CN114726966A - Electromagnetic signal noise reduction method based on anisotropic total variation - Google Patents

Abstract

The invention provides an electromagnetic signal noise reduction method based on anisotropic total variation, and relates to the technical field of signal processing. The electromagnetic signal noise reduction method based on the anisotropy total variation comprises the following processes: s1, information leakage of electromagnetic signals on a video signal reconstruction computer display can occur in a conduction mode through a video cable, the leaked electromagnetic signals are collectively called video signals, when the video signals are transmitted on a VGA cable, actual video signals are composed of RGB signals, line synchronization signals and field synchronization signals, and guidance of the line synchronization signals and the field synchronization signals can be achieved. By using various ATV algorithms under the frame of ADMM, the gradient characteristics of noise in the video signal are analyzed, an ATV-based noise reduction model is established and applied to the noise reduction of the video signal.

Description

Electromagnetic signal noise reduction method based on anisotropic total variation

technical field

The invention relates to the technical field of signal processing, in particular to an electromagnetic signal noise reduction method based on anisotropic total variation.

Background technique

Electronic devices such as computers inadvertently leak electromagnetic signals with information while they are working. After the leaked electromagnetic signal is intercepted, the information in the electromagnetic leakage signal is restored through the information reconstruction technology in the TEMPEST technology, which poses a threat to information security. In the actual electromagnetic environment, the leaked electromagnetic signal will not only be disturbed by the noise in the environment, but also be disturbed by the electromagnetic waves radiated by other electronic devices or within itself. When the leaked electromagnetic signal is interfered by a large amount of noise, the useful information will be covered by the noise. In order to restore and reconstruct the information in the electromagnetic leaked signal, it is very important to remove the interference of the noise.

The leakage methods of electromagnetic signals include radiation leakage and conduction leakage. The video information on the computer monitor can leak through the video cable. The cables used to transmit video signals on the computer include VGA (Video GraphicsArray) cables, DVI (Digital Visual Interface) cables and HDMI (High Definition MultimediaInterface) cables, VGA cables transmit model signals, and DVI cables and HDMI cables transmit digital signals.

Video signal noise reduction is an important technology for signal preprocessing. The classic signal noise reduction methods include median filter noise reduction and wavelet noise reduction. Both of these two noise reduction methods have their own shortcomings. The deviation of threshold selection in wavelet noise reduction may be It will lead to pseudo-Gibbs phenomenon, etc., thus affecting the reconstruction and reproduction of the video signal, and cannot be applied to various and random noise interference.

In recent years, the technology based on total variation energy functional has achieved good results in image denoising. The application of total variation in video signal noise reduction can fully consider the structural characteristics of noise and improve the effect of noise reduction. The noise reduction method based on Anisotropic Total-Variation (ATV) is adopted, and the Alternating Direction Method of Multipliers (ADMM) is used for the noise in the video signal. Gradient feature, iteratively reduces the noise in the video signal, improves the signal-to-noise ratio, and realizes the reproduction of useful information in the video signal.

SUMMARY OF THE INVENTION

(1) Technical problems solved

In view of the deficiencies of the prior art, the present invention provides an electromagnetic signal noise reduction method based on anisotropic total variation, and solves the problem that the classical signal noise reduction methods include median filter noise reduction and wavelet noise reduction. Each has its own shortcomings. The deviation of threshold selection in wavelet noise reduction may lead to pseudo-Gibbs phenomenon, which affects the reconstruction and reproduction of video signals, and cannot be applied to various and random noise interference problems.

(2) Technical solutions

In order to achieve the above purpose, the present invention is achieved through the following technical solutions: an electromagnetic signal noise reduction method based on anisotropic total variation, comprising the following processes:

S1. Video signal reconstruction

The electromagnetic signal on the computer monitor can leak information in the form of conduction through the video cable. The leaked electromagnetic signal is collectively called the video signal. When the video signal is transmitted on the VGA cable, the actual video signal is composed of RGB signals, line It is composed of synchronization signal and field synchronization signal, and can reproduce the image information of the computer display through the guidance of the line and field synchronization signals. The RGB signal is modulated and generated by the pixel clock signal. When only black and white pixels are displayed on the display, the three RGB channels are is the same value;

S2. Video signal noise reduction

In order to simulate the noise interference from the environment and electronic equipment, Gaussian white noise SNR with different signal-to-noise ratios is added to the collected video signal samples. The SNR value refers to the ratio of useful signal power to noise power, and its calculation formula is:

In the formula: x(i) is the original signal;

为降噪后的信号；

is the signal after noise reduction;

N is the signal length, in decibels (dB), and the larger the signal-to-noise ratio, the better the noise reduction effect.

