A new strategy for convergence rates of non-stationary asymptotical regularization method for linear inverse problems

Abstract We study the convergence rates of a non-stationary asymptotical regularization method (ARM) for linear statistical inverse problems from indirect noisy measurements. The convergence rates are usually derived under some range-type source conditions, which are difficult to be verified rigorously in general, especially for the models governed by some partial differential equations. We shall propose a new strategy associated with conditional stability estimates (CSEs) to obtain the error bounds in terms of mean-squared error. To the best of our knowledge, it is the first time to apply CSEs for convergence rates in statistical inverse problems. As an application, an inverse source problem in a wave equation is considered and its CSE is verified rigorously, and therefore the convergence rates are derived immediately. Several numerical experiments for the inverse source problem are also provided to demonstrate the accuracy and efficiency of the non-stationary ARM.