The abbreviation ECG denotes the electrocardiogram wave, named by the Dutch physiologist W. Einthoven (the inventor of the ECG). As shown in Figure 1, he classified one cardiac cycle into P, Q, R, S, and T complex waves (Burrus et al., 1998). The ECG diagnosis mainly depends on the PQRST waves. Therefore, it is necessary to maintain the shape of these waveforms when we add information into ECG signals or perform ECG signals compression.

The DWT is a technique attained by scales and translates a mother wavelet ψ(x). The normalized scaling functions and wavelets are defined as,

where i and n denote the scale and translation parameters, and h_i and g_iare the low-pass and high-pass filters, respectively. It should be noted that orthogonal wavelet basis functions are adopted to ease the work in calculating coefficients expansion so that an input signal can be decomposed into several non-overlapping multi-resolution sub-bands, including low-frequency sub-bands and high-frequency sub-bands (Oran Brigham, 1988; Mallat, 1989, 1999).

The DFT converts a finite sequence of equally spaced samples of a function into a same-length sequence of equally spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware. These implementations usually employ efficient fast Fourier transform (FFT) algorithms, so much so that the terms “FFT” and “DFT” are often used interchangeably (Rao and Yip, 1990; Oppenheim et al., 1999).

The DCT expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. In particular, a DCT is a Fourier-related transform similar to the DFT but using only real numbers (Rao and Yip, 1990; Granville et al., 1994).

Simulated annealing is an artificial intelligent algorithm, which utilizes probabilistic concept to approximate the global optimum of a given function. Specifically, It uses a metaheuristic method to approximate global optimization in a large discrete search space. In general, SA algorithm works as follows. At each time step, SA algorithm gives a solution randomly close to the current one, evaluates its quality, and then decides to move to it or to stay with the current solution based on either one of two probabilities between which it chooses based on the fact that the new solution is better or worse than the current one. During the search, the temperature is progressively decreased from an initial positive value to zero, and this affects the two probabilities: at each step, the probability of moving to a better new solution is either kept as 1 or is changed toward a positive value; instead, the probability of moving to a worse new solution is progressively changed toward zero (Bouttier and Gavra, 2019). The implementation of SA algorithm is easy because of its simple concept and computation.

As shown in Figure 2, the information hiding and detection proposed in this study is introduced as follows. Let S = {s₁,s₂,⋯,s_N} denote an ECG signal with total length N sample points. We then perform three transforms, DWT, DCT, and DFT, independently on the ECG signalS = {s₁,s₂,⋯,s_N}so that the binary bits B = {m_i} can be hidden into the coefficients of each transform domain. Finally, the hidden ECG signal is obtained and denoted by S~={s~1,s~2,⋯,s~N}. The details of the hiding process for each transform are listed below.

DWT: In the information hiding, we first apply Haar DWT with orthogonal wavelet bases to decompose an ECG signal into several non-overlapping sub-bands. In order not to distort or disturb the original ECG as much as possible, we hide the binary bits B = {m_i} into the DWT lowest-frequency coefficients by the following rule,

where {c_i} and {c~i} are the DWT lowest-frequency coefficients before and after hiding, respectively; Q is the hiding strength. By performing the inverse DWT (IDWT), the hidden ECG signal S~ is obtained and the information hiding is completed.

DCT: The hiding rule for DCT multiple coefficients is the same as for DWT. Similarly, we hide the binary bits B = {m_i} into the DCT lowest-frequency coefficients {c_i}, respectively.

DFT: The hiding rule for DFT multiple coefficients is the same as for DWT. Similarly, we hide the binary bits B = {m_i} into the DFT lowest-frequency coefficients {c_i}, respectively.

Theoretically, an ECG signal is modified when embedding patient confidential information. The modification is usually called a distortion. In order to reduce the distortion of ECG signal, we consider the maximum of SNR which is defined as,

where {s_i} represents the original ECG signal sample points, and {s~i} represents the unknown embedded (or modified) ECG signal sample points. Since we implement the DWT with orthogonal wavelet bases, the SNR can be rewritten to the form,

From the point of view on maximizing SNR, we consider to determine the unknown values of {c~i}i=0N by using the following optimization models.