S3. Use anisotropic total variation algorithm to reduce noise and restore the original signal

For the two-dimensional video signal, the anisotropic total variation algorithm is used to analyze the gradient characteristics of the video signal and reduce the noise in the video signal. The noise reduction of the video signal and the restoration of the original signal are essentially an inverse problem solving process. The noise reduction model of the anisotropic total variation algorithm is modeled as follows:

where: F represents the electromagnetic signal recovered by the noise reduction model;

为保真项，使得估计出的原始信号与降噪信号在内容上保持一致；

is the fidelity term, so that the estimated original signal and the noise reduction signal are consistent in content;

G represents electromagnetic signal with noise;

R _ATV (F) is a regular term, representing the original characteristics of the signal;

μ is the balance coefficient between the fidelity term and the regular term;

||·|| ₂ represents the L ₂ norm.

In the above formula, the calculation formula of the regular term R _ATV (F) is:

R _ATV (F)=||K _h *F|| ₁ +||K _v *F|| ₁

where ||K _h *F|| ₁ and ||K _v *F|| ₁ represent the horizontal and vertical differences, respectively;

||·|| ₁ means L ₁ norm;

The symbol * indicates convolution calculation.

Preferably, the field frequency in the step S1 is f _v , the horizontal frequency is f _h , the horizontal frequency and the vertical frequency are the frequency of the horizontal synchronization signal and the frequency of the vertical synchronization signal respectively, and the horizontal frequency refers to the frequency of a row of pixels on the display screen. Refresh frequency, field frequency refers to the update frequency of a frame of image on the display screen, line frequency and field frequency signals can be regarded as periodic square waves in the time domain, and the relationship between field frequency, line frequency and pixel clock frequency can be converted into the following formula:

f _h = f _v ×y

f _p = f _h ×x

Where: f _p is the pixel clock frequency;

y is the number of rows of pixels in a frame of image;

x is the number of pixels in a row.

According to the above formula, the calculation formula of the pixel clock period is:

f _p =x×y×f _v .

Preferably, in the process of noise reduction of the video signal in the step S2, since the blanking area in the leaked video signal will be affected by the electromagnetic environment and the electromagnetic signal acquisition device, the reproduced image information will be skewed and distorted By using the data fine-tuning method, the number of pixels in the column is fine-tuned, so as to correct the inclination of the reproduced image by the video signal and improve the quality of the reproduced image.

Preferably, the anisotropic total variation algorithm noise reduction model proposed in step S3 is a non-smooth convex optimization problem, which can solve the model under the framework of ADMM, and the ADMM algorithm can theoretically guarantee the model's Convergence.

Preferably, the ADMM is an algorithm that combines the decomposability of the dual ascent method with the excellent convergence of the multiplier method, which is suitable for distributed convex optimization and is widely used in various sparse regular term constraints.

Preferably, it includes two parts: signal reconstruction and signal noise reduction. The signal reconstruction is aimed at the VGA video cable, and the one-dimensional electromagnetic signal is reconstructed into a two-dimensional visual video signal according to the information characteristics of the leakage source. The method of anisotropic total variation, after many iterations, reduces the noise in the video signal and improves the quality of the video signal reconstruction.

Preferably, the electromagnetic leakage information collection equipment used in the signal reconstruction process includes NI PXIe-5162 high-speed collector and A.H.Systems BCP-620 caliper, and the model of the collected equipment is a DELL OptiPLex3240 display.

Preferably, the signal reconstruction process uses calipers to collect the video signal leaked by the display from the VGA video cable, the video mode of the display is 640×480@60Hz, the sampling rate is 1M/s, the sampling depth is 5000000, The video leakage signal is used for image reproduction and noise reduction. To ensure the diversity of data, black and white text images and physical images are displayed on the display.

(3) Beneficial effects

The invention provides an electromagnetic signal noise reduction method based on anisotropic total variation. Has the following beneficial effects:

1. The present invention provides an electromagnetic signal noise reduction method based on anisotropic total variation. By using various ATV algorithms under the framework of ADMM, the gradient characteristics of noise in the video signal are analyzed, and an ATV-based noise reduction model is established, And applied to video signal noise reduction, this method can efficiently deal with the video leakage signal disturbed by noise, improve the signal-to-noise ratio of the signal, while suppressing the noise, maintain the details and characteristics of the reproduced image, and accurately restore the leaked information.

