Sparse Component Analysis Using Continuous Wavelet Transform for Blind Source Separation

Blind source separation (BSS) has been widely used in image processing, vibration analysis, signal filtering and other field for many years. Recently, sparse component analysis (SCA), an effective BSS method, has received a lot of attention. Compared with the traditional method, SCA has a wider range of use because it has more relaxed constraints on the observation signal. The sparse representation of signals is an important part in the operational framework of SCA. For this important part, a sparse component analysis method using continuous wavelet transform (CWT) was proposed in this paper. Firstly, this paper introduced the principle of classical blind source separation problem, and explained the framework of sparse component analysis. Then, continuous wavelet transform was introduced to get sparse representation of observation signals and the operation process of the method was explained. Finally, a numerical simulation case was designed and implemented to prove that CWT has higher accuracy than STFT, and the selection rules of various parameters of CWT were discussed. The simulation results showed that the SCA using CWT can extract the mixed matrix with high accuracy and the method still has high efficiency under the noise level of 30dB.