Recovering a function or high-dimensional parameter vector from indirect measurements is
a central task in various scientific areas. Several methods for solving such inverse problems …

Inverse problems with Poisson data arise in many photonic imaging modalities in medicine,
engineering and astronomy. The design of regularization methods and estimators for such …

Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

This paper surveys variational approaches for image reconstruction in dynamic inverse
problems. Emphasis is on variational methods that rely on parametrized temporal models …

Total variation methods and similar approaches based on regularizations with ℓ 1-type
norms (and seminorms) have become a very popular tool in image processing and inverse …

In this paper we present a generalized Deep Learning-based approach for solving ill-posed
large-scale inverse problems occuring in medical image reconstruction. Recently, Deep …

We describe a general strategy for the verification of variational source condition by
formulating two sufficient criteria describing the smoothness of the solution and the degree …

The authors study parameter choice strategies for the Tikhonov regularization of nonlinear ill-
posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining …

In this paper, we study a Tikhonov-type method for ill-posed nonlinear operator equations
g†= F (u†), where g† is an integrable, non-negative function. We assume that data are …

The stable solution of ill-posed non-linear operator equations in Banach space requires
regularization. One important approach is based on Tikhonov regularization, in which case a …