11 citations · 33 across the 9 of their papers we have counts for
5 papers · 1 filter
Statistical inverse learning problems with random observations
Abhishake Rastogi, Tapio Helin, Nicole Mücke
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regulariza…
Statistical Inverse Problems in Hilbert Scales
Abhishake Rastogi
In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise. The regularizing norm in this schem…
Inverse learning in Hilbert scales
Abhishake Rastogi, Peter Mathé
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regula…
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
Abhishake Rastogi
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is cons…
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Abhishake Rastogi, Gilles Blanchard, Peter Mathé
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider t…