Wavelets in the deep learning era - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Mathematical Imaging and Vision Year : 2022

Wavelets in the deep learning era

Abstract

Sparsity-based methods, such as wavelets, have been the state of the art for more than 20 years for inverse problems before being overtaken by neural networks. In particular, U-nets have proven to be extremely effective. Their main ingredients are a highly nonlinear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available datasets for training. It is far from obvious to say which of these three ingredients has the biggest impact on the performance. While the many stages of nonlinearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity-based approaches. The aim of our study is to push the limits of sparsity to use, similarly to U-nets, massive learning and large datasets, and then to compare the results with U-nets. We present a new network architecture, called learnlets, which conserves the properties of sparsity-based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation. We evaluate the model on image denoising tasks. Our conclusion is that U-nets perform better than learnlets on image quality metrics in distribution, while learnlets have better generalization properties.
Fichier principal
Vignette du fichier
learnlets_journal_paper.pdf (5.96 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03346892 , version 1 (16-09-2021)

Licence

Identifiers

Cite

Zaccharie Ramzi, Kevin Michalewicz, Jean-Luc Starck, Thomas Moreau, Philippe Ciuciu. Wavelets in the deep learning era. Journal of Mathematical Imaging and Vision, 2022, 65, ⟨10.1007/s10851-022-01123-w⟩. ⟨hal-03346892⟩
320 View
372 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More