Mode estimation based filtering in digital imaging and application to medical image denoising

(eng) Today, digital images are massively used in all kinds of applications: entertainment, multimedia, meteorology, medical applications. The quality of the acquisition device and the conditions in which the image is taken affect the quality of the resulting image in a drastic way. Depending of these factors, the images can be over or underexposed, blurry or noisy.This thesis focuses on the problem of removing the noise from digital images. The developments proposed in this work aim at improving the denoising results of the statistical filters and provide solutions to use them in the specific case of medical images The statistical filters are essentially mode estimators. As mode separation improves in high dimensional spaces, we propose to adapt the statistical filters to use high-dimensional data. As a result, two new types of filters are created: Patch-based filters and patchwise filters. These filters turns out to be a generalisation of some other patch-based filters proposed in the literature. The statistical filters use the Gaussian kernel as notion of similarity. This kernel is not adapted to the high-dimensional spaces. We propose to use other kernels, constructed in order to avoid the complications linked to the use of high-dimensional data in the statistical filters. In real life applications, such as medical images, the parameters of the filters are chosen in a heuristic way. A new method to model the noise created by a medical scanner is proposed. It estimates the optimal parameters needed to remove the noise from the images taken with that scanner. Some medical images are polluted with a noise that follows a Poisson law. The statistical filters are not designed to filter with this kind of noise. Variance stabilizing transforms are used in order to change the noise on the image to Gaussian noise, and then apply the statistical filters. An integration of the variance stabilizing transforms into the algorithms is proposed.