Related papers: Sampling, approximation, and interpolation of diff…

The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…

A computationally inexpensive k.p-based interpolation scheme is developed that can extend the eigenvalues and momentum matrix elements of a sparsely sampled k-point grid into a densely sampled one. Dense sampling, often required to…

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…

This paper introduces discrete differential form spaces over two-dimensional manifold meshes that feature enhanced subdivision-induced inter-element regularity compared to conventional finite element (FE) spaces. This increase in smoothness…

Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite…

The goal of the paper is to obtain analogs of the sampling theorems and of the Riesz-Boas interpolation formulas which are relevant to the Discrete Hilbert and Kak-Hilbert transforms in $l^{2}$.

We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…

We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis…

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…

Kinetic models provide highly accurate descriptions of plasma waves but involve complex integrals that are computationally expensive to solve. To facilitate a fluid-like treatment of the system, we propose rational approximations for both…

Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…

In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring $k$-space interpolation. However, the interpretability of these methods remains an unresolved issue.…

A rigorous homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent effective admittivity with respect to the membrane…

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space…

We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of $K$-means applied in the image space while addressing its clustering performance issues.…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown to be a powerful way to reduce scanning time without sacrificing image quality. MR…