1 citations · 2 across the 12 of their papers we have counts for
13 papers
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…
On the sample complexity of Fourier compressed sensing: wavelets versus shearlets
Giovanni S. Alberti, Alessandro Felisi, Işıl Güleken
This paper explores the measurement requirements for signal recovery in compressed sensing, comparing the performance of shearlet frames with traditional wavelet systems. Direction…
Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography
Giovanni S. Alberti, Damiana Lazzaro, Serena Morigi +2
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) rem…
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…
MAD: Manifold Attracted Diffusion
Dennis Elbrächter, Giovanni S. Alberti, Matteo Santacesaria
Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy ve…
Deep Unfolding Network for Nonlinear Multi-Frequency Electrical Impedance Tomography
Giovanni S. Alberti, Damiana Lazzaro, Serena Morigi +2
Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of fr…
On the non-convexity issue in the radial Calderón problem
Giovanni S. Alberti, Romain Petit, Clarice Poon +1
A classical approach to the Calderón problem is to estimate the unknown conductivity by solving a nonlinear least-squares problem. It leads to a nonconvex optimization problem whic…
A convex lifting approach for the Calderón problem
Giovanni S. Alberti, Romain Petit, Simone Sanna
The Calderón problem consists in recovering an unknown coefficient of a partial differential equation from boundary measurements of its solution. These measurements give rise to a…
Finite element approximation for quantitative photoacoustic tomography in a diffusive regime
Giovanni S. Alberti, Siyu Cen, Zhi Zhou
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption…
Compressed sensing for inverse problems II: applications to deconvolution, source recovery, and MRI
Giovanni S. Alberti, Alessandro Felisi, Matteo Santacesaria +1
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample co…
Learning sparsity-promoting regularizers for linear inverse problems
Giovanni S. Alberti, Ernesto De Vito, Tapio Helin +3
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an opt…
Localization of point scatterers via sparse optimization on measures
Giovanni S. Alberti, Romain Petit, Matteo Santacesaria
We consider the inverse scattering problem for time-harmonic acoustic waves in a medium with pointwise inhomogeneities. In the Foldy-Lax model, the estimation of the scatterers' lo…
Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems
Giovanni S. Alberti, Luca Ratti, Matteo Santacesaria +1
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori as…