Related papers: Optical tomography on graphs
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in 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…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
We obtain algorithms for computing Tverberg partitions based on centerpoint approximations. This applies to a wide range of convexity spaces, from the classic Euclidean setting to geodetic convexity in graphs. In the Euclidean setting, we…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
This work presents an unsupervised and semi-automatic image segmentation approach where we formulate the segmentation as a inference problem based on unary and pairwise assignment probabilities computed using low-level image cues. The…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
The photon diffusion equation is solved making use of the Born series for the Robin boundary condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph…
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Mat\'ern-type Gaussian field priors that enable flexible modeling…