Dual-channel signal denoising method using noise correlation threshold

Abstract

The invention discloses a dual-channel signal denoising method using a noise correlation threshold, and belongs to the technical field of automation. The method comprises the following steps: framing a dual-channel signal, extracting a power spectrum and a cross-power spectrum by using fast Fourier transform, and updating frequency domain feature estimation through a dynamic smoothing coefficient; and deducing an NCT dynamic calculation formula in combination with the coherence function model and theoretical noise power, and generating a frequency adaptive NCT curve through processing. And mapping the frequency domain NCT into a time-frequency domain wavelet threshold parameter, and processing a signal by adopting multi-scale wavelet decomposition and a soft threshold function to realize frequency domain noise feature and time-frequency domain denoising processing closed-loop linkage. According to the method, through the steps of framing processing, frequency domain analysis, NCT calculation, wavelet denoising and the like, local mutation and detail information of signals can be reserved while noise is removed, calculation efficiency is improved, and denoising robustness is enhanced.

Description

Technical Field

[0001] The invention belongs to the technical field of automation and relates to a dual-channel signal denoising method using a noise-related threshold. Background Art

[0002] With the rapid development of industrial monitoring, biomedical engineering, and environmental perception, higher requirements are placed on the accuracy and robustness of signal denoising technology. In the context of complex noise, traditional single-channel denoising methods (such as wavelet thresholding, empirical mode decomposition, etc.) often cause effective component loss or residual noise interference due to the overlap of noise and signal frequency bands, especially in non-stationary noise and low signal-to-noise ratio scenarios.

[0003] Although dual-channel denoising technology can improve noise suppression capabilities through spatial differences, existing methods still have the following problems: (1) Lack of dynamic correlation modeling, that is, existing methods fail to fully consider the correlation between related channel signals and lack dynamic modeling of such correlation. This makes it impossible to effectively utilize the correlation information between channels when processing signals, thus affecting the denoising effect. (2) Threshold setting lacks adaptability, that is, in the process of wavelet denoising, the threshold is usually set with a fixed value or based on experience, but the signal often has non-stationary characteristics. This fixed or empirical threshold setting method cannot be adaptively adjusted according to the real-time changes of the signal, resulting in the difficulty in achieving the optimal denoising effect. (3) Cross-domain methods are used in isolation, that is, traditional frequency domain filtering methods and time-frequency domain decomposition methods are often used in isolation, and the organic combination and coordinated optimization between the two cannot be achieved. This isolated use method limits the comprehensive performance of denoising technology in complex noise environments. (4) Insufficient adaptability and robustness under complex noise, that is, in the face of complex and changeable noise environments, existing methods are difficult to maintain high robustness while dynamically adjusting, and cannot adapt well to changes in noise characteristics, thus affecting the stability and reliability of the denoising effect. Summary of the invention

[0004] In view of the problems of insufficient utilization of frequency domain correlation, poor threshold adaptive ability and lack of cross-domain optimization in existing dual-channel denoising technology, the present invention proposes a dual-channel signal denoising method using noise-correlated thresholds. This method achieves efficient separation of noise and signal through joint optimization of frame processing, frequency domain coherence analysis and time-frequency wavelet decomposition. First, the input dual-channel signal is framed, and the power spectral density (PSD) and cross-power spectral density of each frame are extracted using fast Fourier transform, and the dynamic smoothing coefficient (such as α) is used to calculate the power spectral density (PSD) and cross-power spectral density of each frame. PSD , α coh)Update the frequency-domain feature estimation to effectively suppress the interference of instantaneous noise fluctuations on the statistical characteristics of the signal. On this basis, combining the coherence function model of the dual-channel signal with the theoretical noise power, a dynamic calculation formula for the noise correlation threshold (NCT) is derived. An NCT curve adaptive to frequency is generated through moving average and clipping processing to quantify the statistical differences between signals and noise in different frequency bands. Further, the frequency-domain NCT is mapped to the time-frequency domain wavelet threshold parameter, and the signal is jointly processed in the time-frequency domain using multi-scale wavelet decomposition. The high-frequency coefficients are nonlinearly compressed using the soft threshold function, and the threshold intensity of each scale is dynamically adjusted during the signal reconstruction process. This process realizes the closed-loop linkage between the frequency-domain noise characteristics and time-frequency domain denoising, not only retaining the signal details but also significantly improving the robustness in non-stationary noise environments.

