My research lies in the broad area of applied and computational harmonic analysis, specifically compressed sensing, matrix completion, composite dilation wavelets, and scientific computing with graphics processing units.
My research is partially supported by the National Science Foundation under the current award:
RUI: Efficient Algorithms for Compressed Sensing and Matrix Completion, NSF DMS 1620390.
My research was previously supported by the National Science Foundation under the following awards:
RUI: Large-scale Algorithm Analysis and GPU Implementations for Compressed Sensing and Matrix Completion, NSF DMS 1112612
International Research Fellowship Program: Stability and Algorithm Analysis in Compressed Sensing, NSF OISE 0854991.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Conjugate Gradient Iterative Hard Thresholding for Structured Sparsity, submitted June 2022. (preprint)
Newton's Method without Division (with Marc Chamberland), American Mathematical Monthly, accepted June 2022. (preprint)
Salvaging College Registrations During COVID-19 via Integer Programming (with Marc Chamberland), Mathematics Magazine, accepted February 2022. (preprint)
GAGA: GPU Accelerated Greedy Algorithms for Compressed Sensing (with Jared Tanner). A software package for solving large compressed sensing problems with millions of unknowns in fractions of a second by exploiting the power of graphics processing units. This software is the focus of GPU Accelerated Greedy Algorithms for Compressed Sensing and was used to generate the data in Performance Comparisons of Greedy Algorithms in Compressed Sensing. (This link takes you to gaga4cs.org.)
GGKS: Grinnell GPU k-Selection (with Tolu Alabi, Bradley Gordon, and Russel Steinbach). This code provides the source code for the k-selection algorithms discussed in Fast K-selection Algorithms for Graphics Processing Units. These algorithms rapidly select a single order statistic from large vectors. (To download: right-click, save-as.)
GGMS: Grinnell GPU Multi-Selection (v2.1.0) (with Erik Opavsky and Emircan Uysaler). This code provides the source code for the algorithm bucketMultiSelect discussed in Selecting Multiple Order Statistics with a Graphics Processing Units. bucketMultiSelect is capable of selecting thousands of order statistics from large vectors in less time than sorting the vector on the GPU. (To download: right-click, save-as.)
The power data readings from the REDD data set used in "Selecting Multiple ..." is available as a .zip file.
MatricialFilterCode.zip (with Kyle Steffen). This zip file of Matlab code verifies the matricial filters equations in the papers Crystallographic Haar-type ... and one example in Matricial Filters ...
This code requires the symbolic toolbox. (To download: right-click, save-as.)
Copyrights for the preprint versions are identical to those of the published version. Submitted papers may change copyright holder without notice.