Denoising low SNR electromagnetic conducted emissions using an improved DnCNN based mode

Abstract

Conducted electromagnetic emissions from interconnecting cables in computer systems can lead to internal information leakage and cause information security problems. However, unintentionally leaked EM signals are characterized by low signal-to-noise ratio and random noise, making it difficult to recover the original signal. In this paper, we propose a denoising model (S-DnCNN) based on an improved DnCNN to better recover the original signal. The network structure consists of three parts: feature mapping generation, low-dimensional feature extraction, and original reconstruction. To improve the noise extraction capability, we use Leaky ReLU as the activation function of the CNN, and introduce a residual structure and a convolutional attention module. The residual structure uses residual hopping to implicitly remove potentially clean images by hidden layer operations, thus training noisy data to recover clean data. We construct a one-dimensional selective convolution kernel (SKConv1d) and fuse it with local paths to form a feature extraction network, which improves the performance of the network. The experimental results show that our proposed method can preserve the details in the effective signal during denoising and shows good generalization to complex SNR data.

Keywords

Information security electromagnetic information leakage feature extraction low signal-to-noise ratio denoising

1 Introduction

Electronic devices such as computers unintentionally leak electromagnetic signals containing information during operation. After the leaked electromagnetic signal is intercepted, the information in the leaked electromagnetic signal is restored by the information reconstruction technique in TEMPEST [1] technology, which poses a threat to information security [2]. By analyzing the existing electromagnetic information leakage detection methods [3, 4] it can be found that the current detection methods have some shortcomings. One of the main points is the low signal-to-noise ratio of electromagnetic leakage signals, and the information leakage characteristics are easily deformed, shifted or even suppressed under the interference of environmental noise.

In actual electromagnetic environments, the leakage of electromagnetic signals will be interfered not only by environmental noise, but also by other electronic devices or their own internal radiation of electromagnetic waves. When leaked electromagnetic signals are interfered with by a large amount of noise, useful information will be covered by noise, and it is difficult to detect electromagnetic leakage and recover effective information by traditional image reproduction means [5 –10]. Existing detection methods have limited adaptability and still need to perform detection work under the premise of clear leakage characteristics. Therefore, defining and finding information leakage characteristics in a standardized way becomes a key problem in electromagnetic information leakage detection.

In order to better detect risks, it is important to more effectively detect electromagnetic leaks in relatively complex electromagnetic environments, discover risk points, and remove noise interference.

The leakage mode of electromagnetic signals includes radiation leakage and conduction leakage, and video information on computer monitors can leak through video cables with conduction leakage [11]. However, when electromagnetic information leakage occurs, the radiated electromagnetic signal contains a large amount of noise that is random, and it is difficult to determine the type of noise by a priori knowledge. The electromagnetic signal picked up in actual environments varies in different environments, and the signal-to-noise ratio of the signal picked up in different environments varies widely, which brings difficulties to further analysis and extraction of the signal. Suppressing the noise in the electromagnetic signal and improving the signal-to-noise ratio is an urgent problem to be solved.

Video signal noise reduction is an important technique for signal preprocessing, and for signal noise, experts have proposed many methods, typically bandpass filtering [12], wavelet transform [13, 14], curvelet transform [15], shearlet transform [16], empirical mode decomposition (EMD) [17], anisotropic full variational noise reduction [18], fuzziness-based electromagnetic leakage reduction image processing methods [19], etc., but all these methods have certain limitations. For example, bandpass filters cannot separate the effective signal and noise in a common frequency band; the performance of EMD degrades due to mode mixing when processing some low signal-to-noise band noise EM signals; sparse transform-based methods, including wavelets, curvelet, and shearlet, rely heavily on the threshold function and manual threshold setting. Deviations in threshold selection in wavelet noise reduction can lead to pseudo-Gibbs phenomenon, which affects the reconstructed reproduction of video signals, and cannot be applied to diverse and random noise interference. Moreover, conventional EM signal denoising algorithms face certain challenges in adjusting the signal-to-noise ratio, especially in complex environments where the ratio between signal and noise may vary significantly. This leads to limitations in the applicability of these algorithms under different conditions. Secondly, electromagnetic signal leakage is usually accompanied by stochastic noise, which is difficult to be accurately modeled and suppressed by conventional methods. As a result, existing algorithms have limitations in effectively handling these random noises. Many algorithms may perform well under low signal-to-noise ratio conditions, but may lose their effectiveness when dealing with electromagnetic signals under complex signal-to-noise ratio conditions, thus requiring better generalization performance.