2. The present invention provides an electromagnetic signal noise reduction method based on anisotropic total variation. By weighting the first-order gradients of the signals in different directions, and fully mining the structure of noise in the signal, the noise can be suppressed while retaining The information features in the electromagnetic signal. In addition, the alternating direction multiplier method framework is used to speed up the solution speed of the model. Compared with the currently commonly used electromagnetic signal noise reduction methods, this method can effectively reduce the noise in the signal and restore it better. The information in the electromagnetic signal has a better noise reduction effect on the signal.

Description of drawings

Fig. 1 is the schematic diagram of field frequency and horizontal frequency signal of the present invention;

Fig. 2 is the modulation principle schematic diagram of the RGB signal of the present invention;

3 is a schematic diagram of the processing flow of the anisotropic total variation noise reduction model of the present invention;

Fig. 4 is the physical image schematic diagram of the present invention;

5 is a schematic diagram of a video signal reproduction image of the present invention;

6 is a schematic diagram of a reproduced image after median filtering and noise reduction of the present invention;

7 is a schematic diagram of a reproduced image after wavelet noise reduction of the present invention;

FIG. 8 is a schematic diagram of a reproduced image after anisotropic total variational noise reduction of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Example 1:

As shown in Figures 1-8, an embodiment of the present invention provides an electromagnetic signal noise reduction method based on anisotropic total variation, including the following processes:

S1. Video signal reconstruction

The electromagnetic signal on the computer monitor can leak information in the form of conduction through the video cable. The leaked electromagnetic signal is collectively called the video signal. When the video signal is transmitted on the VGA cable, the actual video signal is composed of RGB signals, line It is composed of synchronization signal and field synchronization signal, and can reproduce the image information of the computer display through the guidance of the line and field synchronization signals. The RGB signal is modulated and generated by the pixel clock signal. When only black and white pixels are displayed on the display, the three RGB channels are is the same value;

S2. Video signal noise reduction

In order to simulate the noise interference from the environment and electronic equipment, Gaussian white noise SNR with different signal-to-noise ratios is added to the collected video signal samples. The SNR value refers to the ratio of useful signal power to noise power, and its calculation formula is:

In the formula: x(i) is the original signal;

为降噪后的信号；

is the signal after noise reduction;

N is the signal length in decibels (dB), and the larger the signal-to-noise ratio, the better the noise reduction effect.

S3. Use anisotropic total variation algorithm to reduce noise and restore the original signal

For the two-dimensional video signal, the anisotropic total variation algorithm is used to analyze the gradient characteristics of the video signal and reduce the noise in the video signal. The noise reduction of the video signal and the restoration of the original signal are essentially an inverse problem solving process. The noise reduction model of the anisotropic total variation algorithm is modeled as follows:

where: F represents the electromagnetic signal recovered by the noise reduction model;

为保真项，使得估计出的原始信号与降噪信号在内容上保持一致；

is the fidelity term, so that the estimated original signal and the noise reduction signal are consistent in content;

G represents electromagnetic signal with noise;

R _ATV (F) is a regular term, representing the original characteristics of the signal;

μ is the balance coefficient between the fidelity term and the regular term;

||·|| ₂ represents the L ₂ norm.

In the above formula, the calculation formula of the regular term R _ATV (F) is:

R _ATV (F)=||K _h *F|| ₁ +||K _v *F|| ₁

where ||K _h *F|| ₁ and ||K _v *F|| ₁ represent the horizontal and vertical differences, respectively;

||·|| ₁ means L ₁ norm;

The symbol * indicates convolution calculation.

The field frequency in step S1 is f _v , the line frequency is f _h , the line frequency and the field frequency are the frequency of the line synchronization signal and the frequency of the field synchronization signal respectively, the line frequency refers to the refresh frequency of a line of pixels on the display screen, and the field frequency Refers to the update frequency of a frame of image on the display screen. The line frequency and field frequency signals can be regarded as periodic square waves in the time domain, and the relationship between the field frequency, the line frequency and the pixel clock frequency can be converted into the following formula:

f _h = f _v ×y

f _p = f _h ×x

Where: f _p is the pixel clock frequency;

y is the number of rows of pixels in a frame of image;

x is the number of pixels in a row.

According to the above formula, the calculation formula of the pixel clock period is:

f _p =x×y×f _v .

In the process of noise reduction of the video signal in step S2, since the blanking area in the leaked video signal will be affected by the electromagnetic environment and the electromagnetic signal acquisition device, the reproduced image information will be tilted and distorted. The data fine-tuning method is used to fine-tune the number of pixels in the column, so as to correct the inclination of the reproduced image by the video signal and improve the quality of the reproduced image.