[0005] The steps of the method of the present invention include:

[0006] The present invention provides a dual-channel signal denoising method using a noise correlation threshold, and the specific steps are as follows:

[0007] S1: Frame the dual-channel signal x(t) to be denoised to obtain the single-frame signal x frame (t) of each channel;

[0008] S2: Use the fast Fourier transform to extract the signal of the single-frame signal x frame (t); Based on the extracted signal, recursively smooth and update the auto-power spectral density and cross-power spectral density, and calculate the recursively smoothed coherence function coh_smooth n and the coherence function model coh_model;

[0009] S3: Based on the recursively smoothed coherence function coh_smooth n and the coherence function model coh_model, obtain the dynamic calculation formula for the noise correlation threshold; Generate a frequency-adaptive noise correlation threshold curve through moving average and clipping processing to obtain the noise correlation threshold NCT frame ;

[0010] S4: Perform discrete wavelet transform on the single-frame signals x frame (t) of the two channels respectively to decompose the signal into different scales; Use the noise correlation threshold NCT frame to perform soft thresholding on the wavelet coefficients and nonlinearly compress the high-frequency coefficients; Reconstruct through the inverse discrete wavelet transform and splice to obtain the denoised dual-channel single-frame signal

[0011] S5: Restore the denoised dual-channel single-frame signals frame by frame to obtain the denoised dual-channel signal x de (t).

[0012] Preferably, in step S1, the frame segmentation process adopts different frame lengths and overlapping ratios according to the lengths of the dual-channel signals to be denoised and the processing requirements; specifically as follows:

[0013] S101: Calculate the total number of signal frames according to the length T of the dual-channel signal x(t) to be denoised, the set frame length T f and the frame shift; the dual-channel signal x(t) to be denoised belongs to R 2×T ;

[0014] S102: Extract the input signal by looping through the index according to the total number of signal frames to implement the frame segmentation process of the signal and obtain single-frame signals

[0015] Preferably, in step S2, it is specifically as follows:

[0016] S201: Perform a fast Fourier transform on the single-frame signal x frame (t) to obtain the discrete Fourier transform coefficients of the two channels, denoted as and Calculate the squared magnitudes of the discrete Fourier transform coefficients of the two channels respectively, X 1_sq =|X1| 2 , X 2_sq =|X2| 2 ;

[0017] S202: Recursively and smoothly update the auto-power spectral density and the cross-power spectral density:

[0018] auto_PSD1 n =α PSD ·auto_PSD1 n-1 +(1 - α PSD )·X 1_sq

[0019] auto_PSD2 n =α PSD ·auto_PSD2 n-1 +(1 - α PSD )·X 2_sq

[0020]

[0021] In the formula: n represents the nth frame, auto_PSD1 n is the updated auto-power spectral density of the first channel in the nth frame, auto_PSD2 n is the updated auto-power spectral density of the second channel in the nth frame; cross_PSD n is the cross-power spectral density of the two channels in the nth frame; α PSDis the power spectrum retention factor, α PSD ∈ [0, 1]; is the complex conjugate of X1, and ⊙ represents element-wise multiplication of vectors;

[0022] S203: Calculate the recursive smoothing coherence function:

[0023] coh_smooth n = α coh · coh_smooth n-1 +(1 - α coh )· coh tmp

[0024]

