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

Abstract

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.

Keywords

• Penalized least squares regression
• Penalty function (regularization)
• Bayesian estimation
• Denoising