Mechanical fault diagnosis is of great significance to industrial automation, and extracting vibration fault signals is one of the important tasks in mechanical health monitoring and fault diagnosis. However, due to the complex working environment of rolling bearings, a large amount of noise makes it difficult to extract vibration fault signals. Denoising the vibration signal of bearings can remove interference noise, simplify the early identification of signal features, and thus improve diagnostic accuracy and mechanical maintenance efficiency. This paper proposes a rolling bearing fault signal denoising algorithm, which constructs a new feature extraction and denoising function. This method first decomposes the noisy signal into Intrinsic Mode Functions (IMFs) by Intrinsic Computing Expressive Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). Secondly, a new adaptive information entropy threshold function is constructed to extract the noisy IMFs from it. Then, the noisy IMF signal is denoised by a new wavelet threshold function. Finally, the noise-free IMFs are reconstructed to reconstruct the denoised signal. To verify the actual performance of the algorithm, comparative experiments were conducted on a self-collected dataset and a public dataset, the results show that this method improves the continuity of signal reconstruction and can remove various types of vibration fault noise signals more effectively and accurately, \hl{thereby improving the fault detection accuracy by 2%-9%.