Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment

Correntropy is a similarity function capable of extracting high-order statistical information from data. It has been used in different kinds of applications as a cost function to overcome traditional methods in non-Gaussian noise environments. One of the recent applications of correntropy was in the theory of compressive sensing, which takes advantage of sparsity in a transformed domain to reconstruct the signal from a few measurements. Recently, an algorithm called ℓ
₀
-MCC was introduced. It applies the Maximum Correntropy Criterion (MCC) in order to deal with a non-Gaussian noise environment in a compressive sensing problem. However, because correntropy was only defined for real-valued data, it was not possible to apply the ℓ
₀
-MCC algorithm in a straightforward way to compressive sensing problems dealing with complex-valued measurements. This paper presents a generalization of the ℓ
₀
-MCC algorithm to complex-valued measurements. Simulations show that the proposed algorithm can outperform traditional minimization algorithms such as Nesterov's algorithm (NESTA) and the ℓ
₀
-Least Mean Square (ℓ
₀
-LMS) in the presence of non-Gaussian noise.