Improved convergence rates for the Poisson case

Determine whether the convergence rate of the regularized multiplicative updates for Poisson inverse problems can be improved in some cases beyond the established sublinear \(\mathcal{O}(1/k)\) function-value bound.

Background

For Poisson inverse problems with the weighted negative-entropy potential, the paper proves an O(1/k)\mathcal{O}(1/k) convergence rate in function values for the regularized multiplicative updates. Numerical experiments, however, display objective decreases that appear faster than this theoretical bound in some instances.

The authors explicitly formulate the possibility of a sharper rate as a conjecture, while leaving the conditions under which such an improvement holds unresolved.

References

Finally we conjecture that the convergence rate in the Poisson case can be improved for some cases, as numerical experiments show a decrease of the objective faster than the sublinear bound established in theorem \ref{theorem:function-value-rate}.

— Right Bregman proximal gradient with application to Poisson inverse problems *  (2610.06579 - Modrzyk et al., 5 Oct 2026) in Section 6, “Conclusion and discussions”