LAZZARETTI , Marta

We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L^{p(.)}(\Omega)$. Due to their intrinsic space-variant properties, such spaces can be naturally used as solution space and combined...

We propose a continuous non-convex variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution in order to overcome light diffraction barriers. Namely, we consider a variation of the Continuous Exact $\ell_0$ (CEL0) penalty recently introduced to relax the $\ell_2-\ell_0$ problem where a weighted-$\ell_2$ data fidelity...

International audience

International audience

International audience

We propose a scaled adaptive version of the Fast Iterative Soft-Thresholding Algorithm, named S-FISTA, for the efficient solution of convex optimization problems with sparsity-enforcing regularization. S-FISTA couples a non-monotone backtracking procedure with a scaling strategy for the proximal–gradient step, which is particularly effective in...

We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces ppnq pRq. Such non-standard spaces have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in...

Off-the-grid regularisation has been extensively employed over the last decadein the context of ill-posed inverse problems formulated in the continuous settingof the space of Radon measures M(Ω). These approaches enjoy convexity andcounteract the discretisation biases as well the numerical instabilities typical oftheir discrete counterparts. In...