Extraction of transients via the combination of wavelet basis and majorization minimization algorithm

Ill-posed linear inverse problems (IPLIP), such as restoration and reconstruction, are core topics of transient feature extraction in cyclostationary signal processing. This paper presents a novel method for extracting transients through exploiting both the wavelet basis and the majorization minimization algorithm. To solve the objective function, majorization minimization (MM) algorithm is applied with a designed strictly convex quadratic function. To implement the sparsity of the results, an optimal basis with its atom selected by correlation filtering is proposed. Through an iterative optimization procedure, transients hidden in the noisy signal can be converted into sparse coefficients. Simulated study concerning cyclic transient signal shows the effectiveness of this method. Applications on a rotating machine test rig with bearing fault also demonstrate the validity of the technique. Both the simulated study and the applications show that the proposed method is powerful in the representation of transients and is an effective tool to extract the transient features of bearings.