Convergent multiplicative algorithms for regularized Poisson inverse problems

Title

Convergent multiplicative algorithms for regularized Poisson inverse problems

Speaker

Thibaut Modrzyk - CREATIS laboratory (Lyon, France)

Abstract

Poisson inverse problems arise naturally in low-count imaging modalities such as emission tomography, confocal microscopy, and astronomical imaging.

In this setting, the Kullback–Leibler divergence provides a more faithful data-fidelity than a Gaussian least-squares model, but it also leads to optimization problems that fall outside the standard Lipschitz-smooth framework.

This talk will focus on multiplicative update algorithms, also known as Richardson–Lucy or MLEM.

Although these methods have been used in imaging for more than fifty years, their regularization and convergence analysis remain delicate.

I will first present a Plug-and-Play regularization of multiplicative updates based on the Majorization–Minimization framework.

The resulting algorithm combines Poisson-adapted data-fidelity steps with Gaussian denoisers and provably converges to a critical point of an explicit energy, while remaining competitive on deconvolution, PET, and low-dose CT experiments.

In a second part, I will present my recent work on applying Bregman divergences and the relative smoothness framework to the Poisson setting.

This work has led us to study a new Bregman proximal algorithm, and provides a natural extension of multiplicative updates to the regularized setting.

Bio

Thibaut Modrzyk is a PhD candidate in signal processing at CREATIS, Lyon.

His research focuses on optimization algorithms for Poisson inverse problems, in particular multiplicative methods for image reconstruction.

He is especially interested in learning-based regularization and diffusion models, with applications in emission tomography.

He is also a maintainer of DeepInverse, an open-source Python library for imaging inverse problems.

When

Thursday, June 18th, 12:00

Where

room 322, DIMA/DIBRIS, Via Dodecaneso 35