Abstract:

An important problem in image processing, is the reconstruction and the segmentation of an image u, from an observed noisy image u0. The original unknown image u has to be formed by homogeneous regions with sharp edges. This inverse problem can be solved in a variational framework, under additional constraints. An energy functional is constructed, as a sum of several terms. One is the "fidelity" term, which asks u to be close to u0. Another term, the regularizing term, has the role of removing the noise by diffusion, but keeping the edges in the correct locations, or without smoothing them. The proper space to model images with sharp edges is the space of functions of bounded variation, which allows for discontinuities along curves, and while removing the noise.

I will talk about such variational reconstruction techniques, their study on the BV space, together with some experimental results for image reconstruction and segmentation.