51 citations · 388 across the 44 of their papers we have counts for
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Analytic inverse problems with finitely many random measurements
Giovanni S. Alberti, Damiano Poletti, Simone Sanna +1
While infinite-dimensional inverse problems are traditionally analyzed assuming continuous data, practical applications rely on finitely many discrete measurements. Recent determin…
Inverse problems for quasi-linear elliptic systems modeling electrolysers
Giovanni S. Alberti, Wadim Gerner, Matteo Santacesaria
We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we stu…
Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements
Giovanni S. Alberti, Paolo Campodonico, Matteo Santacesaria
Photoacoustic tomography (PAT) is an emerging imaging modality that aims at measuring the high-contrast optical properties of tissues by means of high-resolution ultrasonic measure…
Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data
Giovanni S. Alberti, Matteo Santacesaria
We prove a local Lipschitz stability estimate for Gel'fand-Calderón's inverse problem for the Schrödinger equation. The main novelty is that only a finite number of boundary input…
On an inverse Robin spectral problem
Matteo Santacesaria, Toshiaki Yachimura
We consider the problem of the recovery of a Robin coefficient on a part of the boundary of a bounded domain from the principal eigenvalue and the boundar…
Infinite-dimensional inverse problems with finite measurements
Giovanni S. Alberti, Matteo Santacesaria
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measu…
Calderón's Inverse Problem with a Finite Number of Measurements
Giovanni S. Alberti, Matteo Santacesaria
We prove that an potential in the Schrödinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided…
Note on Calderón's inverse problem for measurable conductivities
Matteo Santacesaria
The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation is the subject of this note. A new strategy,…
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT
Elena Beretta, Stefano Micheletti, Simona Perotto +1
In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal…
Propagation and recovery of singularities in the inverse conductivity problem
Allan Greenleaf, Matti Lassas, Matteo Santacesaria +2
The ill-posedness of Calderón's inverse conductivity problem, responsible for the poor spatial resolution of Electrical Impedance Tomography (EIT), has been an impetus for the deve…
A Holder-logarithmic stability estimate for an inverse problem in two dimensions
Matteo Santacesaria
The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know th…
Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions
Matteo Santacesaria
We study the inverse problem of determining a real-valued potential in the two-dimensional Schrödinger equation at negative energy from the Dirichlet-to-Neumann map. It is known th…
New global stability estimates for the Calderón problem in two dimensions
Matteo Santacesaria
We prove a new global stability estimate for the Gel'fand-Calderón inverse problem on a two-dimensional bounded domain or, more precisely, the inverse boundary value problem for th…
Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems
Roman Novikov, Matteo Santacesaria
We consider two inverse problems for the multi-channel two-dimensional Schrödinger equation at fixed positive energy, i.e. the equation at fixed positive , whe…
Global stability for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
Matteo Santacesaria
We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calderón inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value proble…
Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
Roman Novikov, Matteo Santacesaria
We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation , , where is a…
A global stability estimate for the Gel'fand-Calderon inverse problem in two dimensions
Roman Novikov, Matteo Santacesaria
We prove a global logarithmic stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional domain.
On an inverse problem for anisotropic conductivity in the plane
Gennadi Henkin, Matteo Santacesaria
Let be a bounded domain with smooth boundary and a smooth anisotropic conductivity on . Starting from the Dirichlet-to-Neumann operator…