11 papers
On the sample complexity of Fourier compressed sensing: wavelets versus shearlets
Giovanni S. Alberti, Alessandro Felisi, IÅıl Güleken
This paper explores the measurement requirements for signal recovery in compressed sensing, comparing the performance of shearlet frames with traditional wavelet systems. Direction…
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…
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…
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…
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…