The noise reduction model of the anisotropic total variation algorithm proposed in step S3 is a non-smooth convex optimization problem, which can be solved under the framework of ADMM, and the ADMM algorithm can theoretically guarantee the convergence of the model.

Example 2:

Suppose a convex optimization problem:

minφ ₁ (u)+φ ₂ (v), stAu+Bv=b

where: φ ₁ (u) and φ ₂ (v) are both convex functions.

Its corresponding scaling format augmented Lagrangian function is:

where λ is the Lagrange multiplier and β is the penalty factor.

Substitute the first formula into the ADMM framework, and map it into the intermediate variables Z ₁ =K _h *F, Z ₂ =K _v *F, Z ₃ =FG, corresponding to Lagrange multipliers Λ ₁ , Λ ₂ , Λ ₃ , the augmented Lagrangian objective function is:

The objective function is divided into multiple sub-problems to solve, the noise reduction model is converted into an iterative optimization problem, and the F sub-problem is solved, the iterative solution can be obtained as:

F ^(k+1) = ifft(RHS./LHS)

In the formula: k represents the number of iterations of the formula, ./ represents the point division operation, and ifft represents the inverse Fourier calculation.

In order to avoid the convolution operation of a large matrix in the time domain, it is converted into a dot product operation in the frequency domain to speed up the efficiency of problem solving.

In the formula: . Represents a dot-multiply operation.

The Z ₁ , Z ₂ , Z ₃ , Λ ₁ , Λ ₂ , and Λ ₃ sub-problems in the formula need to be solved.

For the Z ₁ , Z ₂ , and Z ₃ subproblems, use the soft-threshold contraction method to obtain the iterative formula:

Using the gradient ascent method to solve the Lagrangian multipliers Λ ₁ , Λ ₂ , Λ ₃ subproblems, the update rules are obtained:

Accordingly, the anisotropic total variation algorithm model can be iteratively optimized until the noise in the video signal is removed.

Under different signal-to-noise ratio conditions, the anisotropic total variation noise reduction method is compared with median filter noise reduction and wavelet noise reduction, and the signal-to-noise ratio and image reproduction quality are used as the evaluation indicators of signal noise reduction performance for comparison. experiment.

In the experiment, median filter noise reduction, wavelet noise reduction and ATV noise reduction were performed on the video signal under three different SNRs, respectively, and the SNR after noise reduction was calculated for comparison. The results are shown in Table 1 below.

Table 1 Performance comparison of three noise reduction methods under different signal-to-noise ratios

It can be seen from the above table that the SNR value of the video signal increases after ATV noise reduction. Compared with median filter noise reduction and wavelet noise reduction, ATV noise reduction has a better effect and can effectively reduce the noise in the signal. In terms of efficiency, ATV noise reduction is more efficient. The ATV algorithm runs under the framework of ADMM, and transforms the convolution operation of the matrix in the time domain into the point multiplication operation of the matrix in the frequency domain, effectively reducing the signal noise reduction processing time to every The frame image is 0.2397 seconds, and the efficiency of the other two noise reduction algorithms can be improved by about 5.5 times.

One of the main purposes of electromagnetic signal noise reduction is to accurately restore the leaked information from the intercepted signal. Noise will interfere with the reproduction of the video signal, so the quality of the reproduced image can be used as an evaluation index for the noise reduction effect.

Taking the physical image in Figure 4 as an example, the reproduced image of the leaked video signal is shown in Figure 5. Three kinds of noise reduction algorithms are used to process the video signal, and the noise reduction effect of the eye part of the comparison example is shown in Figures 6 and 6. 7 and Figure 8, from the three images in Figure 6, Figure 7 and Figure 8, it can be seen that the reproduced image after median filter noise reduction and wavelet noise reduction is relatively blurred, and the pixels are in blocks. After anisotropic total variation The reproduced image after noise reduction is finer and clearer, and can better retain the characteristics of the video signal.

Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.

Claims (8)

1. The electromagnetic signal noise reduction method based on the anisotropy total variation is characterized by comprising the following processes:

s1. video signal reconstruction

When the video signal is transmitted on the VGA cable, the actual video signal is composed of RGB signal, line synchronizing signal and field synchronizing signal, and the image information of the computer display can be reproduced through the guidance of the line and field synchronizing signal, the RGB signal is generated by the modulation of pixel clock signal, when only black and white pixels are displayed on the display, the values of RGB three channels are the same;

s2. noise reduction of video signal

In order to simulate noise interference from environment and electronic equipment, Gaussian white noise SNR with different signal-to-noise ratios is added to a collected video signal sample, the SNR value refers to the ratio of useful signal power to noise power, and the calculation formula is as follows:

in the formula: x (i) is the original signal;

is the signal after noise reduction;

n is the signal length in decibels (dB), and a larger signal-to-noise ratio indicates a better noise reduction effect.

