Reinterpreting EMML as Mirror Descent for Constrained Maximum Likelihood Estimation
Abstract
The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise.In this paper, we reinterpret EMML as a mirror descent method applied to a reparametrized objective function. This perspective allows us to incorporate convex constraints into the algorithm through appropriately chosen Bregman projections, while preserving the multiplicative structure of the EMML updates to ensure computational efficiency. We then establish the convergence of the resulting algorithm toward a solution of the constrained maximum-likelihood problem. Numerical experiments on hyperspectral unmixing problems demonstrate that the constrained EMML converges in fewer iterations than the classical EMML.
Cite
@article{arxiv.2602.13063,
title = {Reinterpreting EMML as Mirror Descent for Constrained Maximum Likelihood Estimation},
author = {Antonin Clerc and Ségolène Martin and Nicolas Papadakis and Gabriele Steidl},
journal= {arXiv preprint arXiv:2602.13063},
year = {2026}
}
Comments
The assumptions underlying the convergence conditions require substantial revision, and the associated proofs need to be reworked to rigorously establish convergence of the MD method. While the current results are expected to remain valid, their justification is incomplete in the present version and must be supported by alternative, more robust arguments