Stochastic variance reduced gradient method for linear ill-posed inverse problems

Abstract In this paper we apply the stochastic variance reduced gradient method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in Hilbert spaces. Under a priori choices of stopping indices, we derive a convergence rate result when the sought solution satisfies a benchmark source condition and establish a convergence result without using any source condition. To terminate the method in an a posteriori manner, we consider the discrepancy principle and show that it terminates the method in finitely many iteration steps almost surely. Various numerical results are reported to test the performance of the method.