  This paper presents an algorithm tailored for the efficient recovery of
sparse probability measures incorporating $\ell_0$-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 $O(1/k)$ 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.
