Brief Research Description:
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 NSF DMS 1112612.
My research was partially supported by the National Science Foundation International Research Fellowship 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: Observed Noise Stability for Compressed Sensing (with Jared Tanner and Ke Wei), IEEE Transactions on Signal Processing, 63(2): 528-537, 2015. (preprint version), (supplementary material)
- CGIHT: Conjugate Gradient Iterative Hard Thresholding for Compressed Sensing and Matrix Completion (with Jared Tanner and Ke Wei), submitted April 2014, (preprint version)
- Selecting Multiple Order Statistics with a Graphics Processing Unit (with Erik Opavsky and Emircan Uysaler), submitted August 2013, (preprint version)
- Greedy Algorithms for Joint Sparse Recovery (with Michael Cermak, David Hanle, and Yirong Jing), IEEE Transactions on Signal Processing, 62(7): 1694-1704, 2014. (preprint version with supplementary material)
- Performance Comparisons of Greedy Algorithms in Compressed Sensing (with Jared Tanner), Numerical Linear Algebra with Applications, Wiley Early View, July 2014, (preprint version)
- