Related papers: A faster, high precision algorithm for calculating…
Purpose: To simulate effective transverse relaxation ($T_2^*$) as a part of MR simulation. $T_2^*$ consists of reversible ($T_2^{\prime}$) and irreversible ($T_2$) components. Whereas simulations of $T_2$ are easy, $T_2^{\prime}$ is not…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
MRI images of the same subject in different contrasts contain shared information, such as the anatomical structure. Utilizing the redundant information amongst the contrasts to sub-sample and faithfully reconstruct multi-contrast images…
We formulate both Markov chain Monte Carlo (MCMC) sampling algorithms and basic statistical physics in terms of elementary symmetries. This perspective on sampling yields derivations of well-known MCMC algorithms and a new parallel…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which…
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has…
We outline a procedure for jointly sampling substitution matrices and multiple sequence alignments, according to an approximate posterior distribution, using an MCMC-based algorithm. This procedure provides an efficient and simple method by…
We propose three novel metrics for evaluating the accuracy of a set of estimated camera poses given the ground truth: Translation Alignment Score (TAS), Rotation Alignment Score (RAS), and Pose Alignment Score (PAS). The TAS evaluates the…
Strong gravitational lensing by irregular mass distributions, such as galaxy clusters, is generally not well quantified by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
Purpose: To develop a method for rapid sub-millimeter T1, T2, T2* and QSM mapping in a single scan using multi-contrast Learned Acquisition and Reconstruction Optimization (mcLARO). Methods: A pulse sequence was developed by interleaving…
New improvements to compute Mie scattering quantities are presented. They are based on a detailed analysis of the various sources of error in Mie computations and on mathematical justifications. The algorithm developed on these improvements…
We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the…