Related papers: Reconstruction from projections using dynamics: No…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
Proton radiography is an important diagnostic method for laser plasma experiments, and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
Proton radiography is a widely-fielded diagnostic used to measure magnetic structures in plasma. The deflection of protons with multi-MeV kinetic energy by the magnetic fields is used to infer their path-integrated field strength. Here, the…
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
Several variants of Neural Radiance Fields (NeRFs) have significantly improved the accuracy of synthesized images and surface reconstruction of 3D scenes/objects. In all of these methods, a key characteristic is that none can train the…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements.…
We propose an approach for dense semantic 3D reconstruction which uses a data term that is defined as potentials over viewing rays, combined with continuous surface area penalization. Our formulation is a convex relaxation which we augment…
Image reconstruction in X ray tomography consists in determining an object from its projections. In many applications such as non destructive testing, we look for an image who has a constant value inside a region (default) and another…
We describe a new method for imaging ultrafast dynamics in condensed matter using inelastic x-ray scattering (IXS). We use the concepts of causality and irreversibility to construct a general solution to the inverse scattering problem (or…
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…