Weak Signal Detection Based on Combination of Sparse Representation and Singular Value Decomposition

Due to the inevitable acquisition system noise and strong background noise, it is often difficult to detect the features of weak signals. To solve this problem, sparse representation can effectively extract useful information according to the sparse characteristics of signals. However, sparse representation is less effective against non-Gaussian white noise. Therefore, a novel SRSVD method combining sparse representation and singular value decomposition is proposed to further improve the denoising performance of the algorithm. All the signal components highly matched with the dictionary are extracted by sparse representation, and then each component of singular value decomposition is weighted by the evaluation index, PMI, which can indicate the component with useful information in the signal, so that the signal denoising performance of the algorithm is greatly improved. The performance of the proposed method is verified by the processing of weak signals in the circuit and early fault signals of bearings. The results show that SRSVD can successfully suppress noise interference. Compared with other existing methods, SRSVD has better denoising performance.