Work

Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces

Year: 2024

Type: article

Abstract: setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for (possibly nonlinear) infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN. Several numerical simulations, including signal deblurring, illustrate and validate this approach.

Source: Numerical Functional Analysis and Optimization

DOI: 10.1080/01630563.2024.2422064

Authors: Giovanni S. Alberti, Matteo Santacesaria, Silvia Sciutto

Institution: University of Genoa

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: European Commission, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Air Force Office of Scientific Research, HORIZON EUROPE European Research Council

Awards: G1043805054, G2106447494