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 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

Erratum: "Image enhancement via MMSE estimation of Gaussian scale mixture with Maxwell density in AWGN"

In optical techniques, noise signal is a classical problem in medical image processing. Recently, there has been considerable interest in using the wavelet transform with Bayesian estimation as a powerful tool for recovering image from noisy data. In wavelet domain, if Bayesian estimator is used for denoising problem, the solution requires a prior knowledge about the distribution of wavelet coefficients. Indeed, wavelet coefficients might be better modeled by super Gaussian density. The super Gaussian density can be generated by Gaussian scale mixture (GSM). So, we present new minimum mean square error (MMSE) estimator for spherically-contoured GSM with Maxwell distribution in additive white Gaussian noise (AWGN). We compare our proposed method to current state-of-the-art method applied on standard test image and we quantify achieved performance improvement