[Probabilidad-Estadistica-Seminario] Fwd: [Ingenieria.matematica] Tres charlas invitadas — 28 y 30 de julio, FIng UdelaR (salón 727-Gris)

[Laura Aspirot]

Estimadas y estimados,

En el marco de la visita del Prof. Luca Calatroni (Associate Professor,
Computer Science, Bioengineering, Robotics and Systems Engineering
Department (DIBRIS), University of Genoa) y sus estudiantes de doctorado
Simone Sanna y Christian Daniele, quienes dictarán un curso sobre
problemas inversos en procesamiento de imágenes computacional en FIng
la semana del 27 de julio
(https://eva.fing.edu.uy/course/view.php?id=2028), tenemos el agrado de
anunciarles tres charlas abiertas a todas las personas interesadas.

A continuación encontrarán la infomación sobre las tres charlas.
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Martes 28/7, 14h00–15h00 - Salón 727-Gris, piso 7, FIng UdelaR

Charla de Luca Calatroni

Título: Beyond Early Stopping: Self-Tuning Regularisation for
Photon-Counting Microscopy

Resumen: Richardson–Lucy (RL)-type algorithms are the workhorse of
photon-counting image reconstruction, underpinning deconvolution, Image
Scanning Microscopy (ISM) and its three-dimensional extension s$^2$ISM.
Despite their statistical optimality under Poisson noise, these methods
exhibit semi-convergence, making reconstruction quality highly dependent
on heuristic early stopping. In this talk, I will present two
complementary regularisation frameworks that replace heuristic parameter
tuning with statistically grounded alternatives. The first formulates
ISM and s$^2$ISM reconstruction as Bayesian MAP estimation with
sparsity-promoting priors and automatic parameter selection via the
Poisson Residual Whiteness Principle. The second introduces a
morphology-agnostic strategy that exploits independent noise
realisations to distinguish reproducible image content from stochastic
fluctuations, eliminating the need for explicit object priors. Together,
these approaches demonstrate how the statistical structure of
photon-counting measurements can be leveraged to obtain stable,
self-tuning reconstructions across a broad range of fluorescence
microscopy modalities.
-------------------------

Jueves 30/7, 14h00–16h00 - Salón 727-Gris, piso 7, FIng UdelaR

Charla de Simone Sanna de 14h00 a 15h00

Título: Analytic inverse problems with finite random measurements

Resumen: While infinite-dimensional inverse problems are traditionally
analyzed assuming continuous data, practical applications rely on finite
discrete measurements. Recent deterministic approaches establish that
unknowns belonging to a d-dimensional space can be uniquely recovered
from finitely many discrete measurements. However, for severely
ill-posed problems, such as the Calderón problem and inverse
scattering, the deterministic sample complexity inherently scales
exponentially with d. We demonstrate how to improve these estimates
using random sampling. By exploiting the analytic geometry of the
forward maps, we prove that 2d+1 random scalar measurements are
sufficient to guarantee exact recovery almost surely.

Charla de Christian Daniele de 15h00 a 16h00

Título: Deep Equilibrium models for Poisson Imaging Inverse problems
via Mirror Descent

Resumen: Solving imaging inverse problems under non-Gaussian noise
conditions remains a significant challenge due to the complex,
non-linear nature of the data distribution. Deep Equilibrium Models
(DEQs) are implicit neural networks with fixed points that have recently
gained attention for learning image regularization functionals. This is
particularly true in settings involving Gaussian fidelities, where
assumptions on the forward operator ensure the contractiveness of
standard (proximal) Gradient Descent operators. In this talk, we extend
the application of DEQs to Poisson inverse problems, where the data
fidelity term is more appropriately modeled by the Kullback–Leibler
divergence. To this end, we introduce a novel DEQ formulation based on
Mirror Descent, defined in terms of a tailored non-Euclidean geometry
that naturally adapts to the structure of the data term. This approach
enables the learning of neural regularizers within a principled training
framework. We derive sufficient conditions and establish refined
convergence results to guarantee the stability of the learned
reconstruction scheme, while proposing computational strategies that
enable both efficient training and parameter-free inference. Numerical
experiments show that our method outperforms traditional model-based
approaches and performs comparably to Bregman Plug-and-Play methods,
while mitigating their typical drawbacks, such as time-consuming
hyper-parameter tuning. Furthermore, these numerical results demonstrate
the capability of our approach to generalize to unseen forward operators
and noise levels.
-------------------------

¡Las y los esperamos!

Saludos cordiales,

Pablo y Lara
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