Efficient sparse probability measures recovery via Bregman gradient

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating ${\mathrm{\ell }}_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our algorithm achieves sparsity by explicitly solving underlying subproblems. We rigorously establish the convergence properties of the algorithm, showcasing its capacity to converge to a local minimum with a convergence rate of $O(1\mathrm{/}k)$ under mild assumptions. To substantiate the efficacy of our algorithm, we conduct numerical experiments, offering a compelling demonstration of its efficiency in recovering sparse probability measures.