Concept
Square-integrable function
Related publications (33)
Stability of Image-Reconstruction Algorithms
Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla
Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...
2023The inductive bias of deep learning: Connecting weights and functions
Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...
EPFL2023Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023TV-based reconstruction of periodic functions
Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...
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