Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density
The penalized least squares regression (PLSR) is usually used for solving linear inverse problems in signal processing, such as the denoising (noise reduction) and deconvolution problems. Efficiency of this method is based on the penalty function (regularization). Therefore, we propose the novel reg...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | ICT Express |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405959522000121 |
| _version_ | 1797796100658167808 |
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| author | Pichid Kittisuwan |
| author_facet | Pichid Kittisuwan |
| author_sort | Pichid Kittisuwan |
| collection | DOAJ |
| description | The penalized least squares regression (PLSR) is usually used for solving linear inverse problems in signal processing, such as the denoising (noise reduction) and deconvolution problems. Efficiency of this method is based on the penalty function (regularization). Therefore, we propose the novel regularization based on the Pareto distribution. Here, famous regularizations, such as the logarithm and ratio regularizations, are included in the mathematical form of this proposed regularization. Moreover, mathematical models of the Bayesian estimator, such as the maximum a posteriori (MAP) and minimum mean square error (MMSE) estimations, in additive white Gaussian noise (AWGN) are similar to the PLSR. Therefore, we propose denoising methods via PLSRs using the proposed regularization which are equivalent to the MAP and MMSE estimations. In numerical results, proposed methods give good denoising results. |
| first_indexed | 2024-03-13T03:28:05Z |
| format | Article |
| id | doaj.art-21dffb235e374a43a5401cee68f9c2fa |
| institution | Directory Open Access Journal |
| issn | 2405-9595 |
| language | English |
| last_indexed | 2024-03-13T03:28:05Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | ICT Express |
| spelling | doaj.art-21dffb235e374a43a5401cee68f9c2fa2023-06-25T04:43:16ZengElsevierICT Express2405-95952023-06-0193326332Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto densityPichid Kittisuwan0Department of Telecommunication Engineering, Rajamangala University of Technology Rattanakosin, Nakhon Pathom, ThailandThe penalized least squares regression (PLSR) is usually used for solving linear inverse problems in signal processing, such as the denoising (noise reduction) and deconvolution problems. Efficiency of this method is based on the penalty function (regularization). Therefore, we propose the novel regularization based on the Pareto distribution. Here, famous regularizations, such as the logarithm and ratio regularizations, are included in the mathematical form of this proposed regularization. Moreover, mathematical models of the Bayesian estimator, such as the maximum a posteriori (MAP) and minimum mean square error (MMSE) estimations, in additive white Gaussian noise (AWGN) are similar to the PLSR. Therefore, we propose denoising methods via PLSRs using the proposed regularization which are equivalent to the MAP and MMSE estimations. In numerical results, proposed methods give good denoising results.http://www.sciencedirect.com/science/article/pii/S2405959522000121Penalized least squares regressionPenalty function (regularization)Bayesian estimationDenoising |
| spellingShingle | Pichid Kittisuwan Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density ICT Express Penalized least squares regression Penalty function (regularization) Bayesian estimation Denoising |
| title | Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density |
| title_full | Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density |
| title_fullStr | Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density |
| title_full_unstemmed | Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density |
| title_short | Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density |
| title_sort | relation between penalized least squares regression and bayesian estimation in awgn based on novel penalty function of pareto density |
| topic | Penalized least squares regression Penalty function (regularization) Bayesian estimation Denoising |
| url | http://www.sciencedirect.com/science/article/pii/S2405959522000121 |
| work_keys_str_mv | AT pichidkittisuwan relationbetweenpenalizedleastsquaresregressionandbayesianestimationinawgnbasedonnovelpenaltyfunctionofparetodensity |