Research on Noise Reduction Method of Underwater Acoustic Signal Based on CEEMDAN Decomposition-Improved Wavelet Threshold

Due to the complex noise in the ocean environment, the signal-to-noise ratio of the hydrophone receiving signal is often low, making subsequent signal processing difficult. To solve this problem, this paper proposes using CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) decomposition algorithm combined with an improved wavelet threshold algorithm to process the signal, and obtain the reconstructed signal after denoising. In this method, the noise-containing signal is transformed by the function and decomposed into multiple natural mode components with frequencies ranging from high to low using the CEEMDAN algorithm. The correlation component and the non-correlation component are then determined using the cross-correlation function. The non-correlated compinents are denoised using the improved wavelet threshold method and the denoised signal is obtained by reconstructing the signal. Experimental results show that this method can improve the performance of underwater acoustic signal denoising.


Introduction
The topic of reconstructing signals from noisy signals using signal processing methods has been a focal point in the field of underwater acoustic signal processing.Through research advancements, scholars have discovered that common multiplicative noise in underwater acoustic signals can be transformed into Gaussian noise through function conversion, leading to better denoising results [1].Among various noise reduction methods, the use of wavelet thresholds has gained attention due to its excellent denoising performance and low complexity.However, the effectiveness of wavelet threshold denoising relies heavily on threshold selection, as it directly impacts the denoising outcome.
To obtain better thresholds, Huang et al. proposed the empirical mode decomposition (EMD) method [2].This method decomposes the signal into intrinsic mode components (IMFs) in different frequency domains, allowing for the removal of noisy high-frequency components.However, signal aliasing is a common issue.To address this, scholars have introduced an improved method called the Adaptive Noise Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), which effectively handles the transfer of white noise from high frequencies to low frequencies [3]- [7].
To effectively remove noise from underwater acoustic signals, this paper incorporates a correlation function into the CEEMDAN algorithm to determine the optimal decomposition layer, denoted as N.The signal is then decomposed into multiple IMFs ranging from high to low frequencies.[8]- [12] A wavelet threshold is set to filter out noise in the high-frequency IMFs that contain more noise.The result is a reconstructed underwater acoustic signal.The algorithm's effectiveness is verified using classic block waveforms and simulated underwater acoustic signals.

CEEMDAN decomposition
The CEEMDAN algorithm follows a basic principle of adding Gaussian white noise to the original signal and then performing EMD decomposition.This addition of noise extends the frequency range of each IMF, thereby avoiding mode aliasing issues.The final decomposition result is obtained by averaging each IMF [13].The specific steps are as follows: First, Gaussian white noise with a mean value of zero is added K times to the signal Y(t) to be decomposed.This creates a sequence () i t y for decomposition, with a total of K experiments (where i=1, 2, 3, …, K).At this point, the signal can be expressed as: (1) In the formula:  is the weight coefficient of Gaussian white noise; () i t δ is the Gaussian white noise generated in the i-th processing.Second, the above sequence () i t y is decomposed by EMD, and the first modal component obtained by decomposing is denoted as 1 () i IMF t , and its mean value is taken as the first IMF obtained by CEEMDAN decomposition.Use 1 () t r to denote the residual signal after the first decomposition.
Third, adding specific noise to the residual signal of the j-th stage obtained after decomposition, the j-th modal component is represented by () the j-1st stage The weight coefficient of adding noise to the residual signal is denoted by 1 j  − , and the residual signal in the j-th stage is denoted by () j t r , and the EMD decomposition is continued.
Fourth, if the EMD stop condition is satisfied: the residual signal ()  n t r of the n-th decomposition is a monotonic signal, the iteration stops and the decomposition of the CEEMDAN algorithm ends.

Improved wavelet thresholding method
To achieve better denoising performance and address the signal loss issue caused by traditional soft and hard wavelet thresholding methods, this paper adopts a new threshold function and method proposed in existing research [14].The threshold function reduces the error between the original wavelet coefficients and the reduced wavelet coefficients.Its expression is as follows , ., , , ˆ) In the soft threshold function, a weighting factor  is added to the wavelet coefficients larger than the threshold: For this method, the specific steps are: First, the input signal y(t) is subjected to wavelet decomposition.Second, extract the high-frequency wavelet coefficients of each layer.Third, use formula (5) to calculate the threshold for each layer.Fourth, use formula (4) to calculate the wavelet coefficients for each layer.Finally, reconstruct the signal and obtain the denoised waveform.

Algorithm Basic Flow
In order to address the challenge of removing ocean reverberation noise, this paper proposes a method that involves converting the noise into Gaussian noise through function conversion.[15] Next, the high and low frequency components are decomposed using the CEEMDAN algorithm, which incorporates the cross-correlation function.Then, the improved wavelet threshold algorithm is applied to eliminate the noise.Finally, the signal is reconstructed to obtain the denoised waveform.The algorithm flow is illustrated in figure 1.

