Related papers: Sparse aNETT for Solving Inverse Problems with Dee…
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 regularizer consisting of a penalty term that enforces…
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 are well developed and well understood. Recently, novel…
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 encoder-decoder network by including an $\ell^1$-penalty.…
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT…
We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon-…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
Deep Learning (DL), in particular deep neural networks (DNN), by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering…
We propose a non-stationary iterated network Tikhonov (iNETT) method for the solution of ill-posed inverse problems. The iNETT employs deep neural networks to build a data-driven regularizer, and it avoids the difficult task of estimating…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and…
X-ray Computed Tomography (CT) is widely used in clinical applications such as diagnosis and image-guided interventions. In this paper, we propose a new deep learning based model for CT image reconstruction with the backbone network…
A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…
Sparse autoencoders (SAEs) are one of the main methods to interpret the inner workings of deep neural networks (DNNs), decomposing activations into higher-dimensional features. However, they exhibit critical shortcomings where a large…
Deep learning based solutions are being succesfully implemented for a wide variety of applications. Most notably, clinical use-cases have gained an increased interest and have been the main driver behind some of the cutting-edge data-driven…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…
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, S. Antholzer, and M. Haltmeier. NETT: Solving Inverse…
This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time,…
Autoencoders are certainly among the most studied and used Deep Learning models: the idea behind them is to train a model in order to reconstruct the same input data. The peculiarity of these models is to compress the information through a…
The image reconstruction process in medical imaging can be treated as solving an inverse problem. The inverse problem is usually solved using time-consuming iterative algorithms with sparsity or other constraints. Recently, deep neural…
While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach,…