[0025] where: coh tmp is the temporary coherence value; the max(A, ∈) function means comparing each element of vector A with the constant ∈ and taking the larger value; coh_smooth n is the recursive smoothing coherence value of the nth frame; α coh is the coherence function recursive smoothing factor, α coh ∈ [0, 1];

[0026] S204: Calculate the coherence function model:

[0027] coh_model = S / (S + N0)

[0028] N0 = k'·σ 2

[0029] S = (auto_PSD1 n + auto_PSD2 n ) / 2

[0030] where: S is the average of the updated auto-power spectral densities of the first and second channels in the nth frame; N0 is the estimated noise power spectral density; σ 2 is the average variance of the amplitudes of the dual-channel signals; k' is the amplification factor set according to the noise characteristics, and k' takes 0.5, 1, or 1.5 to accurately estimate the noise power spectral density.

[0031] Preferably, in step S3, it is specifically as follows:

[0032] S301: Based on the recursive smoothing coherence function coh_smooth in step S203 n and the coherence function model coh_model in step S204, calculate the temporary estimated value NCT of the noise correlation threshold tmp :

[0033]

[0034] Among them, Re(·) represents taking the real part;

[0035] And perform preprocessing on the temporary estimated value NCT of the noise-related threshold tmp :

[0036]

[0037] thres(·) is the threshold processing function; NCT limits is the range limit of the noise-related threshold, NCT limits ∈R;

[0038] S302: Smooth the preprocessed NCT tmp ’ to obtain the smoothed noise-related threshold NCT_smooth of the nth frame n :

[0039] NCT_smooth n =α NCT ·NCT_smooth n-1 +(1 - α NCT )·NCT tmp ’

[0040] In the formula: α NCT is the recursive smoothing factor of the noise-related threshold, α NCT ∈[0,1];

[0041] S303: Calculate the noise-related threshold NCT of the nth frame frame :

[0042] NCT frame = mean(NCT_smooth n ).

[0043] Preferably, in step S4, it is specifically as follows:

[0044] S401: Denote the single-frame signal of the first channel as Perform J-layer discrete wavelet transform to obtain wavelet coefficients at different scales j and positions k

[0045]

[0046] In the formula: N frame is the length of each frame of the signal; is the number of wavelet coefficients of this frame at scale j; ψ j,k (t) is the wavelet basis function;

[0047] S402: For the wavelet coefficients Perform soft thresholding to obtain the wavelet coefficients after soft thresholding

[0048]

[0049] T frame = α × NCT frame

[0050] In the formula: T frame is the adjusted noise-related threshold; α is the adjustment coefficient, α is a constant; the sgn function is the sign function;

[0051] S403: Reconstruct the denoised single-frame signal of the first channel through inverse discrete wavelet transform

[0052]

[0053] where is the wavelet reconstruction basis function;

[0054] S404: Denote the single-frame signal of the second channel as Repeat steps S401 - S403 to obtain the denoised single-frame signal of the second channel

[0055] S405: Concatenate the denoised single-frame signal of the first channel and the denoised single-frame signal of the second channel to obtain the denoised single-frame signal of the dual-channel

[0056] Preferably, in step S5, the denoised single-frame signals of the dual-channel corresponding to all frames are integrated in the frame order to obtain the denoised dual-channel signal x de (t), x de (t) ∈ R 2×T .

[0057] The beneficial effects of the present invention are as follows:

[0058] (1) A dual-channel signal denoising method using noise-related threshold is proposed. It can utilize the correlation of dual-channel signals at different frequencies, accurately distinguish signals from noise, and adjust the noise-related threshold (NCT) according to signal and noise characteristics, changing the denoising intensity of wavelet denoising, so as to effectively remove noise.

[0059] (2) Frame-by-frame operation is adopted to process the input dual-channel signal. According to the signal length and processing requirements, different frame lengths and overlap ratios are used, and the long signal is divided into multiple relatively independent short frames for parallel calculation, greatly improving the calculation efficiency.