In recent years, neural network denoising algorithms based on DnCNN [20] have achieved better results in image denoising, and the application of this model to video signal noise reduction can fully consider the structural characteristics of noise and improve the noise reduction effect. However, DnCNN is a supervised deep learning method that requires a large amount of highly realistic training data to optimize the network parameters. However, there is no training data suitable for EM signal data under complex signal-to-noise ratio. And the EM video signal contains some negative data with extremely weak capability, which places a higher demand on the effective signal recovery capability of the trained DnCNN model.

To better solve the problem of denoising electromagnetic signals under complex signal-to-noise ratio conditions, we propose a model based on an improved DnCNN called S-DnCNN to overcome the limitations of the existing algorithms.. Based on DnCNN, this paper uses Leaky ReLU as a compensation function to retain more negative components for more complete recovery of the effective signal. Based on the selective convolution kernel (SKConv) proposed in the literature [21], this paper designs a one-dimensional selective convolution kernel (SKConv1d), which is merged with local paths to form a feature extraction network to improve the model effect. Since electromagnetic leakage signals in complex environments have a large range of signal-to-noise ratio variations at different locations, we conduct a simulation experiment and construct a signal-to-noise ratio matrix (SNRM) to adjust the SNR of noise and signal slices, which is used to simulate electromagnetic signal data with multiple SNRs in complex environments. We then verify the adaptability of S-DnCNN for complex SNR data using this multi-random matrix, which is capable of simulating more SNR conditions, to verify the robustness of the trained CNN model to different SNRs. The comprehensive simulation data test and real data test results show that compared with traditional methods, the S-DnCNN method proposed in this paper can recover clean EM signal data by extracting noise features in the video signal, thus improving the signal-to-noise ratio, achieving the reproduction of useful information in the video signal while suppressing random uncertain noise in the EM signal data more effectively, and recovering EM signal data better in terms of details.

2 Network architecture and denoing emthodology

2.1 Network structure

DnCNN is a high-performance noise-canceling neural network that has been successfully applied to the problem of Gaussian white noise suppression in images. Compared with classical neural networks such as LeNet [22], AlexNet [23], and GoogleNet [24], DnCNN introduces residual learning and Batch Normalization(BN) to adjust the optimal mapping relationship between noisy data and denoised data more accurately and faster. The first layer contains a Convolutional Layer(Conv) with ReLU as the activation function, and its main function is to generate feature mappings. The middle layer consists of Conv, BN, and ReLU connected sequentially, and its main function is to extract low-dimensional features from the data by continuous convolution operations and then assemble high-dimensional features. The last layer contains only one Conv whose main function is to reconstruct the output.

Since DnCNN network structures are mostly used in image processing, two-dimensional convolutional kernels are usually used for feature extraction. However, electromagnetic leakage signals received by digital signal acquisition devices are one-dimensional forms of digital sequences. To adapt to the characteristics of one-dimensional electromagnetic leaky signals, we developed a new model.

We designed a CNN structure suitable for denoising electromagnetic information leakage signals, named S-DnCNN, through a large number of experimental comparison tests in the early stage. To adapt to the characteristics of one-dimensional electromagnetic leaky signals, we applied a one-dimensional convolutional kernel and added a local attention mechanism to the structure of DnCNN by constructing a one-dimensional selective convolutional kernel (SKConv1d) and fusing it with SKConv.We added a Leaky ReLU activation function between the first layer and the middle layer, and S- DnCNN adopts Leaky ReLU as the activation function of CNN to improve the recovery ability of the trained network denoising model for weak effective signals.

Considering the comprehensive computational speed and performance, S-DnCNN intermediate layer in this paper performs a total of 15 low-dimensional feature extractions, and S-DnCNN structure is shown in Fig. 1.

Fig. 1

S-DnCNN structure diagram.

The following describes the computational process and the role of each layer of S-DnCNN.

1) Conv1D

We used a one-dimensional convolution kernel to extract the information features in electromagnetic signals. The one-dimensional convolution calculation process extracts local features of the input signal in an orderly manner with a certain step size by sliding the window of the convolution filter. The three parts of convolutional layers are set with corresponding dimensions as shown in Table 1. The first part generates feature mapping, the second part extracts low-dimensional features, and the third part reconstructs the output.