S3, noise reduction and original signal recovery are carried out by adopting an anisotropic total variation algorithm

Aiming at a two-dimensional video signal, the gradient characteristics on the video signal are analyzed by adopting an anisotropic total variation algorithm, the noise in the video signal is reduced, the process of solving an inverse problem is essentially carried out on the video signal for reducing noise and recovering an original signal, and a noise reduction model of the anisotropic total variation algorithm can be modeled as follows:

in the formula: f represents the electromagnetic signal recovered by the noise reduction model;

the estimated original signal and the noise reduction signal are consistent in content due to the fidelity term;

g represents a noisy electromagnetic signal;

R_ATV(F) the signal is a regular term and represents the original characteristics of the signal;

mu is a balance coefficient of the fidelity term and the regular term;

||·||₂represents L₂And (4) norm.

In the above formula, the regularization term R_ATV(F) The calculation formula of (2) is as follows:

R_ATV(F)＝||K_h*F||₁+||K_v*F||₁

in the formula: i K_h*F||₁And K_v*F||₁Respectively representing the lateral and longitudinal differences;

||·||₁represents L₁A norm;

symbol denotes the convolution calculation.

2. The method of claim 1, wherein the step of reducing the noise of the electromagnetic signal comprises: the field frequency in step S1 is f_vLine frequency of f_hThe line frequency and the field frequency are respectively the frequency of the line synchronizing signal and the frequency of the field synchronizing signal, and the line frequency refers to the refreshing of one line of pixel points on the screen of the displayThe field frequency refers to the update frequency of a frame of image on the display screen, the line frequency and the field frequency signal can be regarded as periodic square waves in the time domain, and the relationship between the field frequency, the line frequency and the pixel clock frequency can be converted into the following formula:

f_h＝f_v×y

f_p＝f_h×x

in the formula: f. of_pIs the pixel clock frequency;

y is the number of rows of pixels in a frame of image;

x is the number of pixels in a row.

According to the above formula, the calculation formula of the pixel clock period is:

f_p＝x×y×f_v。

3. the method of claim 1, wherein the step of reducing the noise of the electromagnetic signal comprises: in the step S2, in the process of reducing the noise of the video signal, the blanking area in the leaked video signal is affected by the electromagnetic environment and the electromagnetic signal acquisition device, so that the phenomenon of tilt distortion of the reproduced image information occurs, and the number of the column pixels is finely adjusted by using a data fine adjustment method, so that the tilt problem of the reproduced image of the video signal is corrected, and the quality of the reproduced image is improved.

4. The method of claim 1, wherein the step of reducing the noise of the electromagnetic signal comprises: the anisotropic total variation algorithm noise reduction model proposed in the step S3 is a non-smooth convex optimization problem, which can be solved under the frame of the ADMM, and the ADMM algorithm can theoretically ensure the convergence of the model.

5. The method of claim 4, wherein the step of reducing the noise of the electromagnetic signal comprises: the ADMM is an algorithm combining the resolvability of a dual-rising method and the excellent convergence of a multiplier method, is suitable for distributed convex optimization, and is widely applied to various sparse regular term constraint problems.

6. The anisotropic full-variation-based electromagnetic signal noise reduction model of claim 1, wherein: the method comprises two parts of signal reconstruction and signal noise reduction, wherein the signal reconstruction aims at a VGA video cable, a one-dimensional electromagnetic signal is reconstructed into a two-dimensional visible video signal according to the information characteristics of a leakage source, the signal noise reduction adopts an anisotropic total variation method, the noise in the video signal is reduced through multiple iterations, and the quality of the video signal reconstruction is improved.

7. The anisotropic total variation-based electromagnetic signal noise reduction model of claim 6, wherein: the electromagnetic leakage information acquisition equipment adopted in the signal reconstruction process comprises a NIPXIe-5162 high-speed acquisition device and an A.H.systems BCP-620 caliper, and the model of the acquired equipment is a display of DELL OptiPLex 3240.

8. The anisotropic total variation-based electromagnetic signal noise reduction model of claim 6, wherein: in the signal reconstruction process, calipers are used for collecting video signals leaked by a display from a VGA video cable, the video mode of the display is 640 multiplied by 480@60Hz, the sampling rate is 1M/s, the sampling depth is 5000000, the collected video leakage signals are used for image reproduction and noise reduction, and black and white character images and real object images are displayed on the display to ensure the diversity of data.

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