174 citations · 317 across the 16 of their papers we have counts for
18 papers
Fast and accurate log-determinant approximations
Owen Deen, Colton River Waller, John Paul Ward
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based o…
Discretization and Optimization using Graphs: One-Dimensional Algorithm
John Paul Ward
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining fun…
Locally supported, quasi-interpolatory bases for the approximation of functions on graphs
Edward J. Fuselier, John Paul Ward
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flo…
The Critical Smoothness of Generalized Functions
Julien Fageot, John Paul Ward
For each integrability parameter , the critical smoothness of a periodic generalized function , denoted by is the supremum over the smoothness paramet…
Interpolating splines on graphs for data science applications
John Paul Ward, Francis J. Narcowich, Joseph D. Ward
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential deca…
Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters
Julien Fageot, Michael Unser, John Paul Ward
A convolution algebra is a topological vector space that is closed under the convolution operation. It is said to be inverse-closed if each element of w…
Angular Accuracy of Steerable Feature Detectors
Zsuzsanna Püspöki, Arash Amini, Julien Fageot +2
The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated…
The n-term Approximation of Periodic Generalized Lévy Processes
Julien Fageot, Michael Unser, John Paul Ward
In this paper, we study the compressibility of random processes and fields, called generalized Lévy processes, that are solutions of stochastic differential equations driven by …
A characterization of the Radon-Nikodym property for vector valued measures
Piotr Mikusinski, John Paul Ward
If are positive measures on a measurable space and are elements of a Banach space such that $\sum_{n=1}^\infty \|v_n\| μ_n(X)…
Splines are Universal Solutions of Linear Inverse Problems with Generalized-TV regularization
Michael Unser, Julien Fageot, John Paul Ward
Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operato…
On The Continuous Steering of the Scale of Tight Wavelet Frames
Zsuzsanna Püspöki, John Paul Ward, Daniel Sage +1
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets…
On the Besov Regularity of Periodic Lévy Noises
Julien Fageot, Michael Unser, John Paul Ward
In this paper, we study the Besov regularity of Lévy white noises on the -dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as ge…
Harmonic Singular Integrals and Steerable Wavelets in
John Paul Ward, Michael Unser
Here we present a method of constructing steerable wavelet frames in that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz…
Decay properties of Riesz transforms and steerable wavelets
John Paul Ward, Kunal Narayan Chaudhury, Michael Unser
The Riesz transform is a natural multi-dimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. M…
Operator-Like Wavelet Bases of
Ildar Khalidov, Michael Unser, John Paul Ward
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions th…
Hessian Schatten-Norm Regularization for Linear Inverse Problems
Stamatios Lefkimmiatis, John Paul Ward, Michael Unser
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The pro…
Error Estimates for Approximation by Sobolev Splines and Wendland Functions on
John Paul Ward
It is known that a Green's function-type condition may be used to derive rates for approximation by radial basis functions (RBFs). In this paper, we introduce a method for obtainin…
On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials
A. P. Veselov, J. P. Ward
The behaviour of real zeroes of the Hurwitz zeta function is investigated. It is shown that has no real zeroes $…