Table 1

S-DnCNN structure parameter

Neural network levels	Input channel	Convolution kernel/filter	Calculate step size	Padding	Output channel
Conv1d-1	1	25	1	12	32
Conv1d-2	32	25	1	12	32
Conv1d-3	32	25	1	12	1

The convolution is calculated as follows: $\begin{matrix} X^{(L + 1)} = X^{(L)} \otimes W^{(L)} + B^{(L)}, \end{matrix}$ (1)

2) Leaky ReLU

S-DnCNN chooses Leaky ReLU as the activation function, which is an improved activation function based on ReLU. Compared to ReLU, Leaky ReLU overcomes the “dead ReLU problem” [25]. Leaky ReLU retains some of the negative term components, which is helpful to improve the recovery of weak effective signals by the model after training.

Leaky ReLU is computed as follows: $\begin{matrix} g (x) = max (0, x) + ξ \times min (0, x), \end{matrix}$ (2) where ξ denotes a constant and is taken as 0.02 in this paper.

3) BatchNorm1d

In the second part of S-DnCNN to extract low-dimensional features, this paper uses a one-dimensional batch normalization (BN) layer between Conv and ReLU. Using the BN method to normalize the data after the convolution operation can alleviate overfitting to a certain extent, speed up the training and convergence of the network, control the gradient explosion to prevent gradient disappearance, and improve the training accuracy.

The BN algorithm is as follows:

1) Calculate the mean value of the output data of the previous layer $\begin{matrix} μ_{β} = \frac{1}{m} \sum_{i = 1}^{m} (x_{i}), \end{matrix}$ (3)

Calculate the standard deviation of the output data of the previous layer $\begin{matrix} σ_{β}^{2} = \frac{1}{m} \sum_{i = 1}^{m} (x_{i} - μ_{β}), \end{matrix}$ (4)

2) Normalized calculation $\begin{matrix} \hat{x_{i}} = \frac{x_{i} + μ_{β}}{\sqrt{σ_{β}^{2}} + ɛ}, \end{matrix}$ (5)

3) Reconstructing the normalized data $\begin{matrix} y_{i} = γ \hat{x_{i}} + β, \end{matrix}$ (6)

In Equations (3) to (6): x is the output of the previous layer; m is the size of the training sample batch; ɛ is a very small value close to 0, which can avoid the case that the denominator is 0; β and ɛ are learning parameters.

4) SKConv1d

We constructed a one-dimensional selective convolution kernel SKConv1d based on the SK unit [21]. Different convolution kernels are used to extract features in the form of grouped convolution operations and null convolution, which are then fused by a softmax composed of different information guided by each branch. The convolution of different branches is one-dimensional and the activation function is Leaky ReLU.

This is a dynamic selection mechanism for the convolutional kernel in the CNN, which invokes the convolutional attention mechanism that allows each neuron to adaptively adjust the size of its receptive field (convolutional kernel) according to the multi-scale of the input information. Specifically, a building block called a one-dimensional selective kernel unit (SK) is designed in which multiple branches with different kernel sizes are fused using SoftMax, guided by the information in these branches. The addition of a mesh containing the SKConv1d module allows for better extraction of detailed features.

This unit is mainly divided into three operations: Split, Fuse, and Select. The Split operator generates multiple paths with different kernel sizes, and this paper uses a convolutional kernel branch containing three different sizes where the convolutional kernel sizes are 3, 5, and 7 to meet the accuracy and speed requirements. The Fuse operator combines and aggregates information from multiple paths to obtain a global and integrated representation for the selection weights. The Select operator aggregates the feature maps of different kernel sizes according to the selection weights. The structure is schematically shown in Fig. 2.

Fig. 2

SKConv1d channel attention module.

The specific steps are as follows:

Split. For any input feature mapping X ∈ R^H×W×C, first convolution operations are performed on the input feature mapping 3 × 3, and 5 × 5 and 7 × 7, respectively, to obtain $\tilde{F} : X \to \tilde{U} \in R^{H \times W \times C}$ , and $\hat{F} : X \to \hat{U} \in R^{H \times W \times C}$ and $\overset{⃛}{F} : X \to \overset{⃛}{U} \in R^{H \times W \times C}$ .

