6 papers · 1 filter
Statistical inverse learning and -regularization
Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin +1
We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\…
A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems
Fabian Schneider, Tapio Helin, Leila Taghizadeh
Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive com…
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…
Score-based diffusion models for diffuse optical tomography with uncertainty quantification
Fabian Schneider, Meghdoot Mozumder, Konstantin Tamarov +4
Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed probl…
An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems
Fabian Schneider, Duc-Lam Duong, Matti Lassas +2
Score-based diffusion models (SDMs) have emerged as a powerful tool for sampling from the posterior distribution in Bayesian inverse problems. However, existing methods often requi…
Gradient-Based Non-Linear Inverse Learning
Abhishake, Nicole Mücke, Tapio Helin
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient…