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An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon method, using examples from both astronomical and non-astronomical applications.
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide results o
There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such kn
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the co
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame thresholdi
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from obs