Fuse.The neural network is controlled at the gate level by flowing information from multiple branches and passing these convolutional layers carrying different scales of information to the next layer of the network. First, the $\tilde{U}$ , $\hat{U}$ and $\overset{⃛}{U}$ obtained in the decomposition step are intelligently summed

by the elements to obtain: $\begin{matrix} U = \tilde{U} + \hat{U} + \overset{⃛}{U}, \end{matrix}$ (7)

After obtaining the convolution layer U, s_c is then obtained using the global average pooling operation: $\begin{matrix} s_{c} = F_{gp} (U_{c}) = \frac{1}{H \times W} \sum_{i = 1}^{H} \sum_{j = 1}^{W} U_{c} (i, j), \end{matrix}$ (8)

The global average pooling layer can count the information carried by each channel of the convolutional layer, and then the s_c features are output to the fully connected layer to obtain z. The purpose of reducing the feature dimension and improving the network efficiency is achieved, then z is: $\begin{matrix} z = F_{fc} (s) = δ (β (W_{s})), \end{matrix}$ (9) where: δ with leaky modified linear unit (Leaky ReLU) activation function; β is the BN layer; W_s ∈ R^d×c, $d = max (\frac{C}{r}, L)$ , r is the reduction ratio,L is the minimum value of d.

Select. After the Fuse fusion operation, different spatial scale weight information can be obtained adaptively, then the softmax function for z can obtain α, β, and γ weight channel feature layers, respectively: $\begin{matrix} {\begin{matrix} α = \frac{e^{A_{c} z}}{e^{A_{c} z} + e^{B_{c} z} + e^{C_{c} z}} \\ β = \frac{e^{B_{c} z}}{e^{A_{c} z} + e^{B_{c} z} + e^{C_{c} z}} \\ γ = \frac{e^{C_{c} z}}{e^{A_{c} z} + e^{B_{c} z} + e^{C_{c} z}} \end{matrix}, \end{matrix}$ (10) where A, B ∈ R^c×d; α, β and γ are the soft attention mechanisms $\tilde{U}$ , $\hat{U}$ , and $\overset{⃛}{U}$ , respectively. Then, the output final feature mapping V yields the individual convolutional kernel attention weights, denoted as: $\begin{matrix} V_{c} = α_{c} {\tilde{U}}_{c} + β_{c} {\hat{U}}_{c} + γ_{c} {\overset{⃛}{U}}_{c}; α_{c} + β_{c} + γ_{c} = 1, \end{matrix}$ (11) where V = [V₁, V₂, …, V_c], V_c ∈ R^(H×W).

The parameters of the SK structure designed in this paper are shown in Table 2.

Table 2

SKConv1d structure parameter

Input channel	Calculate step size	Number of branches	Convolution kernel/filter	Length of feature Z	Lower bound of feature Z	Grouped convolution/groups	Output channel
32	1	3	3	16	32	32	32

To show the variability between SKC and normal networks, we also show the performance of our model in Fig. 3:

Fig. 3

Performance of SKConv1d.

In the Fig. 3, “With SKConv Network” is the S-DnCNN network with SKConv module, and “Normal Network” is the normal DnCNN network. Through experiments, we demonstrate that by integrating SKConv into the DnCNN network (as in Fig. 2), we can use its feature of adaptively adjusting the perceptual field size to build multidimensional feature mapping for feature extraction. In terms of details, this can better reproduce the details and features of the image while completing the noise suppression.

2.2 Denoising methodology

The noisy electromagnetic leakage signal can be considered as a linear superposition of the effective signal and the noise: $\begin{matrix} y = e + n, \end{matrix}$ (12) where y, e, and n denote the noisy electromagnetic leakage signal, the pure electromagnetic signal, and the noise, respectively.

We use the residual learning strategy to adjust the optimal mapping relationship between noisy data and noise using S-DnCNN, and the specific process is shown in equation (13): $\begin{matrix} RES (y; θ) = \hat{n} \approx n = y - x, \end{matrix}$ (13) where RES represents the residual learning; θ represents the network parameters, mainly including weights and biases; and n is the noise predicted by S-DnCNN. To make n and $\hat{n}$ infinitely close, we use the MSE denoising loss function in Equation (14) to optimize the network parameters θ. $\begin{matrix} L (θ) = \sum_{i = 1}^{N} | | RES (y_{i}, θ) - n_{i} | |_{F}^{2}, \end{matrix}$ (14) where y_i and e_i denote the noisy feature slices and pure signal label slices, respectively, in the training set denotes the Frobenius parametric number.

