Related papers: Dynamic Discrete Tomography
Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e. linking individual particle positions across time series data. The state-of-the-art tracking…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
This paper introduces an efficient procedure to localize user-defined points on the surface of deformable objects and track their positions in 3D space over time. To cope with a deformable object's infinite number of DOF, we propose a…
We consider the problem of segmenting dynamic regions in CrowdCam images, where a dynamic region is the projection of a moving 3D object on the image plane. Quite often, these regions are the most interesting parts of an image. CrowdCam…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
Time-resolved high-resolution X-ray Computed Tomography (4D $\mu$CT) is an imaging technique that offers insight into the evolution of dynamic processes inside materials that are opaque to visible light. Conventional tomographic…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
The reconstruction of an unknown function $f$ from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
Single-molecule tracking is a powerful way to look at the dynamic organization of plasma membranes. However, there are some limitations to its use. For example, it was recently observed, using numerical simulation, that time-averaging…
Numerical simulations of plasma flows are crucial for advancing our understanding of microscopic processes that drive the global plasma dynamics in fusion devices, space, and astrophysical systems. Identifying and classifying particle…
The Rytov approximation has been commonly used to obtain reconstructed images for optical tomography. However, the method requires linearization of the nonlinear inverse problem. Here, we demonstrate nonlinear Rytov approximations by…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…