A new underwater acoustic signal denoising method based on modified uniform phase empirical mode decomposition, hierarchical amplitude-aware permutation entropy, and optimized improved wavelet threshold denoising

Underwater acoustic signal (UAS) denoising is base and prerequisite for UAS detection, recognition and classification. In order to perform UAS denoising effectively, a new UAS denoising method based on modified uniform phase empirical mode decomposition (MUPEMD), hierarchical amplitude -aware permutation entropy (HAAPE), and improved wavelet threshold denoising (IWTD) method optimized by sand cat swarm optimization (SCSO) (SIWTD), named MUPEMD-HAAPE-SIWTD, is proposed. Firstly, decompose original signal into a battery of intrinsic mode functions (IMFs) by MUPEMD. Secondly, determine the double threshold by HAAPE to classify signal into pure signal, mixed signal and noisy signal. Then, optimize IWTD by SCSO, so that it can adaptively select the optimal wavelet basis function to achieve the denoising of mixed signal. Finally, the denoised mixed signal is reconstructed with pure signal to obtain ultima denoised signal. The denoising experiments on Lorenz signal and Duffing signal demonstrate that signal-to-noise ratio can be improved by 9 dB-13 dB by the proposed method. The denoising experiments on simulating ship radiated noise signals and four kinds of actual ship radiated noise signals (https://www.aigei.com/, accessed on June 1, 2023) demonstrate that the proposed method makes phase diagram smoother and clearer, and makes the ability of suppressing noise higher.