3 Structure of the paper

According to the proposed electromagnetic leakage information denoising method, the electromagnetic leakage information denoising experiment of computer cable is divided into two parts: SNRM-based simulation multiple signal-to-noise ratio denoising experiment and electromagnetic leakage real measurement data denoising experiment. Each part of the experiment includes data acquisition, data preprocessing, model training, model validation, and performance comparison.

This paper evaluates the denoising performance of different methods using the signal-to-noise ratio (SNR) and the root mean square error (RMSE), which are defined by Equations (15) and (16). A higher SNR indicates more effective noise rejection, while a smaller RMSE indicates higher signal retention accuracy. $\begin{matrix} SNR = 10 \log_{10} [\frac{\sum_{n = 1}^{N} x {(n)}^{2}}{\sum_{n = 1}^{N} [x (n) - d (n)]^{2}}], \end{matrix}$ (15) $\begin{matrix} RMSE = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} [d (n) - x (n)]^{2}}, \end{matrix}$ (16) where x (n) and d (n) are the pure and denoised data sets, respectively, and N is the number of sample points.

Since S-DnCNN is a supervised deep learning method, it requires a large amount of training data to optimize the network parameters. In this paper, we adopt the small batch gradient descent method with a batch size of 64, a learning rate of 0.00001, and 400 training epochs to train the network. In each iteration, only part of the noisy feature slices and pure signal label slices are used to compute the gradient, and local gradients are used instead of global gradients, which can improve the computational efficiency and reduce the complexity of the network during training. Finally, we use the trained S-DnCNN to predict noise in noisy EM signal data, and then obtain denoised data sets by subtraction.

3.1 Signal to noise ratio matrix (SNRM)-based method for simulation denoising experimental results and analysis

The diversity and adequacy of the training dataset directly determine the performance of supervised deep learning methods. The training dataset of S-DnCNN in multi-signal-to-noise ratio simulation measurements mainly includes signal dataset and noise-banded dataset, which are related to the effective signal recovery ability and noise suppression ability of the trained CNN model.

Since there is currently no training dataset suitable for EM signal data under complex SNR, and it is difficult to collect EM signals with complex SNR in real measurements in different environments, we constructed multiple SNR test datasets based on the signal-to-noise ratio matrix (SNRM). The steps are as follows:

Step 1: Electromagnetic signal sample set. The sample data were collected from a PHILIPS HWE9220F LCD monitor with a resolution and refresh rate of 1024 x 768@60 Hz. Electromagnetic radiation leakage signals from two images of a cat and an airplane were collected at a sampling rate of 250M S/s (i.e., 250M samples/s, 250M samples per second). Three samples were collected for each of the two states.

Step 2: Due to the relatively large individual data and small sample size at the sampling rate of 250MS/s, it is easy to cauze network overload and insufficient training data. Therefore, we downsampled it to 1MS/s (i.e., 1M samples/s, 1M samples per second). From these pure data sets, each with a sliding length of 2000, we captured 15000 signal patches of length 2000. These signal patches together form the signal dataset of S-DnCNN.

Step 3: To construct the signal dataset with multiple SNRs, we constructed a signal-to-noise ratio matrix (SNRM) before feeding the data into the network for training. Since the batch size was set to 64 in the experiments designed in this paper, we set the size of this matrix to 4000*64, and the elements in the matrix are random floating point numbers between –0.01 –10. Each batch of the network is constructed by adding Gaussian noise to the SNRM, where the size of a random row is the “noisy feature data set”.

During each iteration, we randomly select 64 effective signal slices {x₁, x₂, x₃, …… , x₆₄ }, 64 noise slices {n₁, n₁₂, n₃, …… , n₆₄ }, and take a random row in SNRM {r₁, r₂, r₃, …… , r₆₄ }, {d₁, d₂, d₃, …… , d₆₄ } as the feature data set of S-DnCNN. Here, d_i is added by Gaussian noise to the signal-to-noise ratio magnitude of r_i. The feature data set of S-DnCNN consists of {x₁, x₂, x₃, …… , x₆₄ }. Figure 3.1.1 shows the time domain images of the noisy data and the original data under different signal-to-noise ratios, and Fig. 3.1.2 shows the reproduced images of the noisy data and the original data under different signal-to-noise ratios.

