Related papers: Reconstructing hv-Convex Polyominoes from Orthogon…
In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is…
We consider travel time tomography problems involving detection of high contrast, discrete high velocity structures. This results in a discrete nonlinear inverse problem, for which traditional grid-based models and iterative linearized…
In this paper we study an inverse problem in convex geometry, inspired by a problem in materials science. Firstly, we consider the question of whether a Laguerre tessellation (a partition by convex polytopes) can be recovered from only the…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
Plasma tomography consists in reconstructing the 2D radiation profile in a poloidal cross-section of a fusion device, based on line-integrated measurements along several lines of sight. The reconstruction process is computationally…
Efficiently and completely capturing the three-dimensional data of an object is a fundamental problem in industrial and robotic applications. The task of next-best-view (NBV) planning is to infer the pose of the next viewpoint based on the…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
We propose a direct reconstruction algorithm for Computed Tomography, based on a local fusion of a few preliminary image estimates by means of a non-linear fusion rule. One such rule is based on a signal denoising technique which is…
We present a Machine Learning-based method for tomographic reconstruction of dense layered objects, with range of projection angles limited to $\pm $10$^\circ$. Whereas previous approaches to phase tomography generally require two steps,…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…
Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a…
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…
X-ray tomographic reconstruction typically uses voxel basis functions to represent volumetric images. Due to the structure in voxel basis representations, efficient ray-tracing methods exist allowing fast, GPU accelerated implementations.…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
The reconfiguration problem for homomorphisms of digraphs to a reflexive digraph cycle, which amounts to deciding if a `reconfiguration graph' is connected, is known to by polynomially time solvable via a greedy algorithm based on certain…
In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…