Related papers: The Factorization method for three dimensional Ele…
Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…
LiDAR-based 3D object detection has made impressive progress recently, yet most existing models are black-box, lacking interpretability. Previous explanation approaches primarily focus on analyzing image-based models and are not readily…
We propose a new acquisition geometry for electron density reconstruction in three dimensional X-ray Compton imaging using a monochromatic source. This leads us to a new three dimensional inverse problem where we aim to reconstruct a real…
A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large…
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number…
A non-iterative method of reconstruction is proposed from data of MRI system and of a harmonic electro-magnetic field at Larmor frequency. The method is based on the exact analytic formula for the contrast source function. A geometric…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
Factorization machine (FM) is a prevalent approach to modeling pairwise (second-order) feature interactions when dealing with high-dimensional sparse data. However, on the one hand, FM fails to capture higher-order feature interactions…
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical significance and wide-ranging applications. Despite extensive…
In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…
Grazing incidence waves incident onto a surface will almost always be completely reflected. Here, we focus on removing reflection at grazing incidence, adopting the factorisation method from quantum mechanics and applying it to the…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…