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The inverse problem of X-tray transforms considers reconstructing functions from some data that are easier to measure, which is typically the integral of that function along geodesics. We prove that if the domain has a foliation structure,…
We develop an algorithm for reconstruction of elastic strain fields from their Longitudinal Ray Transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation…
Reconstructing a 3D object from a 2D image is a well-researched vision problem, with many kinds of deep learning techniques having been tried. Most commonly, 3D convolutional approaches are used, though previous work has shown…
Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…
We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be…
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…
We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
We introduce a Graph Transformer framework that serves as a general inverse physics engine on meshes, demonstrated through the challenging task of reconstructing aerodynamic flow fields from sparse surface measurements. While deep learning…
Inverse rendering in a 3D format denoted to recovering the 3D properties of a scene given 2D input image(s) and is typically done using 3D Morphable Model (3DMM) based methods from single view images. These models formulate each face as a…
In this paper we address the following questions: (i) Let $C\subset \mathbb C^2$ be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is $C$ contained in an algebraic curve? (ii) What can be said of a…
In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure…
Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this…
The calculation of the underground density field from measured gravity data has been done by a variety of methods of varied types. The use of the vector gravity components is here addressed in order to develop one accurate gravity inversion…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…