51 citations · 416 across the 43 of their papers we have counts for
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Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems
Giovanni S. Alberti
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often c…
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…
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…
Optimal reinforcing networks for elastic membranes
Giovanni Alberti, Giuseppe Buttazzo, Serena Guarino Lo Bianco +1
In this paper we study the optimal reinforcement of an elastic membrane, fixed at its boundary, by means of a network (connected onedimensional structure), that has to be found in…
Combining the Runge approximation and the Whitney embedding theorem in hybrid imaging
Giovanni S. Alberti, Yves Capdeboscq
This paper addresses enforcing non-vanishing constraints for solutions to a second order elliptic partial differential equation by appropriate choices of boundary conditions. We sh…