Due to the fact that the algorithm of SA is easy to be implemented by its simple concept and calculation mentioned in section “Simulated Annealing,” especially for embedded system, we adopt SA to solve the optimization models approximately. In other words, we apply SA to obtain the optimal solutions of {c~i}i=0N approximately. At each time step in SA, the algorithm randomly selects a solution close to the current one, measures its quality, and then decides to move to it or to stay with the current solution based on either one of two probabilities between which it chooses on the basis of the fact that the new solution is better or worse than the current one. During the search, the temperature is progressively decreased from an initial positive value to zero, which affects the two probabilities: at each step, the probability of moving to a better new solution is either kept as 1 or is changed toward a positive value; instead, the probability of moving to a worse new solution is progressively changed toward zero. In this section, we adopt SA to approach the optimal solution of the proposed optimization model. The detailed procedure of SA in solving the proposed optimization model is introduced in the following steps.

In case ΔE≤0, the probability function P(ΔE,T) is equal to 1 indicating that the current solution S is replaced by new solution S’. In case ΔE > 0, the current solution S is replaced by the new solution S’ when probability function P⁢(Δ⁢E,T)=e(-Δ⁢ET) is greater than a threshold H∈(0,1).

After applying SA to embed patients’ essential body functions into ECG signal S, we obtain an embedded ECG signal S~, respectively.

In the information detection, similar to the information hiding mentioned earlier, we first perform the transforms, DWT, DCT, and DFT on the test ECG signals, respectively. Next, we detect binary bits {mi*} from the hidden coefficients {c~i} of the DWT, DCT, and DFT by the following rule:

Figure 3 shows the architecture of the proposed intelligent multiple-coefficient quantization hiding system for patients’ confidential data communication. First, we install ECG-sensor module, including electrode patch, AD8232 ECG sensor, and Arduino, on patients or dementia patients to obtain their ECG. As the ECG-sensor module shown in the upper left corner of Figure 3, three electrode patches are installed on patient body and connected to AD8232 ECG sensor. At the same time, AD8232 is connected to Arduino which outputs the ECG data to a computer. Next, as in subsections “Information Hiding” and “Information Detection,” we hide the patient’s information into the ECG signal in the transform domain by performing DWT/DFT/DCT and IDWT/inverse DFT (IDFT)/inverse DCT (IDCT). At the other end, the embedded patients confidential data are extracted after the hidden ECG is received through wireless communication and we perform transform domain DWT/DFT/DCT on the hidden ECG.

Without generality, the performance of the proposed scheme is evaluated by SNR, similarity, and RMSE, which are formulated as follows:

where s_i and s~i denote original ECG signal sample point and hidden ECG signal sample point, respectively.

The proposed method provides good quality for each hidden ECG signal. For example, Figures 4A,B show the original ECG signal and hidden ECG signal using DWT lowest-frequency coefficients in 5-level decomposition for dataset ID 1. They look almost indistinguishable. As shown in Figure 4C, the purple curve represents the original ECG signals, and the blue curve represents the hidden ECG signals using DWT and quantization size Q = 4000.

Moreover, as shown in Table 1, the proposed method applies SA to optimize the quality of each hidden ECG signal and then improve the drawback that the quality of each hidden ECG signal is greatly reduced as the quantization size Q is increased. In other words, our method remains high quality, with good RMSE and SNR, for each hidden ECG signal under sufficient hiding capacity no matter how the quantization size Q is increased. In addition, both DFT and DCT also have the same effect on RMSE and SNR.

There are some limitations in the proposed system. The two limitations in our system are that the ECG signals embedded with patients’ confidential data are transmitted to the receiver with an upload speed with a limit of 75 Mbps and a download speed with a limit of 300 Mbps. In future research plan, we will reduce the size of the sensor module and the computer and have a waterproof case without affecting the function.