FISTA-Condat-Vu: Automatic Differentiation for Hyperparameter Learning in Variational Models

TL;DR

This paper introduces a memory-efficient method combining FISTA and Condat-Vu algorithms with automatic differentiation to automatically learn hyperparameters in variational models, specifically applied to industrial computed tomography.

Contribution

It presents a novel bilevel learning approach that efficiently estimates hyperparameters in non-smooth variational models using reduced-memory automatic differentiation.

Findings

Effective hyperparameter estimation demonstrated on industrial CT data

Method achieves low memory usage and fast convergence

Numerical implementation validated with experimental data

Abstract

Motivated by industrial computed tomography, we propose a memory efficient strategy to estimate the regularization hyperparameter of a non-smooth variational model. The approach is based on a combination of FISTA and Condat-Vu algorithms exploiting the convergence rate of the former and the low per-iteration complexity of the latter. The estimation is cast as a bilevel learning problem where a first-order method is obtained via reduced-memory automatic differentiation to compute the derivatives. The method is validated with experimental industrial tomographic data with the numerical implementation available.