88 citations · 197 across the 19 of their papers we have counts for
15 papers · 1 filter
Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition
Andrea Ebner, Jürgen Frikel, Dirk Lorenz +2
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…
Sparse aNETT for Solving Inverse Problems with Deep Learning
Daniel Obmann, Linh Nguyen, Johannes Schwab +1
We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transfo…
Data-consistent neural networks for solving nonlinear inverse problems
Yoeri E. Boink, Markus Haltmeier, Sean Holman +1
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical recons…
Deep synthesis regularization of inverse problems
Daniel Obmann, Johannes Schwab, Markus Haltmeier
Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning met…
Augmented NETT Regularization of Inverse Problems
Daniel Obmann, Linh Nguyen, Johannes Schwab +1
We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a…
Sparse synthesis regularization with deep neural networks
Daniel Obmann, Johannes Schwab, Markus Haltmeier
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an…
NETT Regularization for Compressed Sensing Photoacoustic Tomography
Stephan Antholzer, Johannens Schwab, Johannes Bauer-Marschallinger +2
We discuss several methods for image reconstruction in compressed sensing photoacoustic tomography (CS-PAT). In particular, we apply the deep learning method of [H. Li, J. Schwab,…
Deep learning versus -minimization for compressed sensing photoacoustic tomography
Stephan Antholzer, Johannes Schwab, Markus Haltmeier
We investigate compressed sensing (CS) techniques for reducing the number of measurements in photoacoustic tomography (PAT). High resolution imaging from CS data requires particula…
Photoacoustic image reconstruction via deep learning
Stephan Antholzer, Johannes Schwab, Robert Nuster +1
Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these a…
Deep Learning of truncated singular values for limited view photoacoustic tomography
Johannes Schwab, Stephan Antholzer, Robert Nuster +2
We develop a data-driven regularization method for the severely ill-posed problem of photoacoustic image reconstruction from limited view data. Our approach is based on the regular…
Big in Japan: Regularizing networks for solving inverse problems
Johannes Schwab, Stephan Antholzer, Markus Haltmeier
Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis f…
Deep Null Space Learning for Inverse Problems: Convergence Analysis and Rates
Johannes Schwab, Stephan Antholzer, Markus Haltmeier
Recently, deep learning based methods appeared as a new paradigm for solving inverse problems. These methods empirically show excellent performance but lack of theoretical justific…
NETT: Solving Inverse Problems with Deep Neural Networks
Housen Li, Johannes Schwab, Stephan Antholzer +1
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 proble…
Real-time photoacoustic projection imaging using deep learning
Johannes Schwab, Stephan Antholzer, Robert Nuster +1
Photoacoustic tomography (PAT) is an emerging and non-invasive hybrid imaging modality for visualizing light absorbing structures in biological tissue. The recently invented PAT sy…
A Galerkin least squares approach for photoacoustic tomography
Johannes Schwab, Sergiy Pereverzyev, Markus Haltmeier
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomo…