Abstract
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.
Highlights
In the last years, a great interest has grown in the scientific community around an area called compressive sensing (CS), which takes advantage from the sparsity of signals to reconstruct signals by using fewer measurements than NyquistShannon’s sampling theory would predict [1]
AND DISCUSSION we evaluate the performance of the proposed method 0–Maximum Complex Correntropy Criterion (MCCC) and compare it with Nesterov’s algorithm (NESTA) and 0–LMS
This paper investigates the use of the complex correntropy function to generalize both the 0–LMS and the
Summary
A great interest has grown in the scientific community around an area called compressive sensing (CS), which takes advantage from the sparsity of signals to reconstruct signals by using fewer measurements than NyquistShannon’s sampling theory would predict [1]. Correntropy was used in CS analysis in [27] showing a great potential for nonlinear signal processing and defined a new algorithm called 0–Maximum Correntropy Criterion ( 0–MCC). It puts together an 0 gradient approxi-. This paper introduces a method called 0–MCCC, which uses Maximum Complex Correntropy Criterion (MCCC) in order to solve compressive sensing problems in the presence of non-Gaussian noise.
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