Related papers: Homometric Point Sets and Inverse Problems
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and…
We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenisation theory provides a coarse-grained…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the `most difficult location and scale' at which to cover the set and its…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the…
There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
Recently we have shown that the equivalence classes of metrics on the double of a metric space $X$ form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of $X$, which is more…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables…
Image inpainting consists of filling holes or missing parts of an image. Inpainting face images with symmetric characteristics is more challenging than inpainting a natural scene. None of the powerful existing models can fill out the…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various…