The Correntropy Induced Metric and Cyclic Correntropy Spectrum Method Combined With Singular Value Decomposition for Weak Signal Detection

In recent years, as a simple and effective method of noise reduction, singular value decomposition (SVD) has been widely concerned and applied. The idea of SVD to denoising is mainly to drop out singular components (SCs) with small singular value (SV), which ignores the weak signals buried in strong noise. Aiming to extract the weak signals in strong noise, this paper proposed a method of selecting SCs by the correntropy induced metric (CIM). Then the frequency components of characteristic signals can be found through cyclic correntropy spectrum (CCES) which is the extension of the correntropy (CE). The proposed method SVD-CIM firstly performs SVD on the signal, secondly calculates the CIM between SCs and the original signal, thirdly selects the SCs by CIM, fourthly reconstructs the retained SCs, and finally performs the CCES on the reconstructed signal to enhance the frequency of the characteristic signal. Experimental results have demonstrated that the proposed method can enhance the weak signal features effectively.