We propose a new method for the progressive enhancement of images degraded by noise and blur using shock filters. The originality of our approach lies in the iterative exploitation of nonconservative edge-based force fields normally designed for segmentation to determine both locations and amplitudes of the sharpening action. The proposed nonconservative shock filter (NCSF) produces images with strong discontinuities that can be used as an additional pre-processing step to facilitate higher level tasks such as edge detection or segmentation. NCSF is especially useful when coupled with an anisotropic diffusion equation in noisy configurations. Using the proposed method, edges that are not well defined prior to filtering can be iteratively recovered. We show processing results on various types of images, focusing on medical transrectal ultrasound and brain PET imaging.

We present a multi-scale approach of tumor modeling in order to predict its evolution during radiotherapy. Within this context we focus on three different scales of tumor modeling: microscopic (individual cells in a voxel), mesoscopic (population of cells in a voxel) and macroscopic (whole tumor), with transition interfaces between these three scales. At the cellular level, the description is based on phase transfer probabilities in the cellular cycle. At the mesoscopic scale we represent populations of cells according to different stages in a cell cycle. Finally, at the macroscopic scale, the tumor description is based on the use of FDG PET image voxels. These three scales exist naturally: biological data are collected at the macroscopic scale, but the pathological behavior of the tumor is based on an abnormal cell-cycle at the microscopic scale. On the other hand, the introduction of a mesoscopic scale is essential in order to reduce the gap between the two extreme, in terms of resolution, description levels. It also reduces the computational burden of simulating a large number of individual cells. As an application of the proposed multi-scale model, we simulate the effect of oxygen on tumor evolution during radiotherapy. Two consecutive FDG PET images of 17 rectal cancer patients undergoing radiotherapy are used to simulate the tumor evolution during treatment. The simulated results are compared with those obtained on a third FDG PET image acquired two weeks after the beginning of the treatment.