14 citations · 29 across the 11 of their papers we have counts for
12 papers
Trust your source: quantifying source condition elements for variational regularisation methods
Martin Benning, Tatiana A. Bubba, Luca Ratti +1
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide…
On a fixed-point continuation method for a convex optimization problem
Jean-Baptiste Fest, Tommi Heikkilä, Ignace Loris +4
We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other pr…
On the reconstruction of cavities in a nonlinear model arising from cardiac electrophysiology
Elena Beretta, M. Cristina Cerutti, Dario Pierotti +1
In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac e…
Shearlet-based regularization in statistical inverse learning with an application to X-ray tomography
Tatiana A. Bubba, Luca Ratti
Statistical inverse learning theory, a field that lies at the intersection of inverse problems and statistical learning, has lately gained more and more attention. In an effort to…
Learning the optimal Tikhonov regularizer for inverse problems
Giovanni S. Alberti, Ernesto De Vito, Matti Lassas +2
In this work, we consider the linear inverse problem , where is a known linear operator between the separable Hilbert spaces and , is a random v…
Convex regularization in statistical inverse learning problems
Tatiana A. Bubba, Martin Burger, Tapio Helin +1
We consider a statistical inverse learning problem, where the task is to estimate a function based on noisy point evaluations of , where is a linear operator. The funct…
Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography
Tatiana A. Bubba, Mathilde Galinier, Matti Lassas +3
We propose a novel convolutional neural network (CNN), called DONet, designed for learning pseudodifferential operators (DOs) in the context of linear inverse problems. Our s…
On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements
Elena Beretta, Cecilia Cavaterra, Luca Ratti
In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model, we determine an asymptotic expansion of the pertu…
A posteriori error estimates for the monodomain model in cardiac electrophysiology
Luca Ratti, Marco Verani
We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplifi…
A phase-field approach for the interface reconstruction in a nonlinear elliptic problem arising from cardiac electrophysiology
Elena Beretta, Luca Ratti, Marco Verani
In this work we tackle the reconstruction of discontinuous coefficients in a semilinear elliptic equation from the knowledge of the solution on the boundary of the domain, an inver…
On the inverse problem of detecting cardiac ischemias: theoretical analysis and numerical reconstruction
Elena Beretta, Cecilia Cavaterra, Maria Cristina Cerutti +2
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-depende…
A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem
Elena Beretta, Andrea Manzoni, Luca Ratti
In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of intere…