Learning to solve TV regularized problems with unrolled algorithms
Résumé
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the ℓ1-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually solved using iterative algorithms such as proximal gradient descent, primal-dual algorithms or ADMM. However, such methods can require a very large number of iterations to converge to a suitable solution. In this paper, we accelerate such iterative algorithms by unfolding proximal gradient descent solvers in order to learn their parameters for 1D TV regularized problems. While this could be done using the synthesis formulation, we demonstrate that this leads to slower performances. The main difficulty in applying such methods in the analysis formulation lies in proposing a way to compute the derivatives through the proximal operator. As our main contribution, we develop and characterize two approaches to do so, describe their benefits and limitations, and discuss the regime where they can actually improve over iterative procedures. We validate those findings with experiments on synthetic and real data.
Fichier principal
main.pdf (706.15 Ko)
Télécharger le fichier
bold_deconv_loss_comp_0_1.pdf (207.2 Ko)
Télécharger le fichier
bold_deconv_loss_comp_0_8.pdf (207.07 Ko)
Télécharger le fichier
comparison_AL_A.pdf (296.04 Ko)
Télécharger le fichier
comparison_prox_tv_loss.pdf (273.88 Ko)
Télécharger le fichier
iter_loss_comp_0_1.pdf (210.32 Ko)
Télécharger le fichier
iter_loss_comp_0_8.pdf (210.28 Ko)
Télécharger le fichier
loss_comparison.pdf (213.61 Ko)
Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)