Underwater Acoustic Signal Verification
In this paper, the Bellohop model is utilized to simulate the actual ocean environment.It is assumed that the sampling frequency is 2000kHz, the emission center frequency is 200kHz, the emission sound source level is 200dB, and the bandwidth is 8kHz.The simulation includes the addition of noise and multipath interference, taking into account the effects of ocean turbulence and wind force function.The emitted signal and the signal received by the transducer are depicted in figure 2.  As can be seen from Figure 2, due to the uneven medium and uneven interface in the ocean, discontinuities in the physical properties of the medium will be formed, blocking part of the sound energy that shines on them, and radiating this part of the sound energy back to energy conversion The result is that the echo received by the transducer is seriously distorted in both the time domain and frequency domain, making it impossible to accurately extract the signal, which will have a greater impact on subsequent research.Therefore, choosing a better denoising algorithm will directly affect the results of signal extraction.
In order to verify the effect of the algorithm, two commonly used wavelet correlation underwater acoustic signal denoising algorithms, traditional wavelet threshold denoising and improved wavelet threshold denoising, are compared with the improved wavelet threshold denoising algorithm combined with CEEMDAN decomposition used in this paper.The denoising results are shown in figure 3.As can be seen from Figure 3, neither traditional wavelet threshold denoising nor improved wavelet threshold denoising can achieve good denoising effects.Due to the characteristics of the wavelet threshold denoising algorithm, both denoising algorithms can achieve a certain denoising effect in the high frequency part, but they cannot remove the reverberation noise contained in the low frequency part of the underwater acoustic signal and cannot meet the denoising requirements.Using the method in this article to denoise underwater acoustic signals can achieve a certain denoising effect in the time domain.However, since the algorithm in this article only smoothes the low-frequency IMF part and does not process the low-frequency component after wavelet decomposition, but Direct wavelet reconstruction results in distortion of the waveform restored in the time domain.In the frequency domain, the method in this article can also achieve a certain denoising effect.Regardless of the high-frequency part or the low-frequency part, its peak value and bandwidth are better than the first two algorithms.The signal cannot be recovered well and its waveform is distorted.In the frequency domain, this method can also achieve a certain denoising effect.Regardless of the high-frequency part or the low-frequency part, its peak value and bandwidth are better than the first two algorithms.
To accurately evaluate the denoising performance, signal-to-noise ratio (SNR), mean square error (MSE), and normalized correlation coefficient (NCC) are used.The results are presented in table 1.
Table 1.Performance comparison of different noise reduction algorithms.Table 1 shows that the denoising algorithm used in this paper outperforms the traditional wavelet threshold denoising and the improved wavelet threshold denoising algorithms in terms of denoising effectiveness on underwater acoustic signals.The SNR is significantly higher, indicating better noise reduction.The algorithm also exhibits superior mean square error, with a maximum increase of 52.84%, indicating a small difference between the reconstructed and original signals.The waveform similarity coefficient demonstrates improved denoising performance, with a relatively high overall similarity between the reconstructed and original signals.In summary, the algorithm proposed in this paper achieves better denoising performance in both the time and frequency domains for underwater acoustic signal processing, surpassing the two commonly used wavelet threshold denoising algorithms.

Conclusions
Aiming at the problem of large reverberation noise in underwater acoustic signals, an improved denoising method was proposed.First, the CEEMDAN algorithm is used to decompose the signal.Subsequently, the improved wavelet threshold algorithm is applied to remove the noise and the processed reconstructed signal is obtained.The simulation results show that this method has strong denoising ability in underwater acoustic signal processing.However, since the algorithm only smoothes the low-frequency IMF and directly performs wavelet reconstruction on the low-frequency components after wavelet decomposition, the restored waveform in the time domain is distorted.From the frequency domain point of view, the reconstructed signal spectrum has limited reconstruction ability in the lowfrequency part.In the future, research on the reconstruction algorithm of the low-frequency part will be strengthened.

ω
Journal of Physics: Conference Series 2718 (2024) 012078 IOP Publishing doi:10.1088/1742-6596/2718/1/0120783In the formula: q represents the current decomposition scale, the threshold λ adds a decomposition scale to the general fixed rules, m represents the total number of wavelet decompositions, represents the current wavelet coefficient The decomposition scale is p, and 0 ≤ p ≤ M, M indicates the total number of wavelet coefficients when the scale of wavelet coefficients is 1, and mid(• ) indicates that for , pq ω first take the absolute value and then take the median value.

Figure 1 .
Figure 1.Simple flow chart of the algorithm in this paper.

Figure 2 .
Figure 2. Transmit signal and transducer receive signal.

Figure 3 .
Figure 3.Comparison of Noise Reduction Algorithms for Underwater Acoustic Signals.