Related papers: Optical tomography on graphs
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…
Convergence and stability results for the inverse Born series [Moskow and Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings between Banach spaces. We show that by restarting the inverse Born series one obtains a…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Anomaly detection is a crucial task in complex distributed systems. A thorough understanding of the requirements and challenges of anomaly detection is pivotal to the security of such systems, especially for real-world deployment. While…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
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…
In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different frequencies. An…
We formulate and analyze difference equations on graphs analogous to time-independent diffusion equations arising in the study of diffuse scattering in continuous media. Moreover, we show how to construct solutions in the presence of weak…
We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering…