3 citations · 9 across the 11 of their papers we have counts for
13 papers
Constructing -Dimensional Monogenic Homogeneous Functions
Hamed Baghal Ghaffari, Jeffrey A. Hogan, Joseph D. Lakey
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension by applying t…
Holistic Processing of Colour Images Using Novel Quaternion-Valued Wavelets on the Plane
Neil D. Dizon, Jeffrey A. Hogan
Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable…
Clifford Prolate Spheroidal wave Functions
Hamed Baghal Ghaffari, Jeffrey A. Hogan, Joseph D. Lakey
In the present paper, we introduce the multidimensional Clifford prolate spheroidal wave functions (CPSWFs) defined on the unit ball as eigenfunctions of a Clifford differential op…
Sampling low-spectrum signals on graphs via cluster-concentrated modes: examples
Joseph D. Lakey, Jeffrey A. Hogan
We establish frame inequalities for signals in Paley--Wiener spaces on two specific families of graphs consisting of combinations of cubes and cycles. The frame elements are locali…
Some adjacency-invariant spaces on products of short cycles
Jeffrey A. Hogan, Joseph D. Lakey
We study certain spaces of vertex functions on the Cayley graphs corresponding to N-fold products of the group of integers modulo m, where m=3, 4, or 5, that are invariant under th…
Properties of Clifford Legendre Polynomials
Hamed Baghal Ghaffari, Jeffrey A. Hogan, Joseph D. Lakey
Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on -dimensional euclidean space ${\mathbb…
A Douglas-Rachford construction of non-separable continuous compactly supported multidimensional wavelets
David Franklin, Jeffrey A. Hogan, Matthew K. Tam
After re-casting the -dimensional wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogo…
Constraint reduction reformulations for projection algorithms with applications to wavelet construction
Minh Dao, Neil Dizon, Jeffrey Hogan +1
We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. This technique involves reformulating the original feasibili…
Centering Projection Methods for Wavelet Feasibility Problems
Neil Dizon, Jeffrey Hogan, Scott B. Lindstrom
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and…
Circumcentering Reflection Methods for Nonconvex Feasibility Problems
Neil Dizon, Jeffrey Hogan, Scott B. Lindstrom
Recently, circumcentering reflection method (CRM) has been introduced for solving the feasibility problem of finding a point in the intersection of closed constraint sets. It is cl…
Spatio-spectral limiting on hypercubes: eigenspaces
Jeffrey A. Hogan, Joseph D. Lakey
The operator that first truncates to a neighborhood of the origin in the spectral domain then truncates to a neighborhood of the origin in the spatial domain is investigated in the…
Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling
Jeffrey A. Hogan, Peter R. Massopust
B-splines , $\Sc q > 1$, of quaternionic order , for short quaternionic B-splines, are quaternion-valued piecewise Müntz polynomials whose scalar parts interpolate the cl…
Quaternionic B-Splines
Jeffrey A. Hogan, Peter Massopust
We introduce B-splines on the line of quaternionic order ( in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions …