arXiv subjects

L. Bruni Bruno

Publications and source records attributed to L. Bruni Bruno.

2 recordsLinked to original sources

arXiv2026

pESTO: Iterative p-greedy kernel regression with risk-driven Early STOpping

Kernel-based greedy algorithms select suitable approximation nodes by minimizing point-wise error indicators, such as the power function; in this context, they are usually referred to as p-greedy approaches. In the presence of noisy data, deterministic criteria may fail, as the discrepancy between the true solution and its estimate is influenced by both approximation error and noise amplification, and the balance between the two is unknown. This study explicitly separates these two contributions, which are governed by the power function and a Lebesgue-type term, respectively. These bounds motivate the use of the Stein's unbiased risk estimator (SURE) as a proxy of the mean squared error, which in turn provides a principled and computable stopping criterion for the number of nodes to select in the p-greedy procedure. Numerical experiments demonstrate that this approach effectively balances deterministic accuracy and statistical noise contributions.

stat.ML↗

arXiv2025

Greedy techniques for inverse problems

Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements in the operator codomain, specifically tailored to inverse problems. Our approach employs a two-step scheme combining kernel-based interpolation and extrapolation. Within this framework, greedy schemes can be residual-based, where points are selected according to the current approximation error for a specific target function, or error-based, where points are chosen using a priori error indicators independent of the residual. For the latter, we derive explicit error bounds that quantify the propagation of approximation errors through both interpolation and extrapolation. Numerical applications to solar hard X-ray imaging demonstrate that the proposed greedy sampling strategy achieves high-quality reconstructions using only a few available measurements.

math.NA↗