On unifying randomized methods for inverse problems

Abstract This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing problem in a stochastic optimization setting. By doing so, we show that many are variants sample average approximation (SAA). More importantly, able to prove single theoretical result guarantees asymptotic convergence variety methods. Additionally, viewing as an SAA enables us prove, first time, non-asymptotic error holds under consideration. Another important consequence our unified framework is it allows discover new randomization We present numerical results linear, nonlinear, algebraic, PDE-constrained verify provide discussion on apparently different rates behavior