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Reducing noise pollution in signals is of great significance in the field of signal detection. In order to reduce the noise in the signal and improve the signal-to-noise ratio (SNR), this paper takes the singular value decomposition theory as the starting point, and constructs various singular value decomposition denoising models with multiple multi-division structures based on the two-division recursion singular value decomposition, and conducts a noise reduction analysis on two experimental signals containing noise of different power. Finally, the SNR and mean square error (MSE) are used as indicators to evaluate the noise reduction effect, it is verified that the two-division recursion singular value decomposition is the optimal noise reduction model. This noise reduction model is then applied to the diagnosis of faulty bearings. By this method, the fault signal is decomposed to reduce noise and the detail signal with maximum kurtosis is extracted for envelope spectrum analysis. Comparison of several traditional signal processing methods such as empirical modal decomposition (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet decomposition, etc. The results show that multi-resolution singular value decomposition (MRSVD) has better noise reduction effect and can effectively diagnose faulty bearings. This method is promising and has a good application prospect.