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...
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| Format: | Article |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8871128/ |
| _version_ | 1818411080948383744 |
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| author | Joao P. F. Guimaraes Felipe B. Da Silva Aluisio I. R. Fontes Ricardo Von Borries Allan De M. Martins |
| author_facet | Joao P. F. Guimaraes Felipe B. Da Silva Aluisio I. R. Fontes Ricardo Von Borries Allan De M. Martins |
| author_sort | Joao P. F. Guimaraes |
| collection | DOAJ |
| description | 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<sub>0</sub>-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<sub>0</sub>-MCC algorithm in a straightforward way to compressive sensing problems dealing with complex-valued measurements. This paper presents a generalization of the ℓ<sub>0</sub>-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<sub>0</sub>-Least Mean Square (ℓ<sub>0</sub>-LMS) in the presence of non-Gaussian noise. |
| first_indexed | 2024-12-14T10:25:44Z |
| format | Article |
| id | doaj.art-e20ee33c52bb4abf801889f8259cecc9 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T10:25:44Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e20ee33c52bb4abf801889f8259cecc92022-12-21T23:06:20ZengIEEEIEEE Access2169-35362019-01-01715165215166010.1109/ACCESS.2019.29477648871128Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise EnvironmentJoao P. F. Guimaraes0https://orcid.org/0000-0002-5503-4246Felipe B. Da Silva1Aluisio I. R. Fontes2https://orcid.org/0000-0002-1888-3505Ricardo Von Borries3Allan De M. Martins4Department of Information, Federal Institute of Rio Grande do Norte, João Câmara, BrazilDepartment of Electrical and Computer Engineering, The University of Texas at El Paso, El Paso, TX, USADepartment of Information, Federal Institute of Rio Grande do Norte, Pau dos Ferros, BrazilDepartment of Electrical and Computer Engineering, The University of Texas at El Paso, El Paso, TX, USADept. of Electr. Eng., Fed. Univ. of Rio Grande do Norte, Natal, BrazilCorrentropy 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<sub>0</sub>-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<sub>0</sub>-MCC algorithm in a straightforward way to compressive sensing problems dealing with complex-valued measurements. This paper presents a generalization of the ℓ<sub>0</sub>-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<sub>0</sub>-Least Mean Square (ℓ<sub>0</sub>-LMS) in the presence of non-Gaussian noise.https://ieeexplore.ieee.org/document/8871128/Complex correntropycomplex-valued datacompressive sensingl₀–approximation |
| spellingShingle | Joao P. F. Guimaraes Felipe B. Da Silva Aluisio I. R. Fontes Ricardo Von Borries Allan De M. Martins Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment IEEE Access Complex correntropy complex-valued data compressive sensing l₀–approximation |
| title | Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment |
| title_full | Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment |
| title_fullStr | Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment |
| title_full_unstemmed | Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment |
| title_short | Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment |
| title_sort | complex correntropy applied to a compressive sensing problem in an impulsive noise environment |
| topic | Complex correntropy complex-valued data compressive sensing l₀–approximation |
| url | https://ieeexplore.ieee.org/document/8871128/ |
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