Stochastic gradient descent for linear inverse problems in variable exponent Lebesgue spaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

Stochastic gradient descent for linear inverse problems in variable exponent Lebesgue spaces

Abstract

We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces ppnq pRq. Such non-standard spaces have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in signal and image processing applications. Compared to its use in Hilbert settings, however, the application of SGD in the Banach setting of ppnq pRq is not straightforward, due, in particular to the lack of a closed-form expression and the non-separability property of the underlying norm. In this manuscript, we show that SGD iterations can effectively be performed using the associated modular function. Numerical validation on both simulated and real CT data show significant improvements in comparison to SGD solutions both in Hilbert and other Banach settings, in particular when non-Gaussian or mixed noise is observed in the data.
Fichier principal
Vignette du fichier
main.pdf (1.02 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04031273 , version 1 (15-03-2023)

Identifiers

Cite

Marta Lazzaretti, Zeljko Kereta, Claudio Estatico, Luca Calatroni. Stochastic gradient descent for linear inverse problems in variable exponent Lebesgue spaces. IX conference on Scale Space and Variational Methods in Computer Vision 2023, May 2023, Santa margherita di Pula, Italy. pp.457-470, ⟨10.1007/978-3-031-31975-4_35⟩. ⟨hal-04031273⟩
32 View
30 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More