Complex Correntropy Induced Metric Applied to Compressive Sensing with Complex-Valued Data

The correntropy induced metric (CIM) is a well-defined metric induced by the correntropy function and has been applied to different problems in signal processing and machine learning, but CIM was limited to the case of real-valued data. This paper extends the CIM to the case of complex- valued data, denoted by Complex Correntropy Induced Metric (CCIM). The new metric preserves the well known benefits of extracting high order statistical information from correntropy, but now dealing with complex-valued data. As an example, the paper shows the CCIM applied in the approximation of ℓ ₀ -minimization in the reconstruction of complex-valued sparse signals in a compressive sensing problem formulation. A mathematical proof is presented as well as simulation results that indicate the viability of the proposed new metric.