[0060] (3) By introducing an adaptive smoothing mechanism (adjustment coefficient α), the power spectral density (PSD) and coherence function are dynamically updated, effectively suppressing the instantaneous fluctuations in the estimation process, enhancing the robustness of the noise correlation threshold (NCT), and enabling the algorithm to maintain stable performance in a non-stationary noise environment.

[0061] (4) Innovatively integrating frequency-domain coherence analysis and time-frequency wavelet denoising, dynamically adjusting the time-frequency domain threshold parameters using the frequency-domain correlation characteristics, achieving cross-domain joint optimization, and maximizing the retention of local signal mutations and detailed information while removing noise. Description of the Drawings

[0062] Figure 1 is the overall architecture of the denoising method provided by the present invention;

[0063] Figure 2 is the comparison of the results of the original input signal and the denoised output signal in Example 1. Detailed Embodiments

[0064] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following detailed description of the specific embodiments of the present invention will be provided in conjunction with the accompanying drawings. Many specific details are set forth in the following description to facilitate a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below. The technical features in the various embodiments of the present invention can be combined accordingly without conflict.

[0065] As Figure 1 shown, the present invention provides a dual-channel signal denoising method using a noise correlation threshold, and the specific steps are as follows:

[0066] I. Frame Processing

[0067] Adopt different frame lengths and overlap ratios according to the length of the dual-channel signal to be denoised and the processing requirements; specifically as follows:

[0068] (1) According to the length T of the dual-channel signal x(t) to be denoised, the set frame length T f 、frame shift, calculate the total number of frames of the signal; the dual-channel signal x(t) to be denoised ∈ R 2×T ;

[0069] (2) Extract the input signal by looping through the total number of frames of the signal to achieve frame processing of the signal and obtain single-frame signals

[0070] II. Frequency-Domain Coherence Analysis

[0071] Extract the signal of a single-frame signal \(x(t)\) using the Fast Fourier Transform (FFT); based on the extracted signal, recursively and smoothly update the auto-power spectral density and cross-power spectral density, and calculate the recursively smoothed coherence function \(coh\_smooth\) frame and the coherence function model \(coh\_model\) as follows: n

[0072] (1) Perform the Fast Fourier Transform on the single-frame signal \(x(t)\) to obtain the discrete Fourier transform coefficients of two channels. The discrete Fourier transform coefficients of the first channel are denoted as \(X1\), frame and the discrete Fourier transform coefficients of the second channel are denoted as \(X2\).

[0073] (2) Calculate the squared magnitudes of the discrete Fourier transform coefficients of the two channels respectively:

[0074] \(X\) 1_sq \(=\vert X1\vert\) 2

[0075] \(X\) 2_sq \(=\vert X2\vert\) 2

[0076] where: \(X\) 1_sq is the squared magnitude of the first channel, and \(X\) 2_sq is the squared magnitude of the second channel.

[0077] (3) Recursively and smoothly update the auto-power spectral density and cross-power spectral density:

[0078] \(auto\_PSD1\) n \(=\alpha\) PSD \(\cdot auto\_PSD1\) n-1 \(+(1 - \alpha\) PSD )\(\cdot X\) 1_sq

[0079] \(auto\_PSD2\) n \(=\alpha\) PSD \(\cdot auto\_PSD2\) n-1 \(+(1 - \alpha\) PSD )\(\cdot X\) 2_sq

[0080]

[0081] where: \(n\) represents the \(n\)th frame, \(auto\_PSD1\) n is the updated auto-power spectral density of the first channel for the \(n\)th frame, and \(auto\_PSD2\) n is the updated auto-power spectral density of the second channel for the \(n\)th frame; \(cross\_PSD\) nis the cross-power spectral density of the nth frame for two channels; α PSD is the power spectrum retention factor, α PSD ∈[0, 1]; is the complex conjugate of X1, and ⊙ represents element-wise multiplication of vectors.

