In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it a priori} selection of the stopping index and derive the rate of convergence under a benchmark source condition on the sought solution. Numerical results are provided to test the performance of the method.

翻译：本文研究一种用于求解线性不适定反问题的随机动量法。通过适当选择步长与动量系数，我们在停止索引的先验选取条件下证明了该方法的正则化特性，并在目标解满足基准源条件的假设下推导了收敛速率。数值实验结果验证了该方法的性能表现。