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We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…
This work investigates the detection of instabilities that may occur when utilizing deep learning models for image reconstruction tasks. Although neural networks often empirically outperform traditional reconstruction methods, their usage…
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal…
Deep Neural Networks (DNNs) are becoming integral components of real world services relied upon by millions of users. Unfortunately, architects of these systems can find it difficult to ensure reliable performance as irrelevant details like…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
We propose a new method to tackle the mapping challenge from time-series data to spatial image in the field of seismic exploration, i.e., reconstructing the velocity model directly from seismic data by deep neural networks (DNNs). The…
Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…