[0082] (4) Calculate the recursive smoothing coherence function:

[0083] coh_smooth n = α coh ·coh_smooth n-1 +(1 - α coh )·coh tmp

[0084]

[0085] In the formula: coh tmp is the temporary coherence value; the max(A, ∈) function means comparing each element of vector A with the constant ∈ and taking the larger value; coh_smooth n is the recursive smoothing coherence value of the nth frame; α coh is the recursive smoothing factor of the coherence function, α coh ∈[0, 1].

[0086] (5) Calculate the coherence function model:

[0087] coh_model = S / (S + N0)

[0088] N0 = k'·σ 2

[0089] S = (auto_PSD1 n + auto_PSD2 n ) / 2

[0090] In the formula: S is the average of the updated auto-power spectral densities of the nth frame for the first and second channels; N0 is the estimated noise power spectral density; σ 2 is the average variance of the amplitudes of the two-channel signals; k' is the amplification factor set according to the noise characteristics, and k' takes 0.5, 1, or 1.5 to accurately estimate the noise power spectral density.

[0091] III. Noise-related threshold NCT frame Calculation

[0092] Based on the recursive smoothing coherence function coh_smooth n and the coherence function model coh_model, obtain the dynamic calculation formula for the noise-related threshold; generate a frequency-adaptive noise-related threshold curve through moving average and clipping processing to obtain the noise-related threshold NCT for the nth frameframe , as follows:

[0093] (1) Calculate the temporary estimate value NCT of the noise correlation threshold based on the recursive smoothing coherence function coh_smooth n and the coherence function model coh_model: tmp :

[0094]

[0095] where Re(·) represents taking the real part;

[0096] (2) Preprocess the temporary estimate value NCT of the noise correlation threshold to obtain the preprocessed temporary estimate value NCT' of the noise correlation threshold: tmp tmp ':

[0097]

[0098] thres(NCT tmp , NCT limits ) is a threshold processing function, which means taking the smaller value of NCT tmp and NCT limits ; NCT limits is the noise correlation threshold limit range, NCT limits ∈ R.

[0099] The threshold processing function is a function that limits the input value within a preset range to ensure that the value taken meets the expected range.

[0100] (3) Smooth the preprocessed temporary estimate value NCT' of the noise correlation threshold to obtain the smoothed noise correlation threshold NCT_smooth of the nth frame: tmp ' to obtain the smoothed noise correlation threshold NCT_smooth of the nth frame: n :

[0101] NCT_smooth n = α NCT · NCT_smooth n-1 + (1 - α NCT ) · NCT tmp '

[0102] In the formula: α NCT is the recursive smoothing factor of the noise correlation threshold, α NCT ∈ [0, 1];

[0103] (4) Calculate the noise correlation threshold NCT of the nth frame: frame :

[0104] NCTframe = mean(NCT_smooth n )

[0105] Denotes taking the mean value in the NCT_smooth n vector.

[0106] IV. Joint Denoising in Time-Frequency Domain

[0107] Perform discrete wavelet transform on the single-frame signals x frame (t) of the two channels respectively, and decompose the signals to different scales; use the noise correlation threshold NCT frame in the specified frequency range to perform soft thresholding on the wavelet coefficients and perform non-linear compression on the high-frequency coefficients; reconstruct through the inverse discrete wavelet transform and splice to obtain the denoised single-frame signal of the two channels Specifically as follows:

[0108] (1) Denote the single-frame signal of the first channel as Perform J-layer discrete wavelet transform to obtain the wavelet coefficients at different scales j and positions k

[0109]

[0110] where: N frame is the length of each frame of signal; is the number of wavelet coefficients of this frame at scale j; ψ j,k (t) is the wavelet basis function;

[0111] (2) Perform soft thresholding on the wavelet coefficients to obtain the wavelet coefficients after soft thresholding

[0112]

[0113] T frame = α × NCT frame

[0114] where: T frame is the adjusted noise correlation threshold; α is the adjustment coefficient, α is a constant; the sgn function is the sign function;

[0115] (3) Reconstruct the denoised single-frame signal of the first channel through the inverse discrete wavelet transform

[0116]

[0117] where is the wavelet reconstruction basis function; the wavelet reconstruction basis function and the wavelet basis function ψ j,k(t) can be selected according to specific application scenarios and signal characteristics.

