Single Basepoint Subdivision Scheme for Manifold-Valued Data: Time-Symmetry without Space-Symmetry
(with Tom Duchamp and Gang Xie)(pdf)(bibtex entry)(talk)(Hindsight)

Invariance Property of Proximity Condition in Nonlinear Subdivision
(with Gang Xie)(pdf)(bibtex entry)(Hindsight)

Multiresolution Analysis on a Spherical Domain Based on a Flexible C2 Subdivision Scheme Over a Valence 3 Extraordinary Vertex
(with Sara Grundel)(pdf)(bibtex entry)

On Donoho's Log-Exp Subdivision Scheme: Choice of Retraction and Time-Symmetry
(with Esfandiar Nava-Yazdani)(pdf)(bibtex entry)

Approximation Order Equivalence Properties of Manifold-Valued Data Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)

Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)(Maple spreadsheet suggesting the breakdown of smoothness equivalence of Donoho's log-exp scheme)

Smoothness Equivalence Properties of Interpolatory Lie Group Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)

Smoothness Equivalence Properties of Manifold-Valued Data Subdivision Schemes based on the Projection Approach
(with Gang Xie)(pdf)(bibtex entry)

Cutting Corners on the Sphere
(pdf)(ps)(bibtex entry)

How Data Dependent is a Nonlinear Subdivision Scheme?
--- A Case Study based on Convexity Preserving Subdivision
(pdf)(ps)(bibtex entry)

Jet Subdivision Schemes on the k-Regular Complex
(with Yonggang Xue and Thomas Duchamp)(pdf)(bibtex entry)(Project Page)

Honeycomb and k-fold Hermite Subdivision Schemes
(with Yonggang Xue)(pdf)(ps)(bibtex entry)

Face-based Hermite Subdivision Schemes
(with Bin Han)(pdf)(ps)(bibtex entry)

On a Linearization Principle for Nonlinear p-mean Subdivision Schemes
(with Gang Xie)(pdf)(ps)(bibtex entry)

Smoothness Analysis of Nonlinear Subdivision Schemes of
Homogeneous and Affine Invariant Type
(with Gang Xie) (pdf)(ps)(bibtex entry)

 Non-Interpolatory Hermite Subdivision Schemes
(with Bin Han and Yonggang Xue)(pdf)(ps)(bibtex entry)

Continuous M-Estimators and their Interpolation by Polynomials
(with Jong-Shi Pang)(pdf)(ps)(bibtex entry)(Matlab Code)

Design of Hermite Subdivision Schemes aided by  Spectral Radius Optimization
(with Bin Han and Michael Overton)(pdf)(ps)(bibtex entry)

Multivariate Refinable Hermite Interpolants
(with Bin Han and Bruce Piper)(pdf)(ps)(bibtex entry) 

A Greedy, Non-recursive Algorithm for Minimum-Time Rendering of Triangle Meshes
(with Gang Lin) (pdf)(ps) 

Parametric Families of Hermite Subdivision Schemes in Dimension 1
(pdf)(ps)(software)(bibtex entry)
Most of the results in this unpublished manuscript are improved and published in:
Approximation Order/Smoothness Tradeoff in Hermite Subdivision Schemes
(pdf)(ps)(bibtex entry)
On the Regularity Analysis of Interpolatory Hermite Subdivision Schemes
(pdf)(ps)(bibtex entry)

Nonlinear "Wavelet Transform" Based on Median-Interpolation
(with David Donoho)(pdf)(ps)
Final version appeared in SIAM Journal on Math. Analysis:
Nonlinear Pyramid Transform Based on Median-Interpolation
 (pdf)(ps)(bibtex entry)
A condensed version appeared in the proceedings of Asilamor '97
(pdf)(ps)

Interpolation of Medians
(with Tim Goodman) (pdf)(ps)(bibtex entry)

Smooth Multiwavelet Duals of Alpert Bases By Moment-Interpolating Refinement
(with David Donoho, Nira Dyn & David Levin) (pdf)(ps)(bibtex entry)

Deslaueriers-Dubuc: Ten Years After
(with David Donoho) (pdf)(ps)(bibtex entry)

Denoising of Electron Tomographic Reconstructions from Biological Specimens
(with Arne Stoschek & Reiner Hegerl) (pdf)(ps)(Proc. of ICASSP 97, Pg. 2793-2796)

Translation- and Direction-Invariant Denoising of 2-D and 3-D Images
(with Arne Stoschek & David Donoho)(Webpage)

The research presented at this page has been supported by NSF grants CCR 9984501 (CAREER Award), DMS 0542237, DMS 0915068 and DMS 1115915.

Research software:
SubdivisionLab

Teaching:
Winter 2012:

Math 312: Probability and Statistics II

Math321: Vector Calculus

Fall 2011

Math 305: Introduction to Optimization Theory

Drexel links:

Term Master Schedule

Final Schedule

Intructional Media Services

MathSciNet