Fig. 3.1.1

Time domain images of the noisy data and the original data at multiple signal-to-noise ratios.

Fig. 3.1.2

Reproduced images of noisy data and original data under multiple signal-to-noise ratio.

In this part of the experiment, pure data obtained from a digital signal acquisition device is used as the label and synthesized noisy data is used as the feature data, which we use as the data set for the simulation experiment. We randomly divide the data set into three parts as 8 : 1:1 for training data set, validation data set, and test data set, respectively. The training set is used for training samples, mainly to train the parameters in the neural network. The validation set is used to verify the performance of the model. After training different neural networks on the training set, we use the validation set to compare the performance of each model. Finally, we use the test set to objectively evaluate the performance of the neural network.

To verify the performance of Leaky ReLU in denoising electromagnetic leakage signal data, we call the network with ReLU activation function replaced by Leaky ReLU DnCNNS.

The SNR and RMSE of the denoising results of the five methods are shown in Table 3 for DnCNN, DnCNNS, S-DnCNN, BRDNet [26] and wavelet threshold denoising in the simulation experiments.The comparison results are shown in Fig. 3.1.3(a), (b), where the SNR and RMSE in the initial state are –5.06 dB and 23.06, respectively.

Fig. 3.1.3

Comparison chart of the simulation experiment algorithms.

Table 3

Comparison of three methods for simulation data denoising performance

Method	DnCNN	DnCNNS	S-DnCNN	BRDNet	Wavelet
SNR(dB)	10.38	10.48	11.02	5.72	0.36
RMSE	3.87	3.85	3.57	6.47	12.70

3.2 Experimental results and analysis of the noise reduction of the electromagnetic leakage data

We collected two-channel electromagnetic leakage data from measured signals using digital signal acquisition equipment. Channel 0 was used to capture the noisy electromagnetic signals, which serve as features, with a caliper. Meanwhile, channel 1 was used with a probe to capture the pure electromagnetic signal labels. Both channels provided data sets of 5,000,000 data points each, sampled at a rate of 250 million samples per second (250M S/s). These measurements were taken from a display operating at a resolution of 1024 x 768 pixels and a refresh rate of 60 Hz. The data included both textual and visual content, with the visual content coming from the publicly available CIFAR-10 dataset. We used a data slicing approach to segment the data into 5,000 individual sets of features and labels. This segmentation was achieved by sliding a window of 20,000 data points over the original data. It’s important to note that apart from the data set used, the structural parameters of the neural network remained consistent between the real measurement experiment and the simulation experiment.

The unwanted electromagnetic emission signals in the experiment were collected in a normal indoor environment without any shielding measures. Figure 3.2 shows the experimental setup consisting of a signal detector and a signal receiver. The signal detector consists of a TEMPEST current monitoring probe and a caliper type electromagnetic signal probe that captures the electromagnetic radiation emitted from the VGA cable on the monitor. The signal receiver is used to sample and store the signals emitted from the monitor.

Fig. 3.2

Experimental device.

The SNR and RMSE of the denoising results of the five methods for DnCNN, DnCNNS, S-DnCNN, BRDNet and Wavelet in the experiments of the measured data are shown in Table 4, and the comparison results are shown in Fig. 3.2.3(a), (b), where the SNR and RMSE of the initial state are –0.4dB and 5.26, respectively.

Table 4

Comparison of three methods for denoising performance of measured data

Method	DnCNN	DnCNNS	S-DnCNN	BRDNet	Wavelet
SNR(dB)	5.85	5.91	6.53	2.17	–0.07
RMSE	2.38	2.34	2.24	3.78	4.99

Signal-to-Noise Ratio (SNR): The Signal-to-Noise Ratio (SNR) serves as a critical performance metric that quantifies the relative strength difference between the denoised signal and the underlying noise. In our experiment, the SNR of S-DnCNN is 6.53 decibels (dB), a significant improvement over other methods such as DnCNN and DnCNNS, which have SNRs of 5.85 dB and 5.91 dB, respectively. This discrepancy underscores S-DnCNN’s superior ability to effectively extract the desired signal and more efficiently suppress noise during the denoising process.

