51 citations · 211 across the 29 of their papers we have counts for
35 papers
From plans to maps: Nonlocal regularization of optimal transport
Marcello Carioni, Leonardo Del Grande, José A. Iglesias +1
We introduce a nonlocal regularization of optimal transport that bridges Kantorovich and Monge formulations. The regularization penalizes oscillations through an interaction kernel…
Approximation Rates for Metaplectic Neural Networks
Ahmed Abdeljawad, Marcello Carioni, Elena Cordero
In this paper we develop quantitative approximation results for shallow neural networks constructed using a dictionary based on metaplectic operators. First, we extend the concept…
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune +1
Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the o…
Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows
Alex Massucco, Leonardo Del Grande, Marcello Carioni +2
In recent years, transformer architectures have revolutionized the field of language processing, opening the door to previously unforeseen possibilities. However, from a theoretica…
Atomic Gradient Flows: Gradient Flows on Sparse Representations
Christian Amend, Marcello Carioni, Konstantinos Zemas
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the pro…
A Dual Certificate Approach to Sparsity in Infinite-Width Shallow Neural Networks
Leonardo Del Grande, Christoph Brune, Marcello Carioni
In this paper, we study total variation (TV)-regularized training of infinite-width shallow ReLU neural networks, formulated as a convex optimization problem over measures on the u…
An invertible generative model for forward and inverse problems
Christoph Brune, Marcello Carioni, Tristan van Leeuwen +1
We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.e., sampling from the likelihood) and inferen…
Dynamic Optimal Transport with optimal star shaped graphs
Marcello Carioni, Juliane Krautz, Jan-F. Pietschmann
We study an optimal transport problem in a compact convex set where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (…
Sparsity for dynamic inverse problems on Wasserstein curves with bounded variation
Marcello Carioni, Julius Lohmann
We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein- distance. It naturally extends well-known static problems such as las…
Dynamic Optimal Transport with Optimal Preferential Paths
Marcello Carioni, Juliane Krautz, Jan-F. Pietschmann
We study a dynamic optimal transport type problem on a domain that consists of two parts: a compact set (bulk) and a non-intersecting and sufficiently regul…
Perturbation-Aware Distributionally Robust Optimization for Inverse Problems
Floor van Maarschalkerwaart, Subhadip Mukherjee, Malena Sabaté Landman +2
This paper builds on classical distributionally robust optimization techniques to construct a comprehensive framework that can be used for solving inverse problems. Given an estima…
Nonlocal perimeters and variations: Extremality and decomposability for finite and infinite horizons
Marcello Carioni, Leonardo Del Grande, José A. Iglesias +1
We analyze the extremality and decomposability properties with respect to two types of nonlocal perimeters available in the literature, the Gagliardo perimeter based on the eponymo…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…
Exact Sparse Representation Recovery in Signal Demixing and Group BLASSO
Marcello Carioni, Leonardo Del Grande
In this short article we present the theory of sparse representations recovery in convex regularized optimization problems introduced in (Carioni and Del Grande, arXiv:2311.08072,…
Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
Marcello Carioni, Subhadip Mukherjee, Hong Ye Tan +1
Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction opera…
A General Theory for Exact Sparse Representation Recovery in Convex Optimization
Marcello Carioni, Leonardo Del Grande
In this paper, we investigate the recovery of the sparse representation of data in general infinite-dimensional optimization problems regularized by convex functionals. We show tha…
A sparse optimization approach to infinite infimal convolution regularization
Kristian Bredies, Marcello Carioni, Martin Holler +2
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regul…
Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI
Simone Saitta, Marcello Carioni, Subhadip Mukherjee +2
4D flow MRI is a non-invasive imaging method that can measure blood flow velocities over time. However, the velocity fields detected by this technique have limitations due to low r…
Extremal points and sparse optimization for generalized Kantorovich-Rubinstein norms
Marcello Carioni, José A. Iglesias, Daniel Walter
A precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and optimality conditions in general…
Regularization Graphs -- A unified framework for variational regularization of inverse problems
Kristian Bredies, Marcello Carioni, Martin Holler
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow t…
Asymptotic linear convergence of fully-corrective generalized conditional gradient methods
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regula…
End-to-end reconstruction meets data-driven regularization for inverse problems
Subhadip Mukherjee, Marcello Carioni, Ozan Öktem +1
We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framewor…
CAFLOW: Conditional Autoregressive Flows
Georgios Batzolis, Marcello Carioni, Christian Etmann +3
We introduce CAFLOW, a new diverse image-to-image translation model that simultaneously leverages the power of auto-regressive modeling and the modeling efficiency of conditional n…
A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in (Bre…