924 citations · 2.2k across the 37 of their papers we have counts for
13 papers · 1 filter
Uniform Chebyshev approximations of functions satisfying a variation-type condition: reconstruction of time-varying signals on graphs
Davide Bianchi, Sandra Saliani, Dimitrios Vavitsas
We prove uniform approximation theorems for Chebyshev expansions of continuous functions of two variables. Under a variation-type condition on the square , a continuous f…
Uniformly convex neural networks and non-stationary iterated network Tikhonov (iNETT) method
Davide Bianchi, Guanghao Lai, Wenbin Li
We propose a non-stationary iterated network Tikhonov (iNETT) method for the solution of ill-posed inverse problems. The iNETT employs deep neural networks to build a data-driven r…
Asymptotic spectra of large (grid) graphs with a uniform local structure (part II): numerical applications
Andrea Adriani, Davide Bianchi, Paola Ferrari +1
In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain , . When $Ω…
Graph approximation and generalized Tikhonov regularization for signal deblurring
Davide Bianchi, Marco Donatelli
Given a compact linear operator $\K$, the (pseudo) inverse $\K^\dagger$ is usually substituted by a family of regularizing operators which depends on $\K$ itself. Naturally,…
Graph Laplacian for image deblurring
Davide Bianchi, Alessandro Buccini, Marco Donatelli +1
Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variation…
Compatibility, embedding and regularization of non-local random walks on graphs
Davide Bianchi, Marco Donatelli, Fabio Durastante +1
Several variants of the graph Laplacian have been introduced to model non-local diffusion processes, which allow a random walker to {\textquotedblleft jump\textquotedblright} to no…
Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators
Davide Bianchi
Given a linear self-adjoint differential operator along with a discretization scheme (like Finite Differences, Finite Elements, Galerkin Isogeometric Analysis, etc.),…
Generalized Structure Preserving Preconditioners for Frame-Based Image Deblurring
Davide Bianchi, Alessandro Buccini
We are interested in fast and stable iterative regularization methods for image deblurring problems with space invariant blur. The associated coefficient matrix has a Block Toeplit…
Asymptotic spectra of large (grid) graphs with a uniform local structure
Andrea Adriani, Davide Bianchi, Stefano Serra-Capizzano
We are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain , . We assume to be Lebesgu…
Analysis of the spectral symbol function for spectral approximation of a differential operator
Davide Bianchi
Given a differential operator along with its own eigenvalue problem and an associated algebraic equation $\mathcal{L}^{(n)} \mathbf{u}_n = λ\mathb…
Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts
Yuantao Cai, Marco Donatelli, Davide Bianchi +1
Thresholding iterative methods are recently successfully applied to image deblurring problems. In this paper, we investigate the modified linearized Bregman algorithm (MLBA) used i…
Iterated fractional Tikhonov regularization
Davide Bianchi, Alessandro Buccini, Marco Donatelli +1
Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve th…
Optimal order conditions for filter based regularization methods, with applications to variants of the Tikhonov method
Davide Bianchi, Marco Donatelli, Stefano Serra-Capizzano
We study filter based regularization methods for linear ill-posed problems between Hilbert spaces. We derive optimal order conditions under a-priori choice rules for the regulariza…