Maximum Likelihood-Based Image Denoising under Different Noise Models

Abstract

Image denoising is an essential task in image processing, where noise inevitably arises during image acquisition and transmission and may severely degrade further computer vision results. Although many approaches have been suggested, most are developed under specific noise assumptions, and relatively few studies compare different statistical models in a systematic manner within a common maximum-likelihood framework. The present paper fills this gap by discussing three popular noise models: Gaussian, Laplacian and Poisson in the context of maximum likelihood estimation (MLE). The loss functions (the -norm for Gaussian noise, the -norm for Laplacian noise and the Poisson negative log-likelihood) are derived and explained both in terms of their statistical foundations and implications in practice. Based on this theoretical background, some common applications of each model are further presented, including consumer photography, remote sensing, fluorescence microscopy and low-light imaging. The analysis demonstrates that the noise model is not merely a technical detail but a principled choice reflecting the dominant noise properties of the imaging system. This paper will offer an easy-to-understand theoretical reference as well as practical advice in terms of choosing appropriate data terms in image restoration algorithms by placing the three models side by side.