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The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…

We introduce the use of the Fast Multipole Method (FMM) to speed up gravitational lensing ray tracing calculations. The method allows very fast calculation of ray deflections when a large number of deflectors, $N_*$, is involved, while…

Approximating radiance fields with volumetric grids is one of promising directions for improving NeRF, represented by methods like Plenoxels and DVGO, which achieve super-fast training convergence and real-time rendering. However, these…

In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted…

In quantitative Magnetic Resonance Imaging, traditional methods suffer from the so-called Partial Volume Effect (PVE) due to spatial resolution limitations. As a consequence of PVE, the parameters of the voxels containing more than one…

Neural Radiance Fields (NeRF) has shown great success in novel view synthesis due to its state-of-the-art quality and flexibility. However, NeRF requires dense input views (tens to hundreds) and a long training time (hours to days) for a…

Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin-relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects…

Magnetic resonance fingerprinting (MRF) is a new technique for simultaneously quantifying multiple MR parameters using one temporally resolved MR scan. But its brute-force dictionary generating and searching (DGS) process causes a huge disk…

In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…

The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective…

The generation of high-fidelity view synthesis is essential for robotic navigation and interaction but remains challenging, particularly in indoor environments and real-time scenarios. Existing techniques often require significant…

Neural surface reconstruction aims to reconstruct accurate 3D surfaces based on multi-view images. Previous methods based on neural volume rendering mostly train a fully implicit model with MLPs, which typically require hours of training…

Indoor scene reconstruction from monocular images has long been sought after by augmented reality and robotics developers. Recent advances in neural field representations and monocular priors have led to remarkable results in scene-level…

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast…

Influence function, a technique rooted in robust statistics, has been adapted in modern machine learning for a novel application: data attribution -- quantifying how individual training data points affect a model's predictions. However, the…

The present study seeks to investigate mathematical structures of a multi-frequency subspace migration weighted by the natural logarithmic function for imaging of thin electromagnetic inhomogeneities from measured far-field pattern. To this…

This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…

Transfer Function (TF) generation is a fundamental problem in Direct Volume Rendering (DVR). A TF maps voxels to color and opacity values to reveal inner structures. Existing TF tools are complex and unintuitive for the users who are more…

To effectively retrieve objects from large corpus with high accuracy is a challenge task. In this paper, we propose a method that propagates visual feature level similarities on a Markov random field (MRF) to obtain a high level…

Gaussian Random Fields (GRFs) with Mat\'ern covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness…