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Last name: CALATRONI
First name: Luca
Email: Luca.CALATRONI@univ-cotedazur.fr
Institution: UCA
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In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly convex composite optimisation problems. In particular, we address here the sole (non-strongly) convex...
We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed algorithm is combined with an adaptive (non-monotone) backtracking strategy, which allows for the adjustment of...
In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly convex composite optimisation problems. In particular, we address here the sole (non-strongly) convex...
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...
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A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface diffusion flows. Its numerical discretization is challenging due to the degeneracy of the mobilities, which...
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...
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We propose a new class of exact continuous relaxations of l0-regularized criteria involving non-quadratic data terms such as the Kullback-Leibler divergence and the logistic regression, possibly combined with an l2 regularization. We first prove the existence of global minimizers for such problems and characterize their local minimizers.Then,...
The resolution of optimization problems involving the ℓ0 pseudo-norm has proven to be of importance in signal processing and machine learning applications for selecting relevant variables. Among the vast class of existing approaches dealing with the intrinsic NP-hardness of such problems, continuous (possibly non-convex) relaxations have been...
We consider a variational model for single-image super-resolution based on the assumption that the image gradient of the target image is sparse. To promote jump sparsity, we use an isotropic and anisotropic $\ell^{0}$ inverse Potts gradient regularisation term combined with a quadratic data fidelity, similarly as studied in [1] for general...
We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $ℓ^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in \cite{Storath14} for...
We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional...
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with strongly convex regularization and general data-fit functions. We develop an inertial approach of which we analyze both convergence and stability properties. Using tools from inexact proximal calculus, we prove early...
We propose an adaptive, smooth, non-convex and sparsity-promoting variational model for singleimage super-resolution of real murine Optical Coherence Tomography (OCT) data. We follow a sparse-representation approach where sparsity is modelled with respect to a suitable dictionary generated from high-resolution OCT data. To do so, we employ...
Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ℓ 1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic...
We propose an automatic parameter selection strategy for variational image super-resolution of blurred and down-sampled images corrupted by additive white Gaussian noise (AWGN) with unknown standard deviation. By exploiting particular properties of the operators describing the problem in the frequency domain, our strategy selects the optimal...
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...
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