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The growing role of data-driven approaches to scientific discovery has unveiled a large class of models that involve latent transformations with a rigid algebraic constraint. Three-dimensional molecule reconstruction in Cryo-Electron…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two…
Limited-angle computerized tomography stands for one of the most difficult challenges in imaging. Although it opens the way to faster data acquisition in industry and less dangerous scans in medicine, standard approaches, such as the…
Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge…
Determining atomistic structures from characterization data is one of the most common yet intricate problems in materials science. Particularly in amorphous materials, proposing structures that balance realism and agreement with experiments…
Low-dose Computed Tomography is a common issue in reality. Current reduction, sparse sampling and limited-view scanning can all cause it. Between them, limited-view CT is general in the industry due to inevitable mechanical and physical…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
Recovering spherical magnetizations $m$ from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy-Hodge decomposition supplies information on what contributions of the magnetization $m$ are recoverable but…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
This paper presents a novel approach 4DRecons that takes a single camera RGB-D sequence of a dynamic subject as input and outputs a complete textured deforming 3D model over time. 4DRecons encodes the output as a 4D neural implicit surface…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
A central question in General Relativity (GR) is how to determine whether singularities are geometrical properties of spacetime, or simply anomalies of a coordinate system used to parameterize the spacetime. In particular, it is an open…
The conical Radon transform, which assigns to a given function $f$ on $\mathbb R^3$ its integrals over conical surfaces, arises in several imaging techniques, e.g. in astronomy and homeland security, especially when the so-called Compton…
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…
In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The `factoring' approach alleviates this difficulty by deriving a PDE for a new (locally smooth) variable while…
We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…
We study the broken ray transform on $n$-dimensional Euclidean domains where the reflecting parts of the boundary are flat and establish injectivity and stability under certain conditions. Given a subset $E$ of the boundary $\partial…