[0118] (4) Denote the single-frame signal of the second channel as Repeat steps (1) to (3) to obtain the denoised single-frame signal of the second channel

[0119] (5) Concatenate the denoised single-frame signal of the first channel and the denoised single-frame signal of the second channel to obtain the denoised two-channel single-frame signal

[0120] V. Frame-by-frame restoration

[0121] Integrate all the denoised two-channel single-frame signals corresponding to each frame in the frame order to obtain the denoised two-channel signal x de (t), x de (t) ∈ R 2×T .

[0122] Embodiment 1

[0123] This embodiment is based on a randomly generated two-channel signal with noise. The example signal includes a fundamental frequency attenuation envelope (exponential decay curve) and high-frequency noise (random spikes). The signal length T = 10000, then the two-channel signal x(t) ∈ R 2 ×10000 .

[0124] Set the parameters of the noise-related threshold: the initial estimated value of the auto-power spectral density auto_PSD10 = auto_PSD20 = 0, the initial estimated value of the cross-power spectral density cross_PSD0 = 0, the initial recursively smoothed coherence value coh_smooth0 = 0, and the initial smoothed noise-related threshold NCT_smooth0 = 0.

[0125] (1) Divide the two-channel signal x(t) ∈ R 2×T to be denoised into several frames. Denote a frame of the signal as In this example, the frame length T f is taken as 64, and the frame shift is taken as 64, then x frame (t) ∈ R 2×64 .

[0126] (2) Assume that the discrete Fourier transform coefficients (DFT) of the two channels of x frame (t) are X1 ∈ R 1×64 and X2 ∈ R 1 ×64 , respectively calculate the square of the amplitude of the two-channel signals, X 1_sq = |X1|2 , X 2_sq = |X2| 2 .

[0127] (3) Recursively smooth and update the auto-power spectral density and cross-power spectral density. It is implemented using the following formula:

[0128] auto_PSD1 n = α PSD · auto_PSD1 n-1 + (1 - α PSD ) · X 1_sq

[0129] auto_PSD2 n = α PSD · auto_PSD2 n-1 + (1 - α PSD ) · X 2_sq

[0130]

[0131] α PSD is the power spectrum retention factor. In this embodiment, α PSD = 0.5.

[0132] (4) Calculate the recursively smoothed coherence function:

[0133] coh_smooth n = α coh · coh_smooth n-1 + (1 - α coh ) · coh tmp

[0134]

[0135] α coh is the coherence function recursive smoothing factor. In this embodiment, α coh = 0.5.

[0136] (5) Calculate the coherence function model:

[0137] coh_model = S / (S + N0)

[0138] N0 = k' · σ 2

[0139] S = (auto_PSD1 n + auto_PSD2 n ) / 2

[0140] σ 2 is the average variance of the amplitudes of the two-channel signals. Then N0 = k' · σ2 and extend it to the same dimension R as S 1×64 In this embodiment, k' is taken as 1.

[0141] (6) Calculate the temporary estimate value NCT of the noise correlation threshold tmp :

[0142]

[0143] where Re(·) represents taking the real part.

[0144] (7) Preprocess the temporary estimate value NCT of the noise correlation threshold tmp and implement it using the following formula:

[0145]

[0146] In this embodiment, NCT limits = [0, 1].

[0147] (8) Smooth the preprocessed temporary estimate value NCT of the noise correlation threshold tmp ':

[0148] NCT_smooth n = α NCT ·NCT_smooth n-1 + (1 - α NCT )·NCT tmp '

[0149] α NCT is the recursive smoothing factor of the noise correlation threshold. In this embodiment, α NCT is a fixed value of 0.5.

