Embedding the watermark through the latent variable (z) with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (B) Embedding the watermark through the latent variable (z) with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (C) Embedding the watermark through the latent variable (z) noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking.

Figure 10

(A) Embedding the watermark through the latent variable (z) with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (B) Embedding the watermark through the latent variable (z) with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking. (C) Embedding the watermark through the latent variable (z) noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; and (c) VAE-reconstructed signal with watermarking.

Figure 11

(A) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; (c) VAE-reconstructed signal without watermarking; and (d) VAE-reconstructed signal with watermarking. (B) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; (c) VAE-reconstructed signal without watermarking; and (d) VAE-reconstructed signal with watermarking. (C) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; (c) VAE reconstructed signal without watermarking; and (d) VAE reconstructed signal with watermarking.

Figure 11

(A) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.1: (a) first original training signal; (b) mean of all training signals; (c) VAE-reconstructed signal without watermarking; and (d) VAE-reconstructed signal with watermarking. (B) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.3: (a) first original training signal; (b) mean of all training signals; (c) VAE-reconstructed signal without watermarking; and (d) VAE-reconstructed signal with watermarking. (C) Post-reconstruction watermarking, embedding watermarks through the frequency domain with noise_factor = 0.5: (a) first original training signal; (b) mean of all training signals; (c) VAE reconstructed signal without watermarking; and (d) VAE reconstructed signal with watermarking.