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WPA1. Mathematical analysis of the total variation based denoising problem: total variation flows.

The role of total variation in developing image models and algorithms has been increasing since its introduction by Rudin-Osher-Fatemi in 1992. To understand its qualitative properties, we propose to compute explicit solutions of the total variation denoising problem. We propose also to study the regularity properties of its solutions of and of solutions of the minimizing total variation flow. We will study primal-dual algorithms and work on the development of fast algorithms to solve these problems. Finally, we will consider its application to image segmentation and disparity computation in stereo.

WPA2. Non-local variational formulation of the image inpainting problem and High Angular Resolution Diffusion Imaging: a multi-scale geometrical point of view.

The unification of geometric and texture-based methods is a very interesting research trend that can lead to the development of robust and performant inpainting methods. Diffusion Magnetic Resonance Imaging is a biomedical acquisition protocol that produces in vivo images of fibrous tissue, such as brain white matter and muscle. Popular approaches utilise Diffusion Tensor Imaging (DTI) or, more generally, High Angular Resolution Diffusion Imaging (HARDI), to obtain information on local water diffusivity profiles, which are believed to be indicative of underlying fibrous structures. Tractography and connectivity analysis can be employed to extract candidate fibres in the form of geodesic curves, or congruences of such curves emanating from a fiducial origin or region of interest in a Hamilton-Jacobi framework.

WPA3. Adaptive and directional local processing in Image processing

We propose to go beyond of this idea (proposed by Bruckstein et al in 1994) in several different directions. In particular connecting this idea with a different approach to image processing and analysis, closely related to and influenced by a multi-scale view that comes from diffusion-based “scale-space” ideas: an approach based on a new way of doing harmonic analysis by wavelet bases.

WPA4. Variational methods in Image Processing: application to ill-posed problems.

An application of variational methods is related to optical flow based upon mean curvature will be developed with special application to models which initially are ill-posed (as it is the case of the Perona-Malik equation) but for which it is possible to get a coherent theory on their solutions, at least for suitable initial data.






ESR 1 This position has been filled

Madrid (18)



 Total variation based denoising problem

ESR 2 This position has been filled


Zurich (12)





Rome (6)


ESR 4 This position has been filled

Haifa (23)


 Non-local variational formulation of the image inpainting problem and High Angular Resolution Diffusion Imaging: a multi-scale geometrical point of view



Paris (12)


ESR 6 This position has been filled

Eindhoven (12)



 Adaptive and directional local processing

ESR7 This position has been filled


Haifa (12)





Paris (12)


ESR 9 This position has been filled

Rome (30)


Variational methods: ill-posed problems

ESR 10


Zurich  (6)



Total=143 Researcher-months




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