Root Mean Square Error (RMSE): The Root Mean Square Error (RMSE) measures the root mean square difference between the denoised signal and the original signal. S-DnCNN has an RMSE of 2.24, significantly lower than alternative methods. For example, the BRDNet and Wavelet denoising methods yield RMSEs of 3.78 and 4.99, respectively. This discrepancy underscores S-DnCNN’s ability to maintain signal accuracy.

Fig. 3.2.1

Reproductions of measured noisy data and original data.

Fig. 3.2.2

Denoising results of measured data.

Effectiveness of Leaky ReLU: Experimental results highlight the positive impact of using Leaky ReLU as the activation function within the S-DnCNN model. This choice helps to preserve negative components more effectively, which subsequently improves the model’s ability to recover weak signals. The performance of DnCNNS further supports this observation.

Impact of the One-Dimensional Selective Convolutional Kernel (SKConv1d): S-DnCNN introduces a one-dimensional selective convolutional kernel, which plays an important role in the feature extraction of the model.By comparing the performance metrics of S-DnCNN (with the addition of SKConv1d on the DnCNNS) with the DnCNN and by observing the synchronized signals in the denoised image on the synchronized signals, we can observe that it helps to capture the detailed features in a better way, and improves the noise reduction effect of the model.

Overall, S-DnCNN demonstrates outstanding performance in addressing one-dimensional signal noise reduction challenges, with higher signal-to-noise ratio, reduced root mean square error, and improved signal retention accuracy. These results underscore the effectiveness of S-DnCNN, particularly in addressing noise reduction scenarios characterized by low signal-to-noise ratios, such as those encountered in cases of electromagnetic signal leakage

Although our S-DnCNN algorithm has shown good performance in some experiments, we would like to acknowledge that there are still some limitations and challenges in certain aspects. The main limitations include the fact that our algorithm relies on training data, and there are no large-scale training datasets of electromagnetic signal data suitable for complex signal-to-noise ratio conditions, so our denoising algorithm performs well in processing textual image data, but it has not yet reached the desired level in denoising visual image data. This may impose some limitations on the performance and adaptability of the algorithm. Our algorithms may not be ideal for handling complex real-world replicated data. These data may have more noise and variation, and more research is needed to further improve the performance of the algorithm.

Specifically, our text denoising results are as follows:

The waveforms and replication plots of the original data and the measured noisy data under DnCNN, DnCNNS, and S-DnCNN real data are shown in Fig. 3.2.1(a), (b), and the denoising results are shown in Fig, 3.2.2(a), (b), (c), respectively.

Fig. 3.2.3

Comparison chart of real experimental algorithms.

It is clear from the labels in the figure that the S-DnCNN algorithm can better preserve the details and features of the reproduced images and achieve noise reduction.

Our denoising algorithm shows strong performance on retext images, as shown in the denoised images, which clearly demonstrate our algorithm’s enhanced ability to preserve and recover fine textual detail. This results in a much clearer and more recognizable output. Despite the significant progress we have made in this area, we readily acknowledge that there are opportunities for further improvement. As a result, we remain committed to refining the performance of our text image denoising algorithms to better meet the needs and expectations of our user base.

4 Conclusion

To deal with the one-dimensional electromagnetic signal leakage problem, we design a S-DnCNN model structure with a one-dimensional convolutional kernel, which is specifically used to deal with electromagnetic radiation leakage due to interconnecting cables in a computer system, and introduce an attention mechanism so that the network is able to adaptively adjust the sensory field according to the multi-scale of the input signals, and thus better extract the detailed signal features in complex noise environments. Compared with the traditional ReLU, the leaky ReLU is used as the activation function in this paper, which helps to recover information from weak effective signals and improves the model’s ability to handle low signal-to-noise ratio situations. The experimental results show that S-DnCNN not only exhibits superior noise reduction capability in simulated environments, but also successfully handles complex electromagnetic signal leakage scenarios in real environments. This comprehensive performance validates the practicality and robustness of the model, and provides a powerful tool and method for the field of information security.

Footnotes

Acknowledgments

The authors would like to acknowledge the financial support of the Fujian Provincial Natural Science Foundation under project number 2021J01858, 2023J01800 and Xiamen Science and Technology Subsidy Project under project number 2023CXY0318. We also thank the individuals who have provided assistance in the course of this research.

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