Sparse stochastic processes are continuous-domain processes that are specified as solutions of linear stochastic differential equations driven by white Lévy noise. These processes admit a parsimonious representation in some matched wavelet-like basis. Such models are relevant for image compression, compressed sensing, and, more generally, for the derivation of statistical algorithms for solving ill-posed inverse problems. The hybrid processes of this talk are formed by taking a sum of such elementary processes plus an optional Gaussian component. We apply this hybrid model to the derivation of image reconstruction algorithms from noisy linear measurements. In particular, we derive a hybrid MAP estimator, which is able to successfully reconstruct signals, while identifying the underlying signal components. Our scheme is compatible with classical Tikhonov and total-variation regularization, which are both recovered as limit cases. We present an efficient ADMM implementation and illustrate the advantages of the hybrid model with concrete examples.
By Sylvain Lefèbvre
By Julien Rabin
By Ron Kimmel
By Michael Lindenbaum
By Cécile Louchet
By Michael Unser
By Hermine Biermé
By Pierre Chainais
By Jérémie Bigot
By Gersende Fort
By Remco Duits
By Stéphanie Allassonnière
By Charles Kervrann
By Xavier Descombes
By Marie-Paule Cani
By Irène Kaltenmark
By Joan Glaunès
By Marcelo Pereyra
By Alain Trouvé
By Giulio Biroli
By Giulio Biroli
By Gérard Ben Arous
By Gérard Ben Arous