[0150] (9) Calculate the noise correlation threshold NCT of the nth frame frame :

[0151] NCT frame = mean(NCT_smooth n )

[0152] represents taking the mean value in the NCT_smooth n vector.

[0153] (10) Denote the single-frame signal of the first channel as perform J-layer discrete wavelet transform to obtain wavelet coefficients at different scales j and positions k

[0154]

[0155] In this embodiment, J = 3, and the selected wavelet basis function is db4.

[0156] (11) Perform soft threshold processing on the obtained wavelet coefficients to obtain the wavelet coefficients after soft threshold processing

[0157]

[0158] T frame =α×NCT frame

[0159] α is an adjustment coefficient, and in this embodiment, α=0.3.

[0160] (12) Reconstruct the denoised single-frame signal of the first channel through inverse discrete wavelet transform

[0161]

[0162] in It is the wavelet reconstruction basis function. In this embodiment, the wavelet reconstruction basis function selects db4 corresponding to the wavelet basis function.

[0163] (13) The single frame signal of the second channel is recorded as Repeat steps (10) to (12) to obtain the denoised single-frame signal of the second channel.

[0164] (14) Splicing and get Denoised signals corresponding to all frames Integrate according to the original frame order to obtain the final denoised signal x de (t)∈R 2×10000 .

[0165] Figure 2 The upper part of is the original noisy signal. Figure 2 The lower part is the signal after denoising, and the energy of the noise is attenuated by about 70% compared with the original signal, which shows that the method provided by the present invention can effectively denoise.

[0166] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A two-channel signal denoising method using a noise correlation threshold, characterized in that, The specific steps are as follows: S1: Frame the two-channel signal x(t) to be denoised to obtain the single-frame signal x frame (t) of each channel; S2: Extract the signal of a single-frame signal x frame (t) using the fast Fourier transform; based on the extracted signal, recursively and smoothly update the auto-power spectral density and cross-power spectral density, and calculate the recursively smoothed coherence function coh_smooth n and the coherence function model coh_model; S3: Based on the recursive smoothing coherence function coh_smooth n and the coherence function model coh_model, obtain the dynamic calculation formula for the noise correlation threshold; generate a frequency-adaptive noise correlation threshold curve through moving average and clipping processing to obtain the noise correlation threshold NCT frame ; S4: Discretely wavelet transform the single-frame signals x frame (t) of the two channels respectively, and decompose the signals to different scales; Use the noise correlation threshold NCT frame to perform soft thresholding on the wavelet coefficients and nonlinearly compress the high-frequency coefficients; Reconstruct through the inverse discrete wavelet transform and splice to obtain the denoised dual-channel single-frame signal S5: For the denoised dual-channel single-frame signal Restore frame by frame to obtain the denoised dual-channel signal x de (t).

