We consider variational networks for a class of nonlinear-ill-posed least squares inverse problems. These problems are addressed by regularized Gauss-Newton type optimization algorithms where the regularization is learned by a neural network. Two different data-driven approaches will be investigated. First, we present a learned-regularizer integrated into an unrolled Gauss-Newton network. As an alternative approach, we derive a proximal regularized quasi-Newton (PRQN) method and we unfold the PRQN into a deep network which consists of a cascade of multiple proximal mappings. Therefore the proximal operator is learned directly through a variable metric denoiser network. As a practical application, we show how our methods have been successfully applied to solve the parameter identification problem in elliptic PDEs, such as the nonlinear Electrical Impedance Tomography inverse problem.

Learning regularized Gauss-Newton methods / Francesco Colibazzi; Damiana Lazzaro; Serena Morigi; Andrea Samorè. - STAMPA. - (2022). (Intervento presentato al convegno Mathematics of Deep Learning tenutosi a Cambridge, United Kindom nel 28 February 2022 - 4 March 2022).

Learning regularized Gauss-Newton methods

Francesco Colibazzi
Primo
;
Damiana Lazzaro
Secondo
;
Serena Morigi
Penultimo
;
Andrea Samorè
Ultimo
2022

Abstract

We consider variational networks for a class of nonlinear-ill-posed least squares inverse problems. These problems are addressed by regularized Gauss-Newton type optimization algorithms where the regularization is learned by a neural network. Two different data-driven approaches will be investigated. First, we present a learned-regularizer integrated into an unrolled Gauss-Newton network. As an alternative approach, we derive a proximal regularized quasi-Newton (PRQN) method and we unfold the PRQN into a deep network which consists of a cascade of multiple proximal mappings. Therefore the proximal operator is learned directly through a variable metric denoiser network. As a practical application, we show how our methods have been successfully applied to solve the parameter identification problem in elliptic PDEs, such as the nonlinear Electrical Impedance Tomography inverse problem.
2022
Mathematics of Deep Learning
Learning regularized Gauss-Newton methods / Francesco Colibazzi; Damiana Lazzaro; Serena Morigi; Andrea Samorè. - STAMPA. - (2022). (Intervento presentato al convegno Mathematics of Deep Learning tenutosi a Cambridge, United Kindom nel 28 February 2022 - 4 March 2022).
Francesco Colibazzi; Damiana Lazzaro; Serena Morigi; Andrea Samorè
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/878821
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