Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density

卷:9

Article

关键词: PARTIAL EIV MODEL;    SPARSE;    RECOVERY;   

DOI  :  10.1016/j.icte.2022.01.012

来源: SCIE

【 摘 要 】

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.& COPY; 2022 Published by Elsevier B.V. on behalf of The Korean Institute of Communications and Information Sciences. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).