Sparsity-enabled signal transient feature extraction using wavelet basis and constrained optimization algorithm

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are core topics of transient feature extraction in cyclostationary signal processing. A standard formulation for solving these problems consists of a constrained optimization problem with a regularization function minimized. In this paper, a method combining sparse representation and special wavelet basis is proposed to handle one class of constrained problems tailored to transient feature extraction applications. Simulation study concerning cyclic transients signal shows the effectiveness of this method. Application in transient feature extraction of fault gearbox vibration signal shows that the proposed method can extract the transient feature effectively.