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Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance $\epsilon$ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local…
Fourier Ptychographic Microscopy (FPM) is a computational imaging technique that enables high-resolution imaging over a large field of view. However, its application in the biomedical field has been limited due to the long image…
A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posedness of the inverse problem poses a huge challenge to FMT reconstruction. Although end-to-end deep…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…
Density Compensation Function (DCF) is widely used in non-Cartesian MRI reconstruction, either for direct Non-Uniform Fast Fourier Transform (NUFFT) reconstruction or for iterative undersampled reconstruction. Current state-of-the-art…
Reconstruction of PET images is an ill-posed inverse problem and often requires iterative algorithms to achieve good image quality for reliable clinical use in practice, at huge computational costs. In this paper, we consider the PET…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…
The Grassmannian manifold G(k, n) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a…
Training machine learning interatomic potentials that are both computationally and data-efficient is a key challenge for enabling their routine use in atomistic simulations. To this effect, we introduce franken, a scalable and lightweight…
The computational imaging technique of Fourier Ptychographic Microscopy (FPM) enables high-resolution imaging with a wide field of view and can serve as an extremely valuable tool, e.g. in the classification of cells in medical…
The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…