We present a unifying view on various statistical estimation techniques including
penalization, variational, and thresholding methods. These estimators are analyzed in the …

This paper discusses the properties of certain risk estimators recently proposed to choose
regularization parameters in ill-posed problems. A simple approach is Stein's unbiased risk …

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 …

Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal
Lepskiĭ-Inspired Tuning - IOPscience Skip to content IOP Science home Accessibility Help …

We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent
unbiased measurements of the right-hand side are available. A natural approach is to take …

We investigate a posteriori parameter choice methods for filter based regularizations f ̂ α=
q α T∗ TT∗ Y ̂ f_ α= q_ α\left (T^* T\right) T^* Y in statistical inverse problems Y= Tf+ σξ …

An inverse problem motivated by packet sampling in communication networks and edge
sampling in directed complex networks is studied through the operator perspective. The …

In this work, we propose a new criterion for choosing the regularization parameter in
Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower …

In this note we consider spectral cut-off estimators to solve a statistical linear inverse
problem under arbitrary white noise. The truncation level is determined with a recently …

In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the
loss function is the Kullback–Leibler divergence, in order to define a regularization …