2. The two-channel signal denoising method using a noise correlation threshold according to claim 1, wherein, In step S1, the frame splitting process adopts different frame lengths and overlapping ratios according to the lengths of the dual-channel signals to be denoised and the processing requirements; specifically as follows: S101: Calculate the total number of signal frames according to the length T of the two-channel signal x(t) to be denoised, the set frame length T f and the frame shift; the two-channel signal x(t) to be denoised belongs to R 2×T ; S102: Extract the input signal by cycling and indexing according to the total number of signal frames, implement frame-by-frame processing of the signal, and obtain single-frame signals 3. The dual-channel signal denoising method using a noise correlation threshold according to claim 1, wherein Specifically in step S2 as follows: S201: Single-frame signal x frame (t) is subjected to fast Fourier transform to obtain discrete Fourier transform coefficients of two channels, denoted as and Calculate the squared magnitudes of the discrete Fourier transform coefficients of the two channels, X 1_sq = |X1| 2 , X 2_sq = |X2| 2 ; S202: Recursively smooth and update the auto-power spectral density and cross-power spectral density: auto_PSD1 n = α PSD · auto_PSD1 n-1 + (1 - α PSD )· X 1_sq auto_PSD2 n = α PSD · auto_PSD2 n-1 +(1 - α PSD )· X 2_sq where: n represents the nth frame, auto_PSD1 n is the updated auto-power spectral density of the nth frame of the first channel, auto_PSD2 n is the updated auto-power spectral density of the nth frame of the second channel; cross_PSD n is the cross-power spectral density of the nth frame of the two channels; α PSD is the power spectrum retention factor, α PSD ∈[0,1]; is the complex conjugate of X1, and ⊙ represents element-wise multiplication of vectors; S203: Calculate the recursively smoothed coherence function: coh_smooth n = α coh · coh_smooth n-1 + (1 - α coh )· coh tmp where: coh tmp is the temporary coherence value; the max(A, ∈) function means comparing each element of vector A with the constant ∈ and taking the larger value; coh_smooth n is the recursively smoothed coherence value of the nth frame; α coh is the coherence function recursive smoothing factor, α coh ∈ [0, 1]; S204: Calculate the coherence function model: coh_model = S / (S + N0) N0 = k'·σ 2 S = (auto_PSD1 n + auto_PSD2 n ) / 2 Where: S is the average value of the auto-power spectral density updated for the nth frame of the first channel and the second channel; N0 is the estimated noise power spectral density; σ 2 is the average variance of the amplitudes of the dual-channel signals; k′ is the amplification factor set according to the noise characteristics, and k′ takes 0.5, 1 or 1.5 to accurately estimate the noise power spectral density.

4. The two-channel signal denoising method using a noise correlation threshold according to claim 1, wherein Specifically in step S3 as follows: S301: Calculate a temporary estimated value NCT of the noise correlation threshold based on the recursive smoothing coherence function coh_smooth in step S203 n and the coherence function model coh_model in step S204 tmp : Where Re(·) represents taking the real part; And perform preprocessing on the temporarily estimated value of the noise correlation threshold NCT tmp : thres(·) is a threshold processing function; NCT limits is the noise-related threshold limit range, NCT limits ∈R; S302: Smooth the preprocessed NCT tmp ’ to obtain the smoothed noise correlation threshold NCT_smooth of the nth frame n : NCT_smooth n = α NCT · NCT_smooth n-1 + (1 - α NCT ) · NCT tmp ’ Where: α NCT is the recursive smoothing factor of the noise correlation threshold, and α NCT ∈ [0, 1]; S303: Calculate the noise correlation threshold NCT of the nth frame frame : NCT frame = mean(NCT_smooth n )。 5. The two-channel signal denoising method using a noise correlation threshold according to claim 1, wherein Specifically in step S4 as follows: S401: Denote the single-frame signal of the first channel as Perform J-level discrete wavelet transform to obtain wavelet coefficients at different scales j and positions k Where: N frame is the length of each frame signal; is the number of wavelet coefficients of this frame at scale j; ψ j,k (t) is the wavelet basis function; S402: Perform soft thresholding on the wavelet coefficients to obtain the wavelet coefficients after soft thresholding T frame = α × NCT frame Where: T frame is the adjusted noise correlation threshold; α is an adjustment coefficient, α is a constant; the sgn function is the sign function; S403: Reconstruct the denoised single-frame signal of the first channel through inverse discrete wavelet transform wherein is a wavelet reconstruction basis function; S404: Denote the single-frame signal of the second channel as Repeat steps S401 to S403 to obtain the denoised single-frame signal of the second channel S405: Stitch the denoised single-frame signal of the first channel with the denoised single-frame signal of the second channel to obtain the denoised single-frame signal of the dual channel 6. The two-channel signal denoising method using a noise correlation threshold according to claim 1, wherein In step S5, the denoised dual-channel single-frame signals corresponding to all frames are integrated in the frame sequence to obtain the denoised dual-channel signal x de (t), where x de (t) ∈ R 2×T .

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