In this paper we formulate the convergence rates of the iteratively regularized Gauss–
Newton method by defining the iterates via convex optimization problems in a Banach space …

We study a non-linear statistical inverse problem, where we observe the noisy image of a
quantity through a non-linear operator at some random design points. We consider the …

We study a constrained optimization problem of stable parameter estimation given some
noisy (and possibly incomplete) measurements of the state observation operator. In order to …

For the Tikhonov regularization of ill-posed nonlinear operator equations, convergence is
studied in a Hilbert scale setting. We include the case of oversmoothing penalty terms, which …

We provide an overview of recent progress in statistical inverse problems with random
experimental design, covering both linear and nonlinear inverse problems. Different …

In this work we analyze the inverse problem of recovering a space-dependent potential
coefficient in an elliptic/parabolic problem from distributed observation. We establish novel …

In Banach spaces, the convergence analysis of iteratively regularized Landweber iteration
(IRLI) is recently studied via conditional stability estimates. But the formulation of IRLI does …

In this work, we introduce a novel two-point Landweber-type method to solve the non-
smooth ill-posed problems in Banach spaces. The method comprises of inner solvers and …

In this paper, we study Tikhonov regularization scheme in Hilbert scales for a nonlinear
statistical inverse problem with general noise. The regularizing norm in this scheme is …

We interpret steady linear statistical inverse problems as artificial dynamic systems with
white noise and introduce a stochastic differential equation system where the inverse of the …