Compressed sensing based on dictionary learning for extracting impulse components

It is essential to extract impulse components embedded in heavy background noise in engineering applications. The methods based on wavelet have obtained huge success in removing noises, leading to state-of-the-art results. However, complying with the minimum noise principle, the shrinkage/thresholding algorithms unreasonably remove most energy of the features, and sometimes even discard some important features. Thus it is not easy to guarantee satisfactory performance in actual applications. Based on a recently proposed theory named compressed sensing, this paper presents a new scheme, Sparse Extraction of Impulse by Adaptive Dictionary (SpaEIAD), to extract impulse components. It relies on the sparse model of compressed sensing, involving the sparse dictionary learning and redundant representations over the learned dictionary. SpaEIAD learns a sparse dictionary from a whole noisy signal itself and then employs greedy algorithms to search impulse information in the learned sparse dictionary. The performance of the algorithm compares favourably with that of the mature shrinkage/thresholding methods. There are two main advantages: firstly, the learned atoms are tailored to the data being analyzed and the process of extracting impulse information is highly adaptive. Secondly, sparse level of representation coefficients is promoted largely. This algorithm is evaluated through simulations and its effectiveness of extracting impulse components is demonstrated on vibration signal of motor bearings. The advantage of SpaEIAD is further validated through detecting fault components of gearbox, which illustrates that SpaEIAD can be generalized to engineering application, such as rotating machinery signal processing. (C) 2013 Elsevier B.V. All rights reserved.