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A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
Current large-aperture cosmic microwave background (CMB) telescopes have nearly maximized the number of detectors that can be illuminated while maintaining diffraction-limited image quality. The polarization-sensitive detector arrays being…
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
We introduce a numerical scheme for the full multi-species Boltzmann equation based on Hermite spectral method. With the proper choice of expansion centers for different species, a practical algorithm is derived to evaluate the complicated…
This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
Realizing high-throughput aberration-corrected Scanning Transmission Electron Microscopy (STEM) exploration of atomic structures requires rapid tuning of multipole probe correctors while compensating for the inevitable drift of the optical…
Classical lens design minimizes optical aberrations to produce sharp images, but is typically decoupled from downstream computer vision tasks. Existing end-to-end optical design learns optical encoding through joint optimization, but often…
This work deals with special nested objects arising in massive higher order perturbative calculations in renormalizable quantum field theories. On the one hand we work with nested sums such as harmonic sums and their generalizations…
Lucky imaging is a high-resolution astronomical image recovery technique with two classic implementation algorithms, i.e. image selecting, shifting and adding in image space and data selecting and image synthesizing in Fourier space. This…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
High precision astrometry aims at source position determination to a very small fraction of the diffraction image size, in high SNR regime. One of the key limitations to such goal is the optical response variation of the telescope over a…
This paper proposes a new two-step procedure for sparse-view tomographic image reconstruction. It is called RISING, since it combines an early-stopped Rapid Iterative Solver with a subsequent Iteration Network-based Gaining step. So far,…
We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…
Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert…
Lightweight semantic segmentation is essential for many downstream vision tasks. Unfortunately, existing methods often struggle to balance efficiency and performance due to the complexity of feature modeling. Many of these existing…
Computer simulations serve as powerful tools for scientists and engineers to gain insights into complex systems. Less costly than physical experiments, computer experiments sometimes involve large number of trials. Conventional design…
A holographic microscope captures interference patterns, or holograms, that encode three-dimensional (3D) information about the object being viewed. Computation is essential to extracting that 3D information. By wrapping low-level…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…