Illumination problems in digital images. A statistical point of view

This paper focuses on the statistical treatment of illumination artefacts on digital images in the presence of an additional random noise. We assume that this artefact consists of smooth variations of the intensity of the signal of interest R. Such an assumption is classically modelled using a function L which acts in a multiplicative way on R. Our goal is to estimate R from observations of a random variable Y which obeys the regression model Y = RL + epsilon. Our main contribution lies in the derivation of a new estimator of R which is shown to be consistent under suitable identifiability and regularity conditions. The accuracy of this new estimation procedure is studied from a theoretical point of view through the rate of convergence of the uniform risk. Applications to real Scanning Electron Microscopy images are presented, as well as a qualitative study of the performances of our method with respect to other image processing techniques. (C) 2016 Elsevier Inc. All rights reserved.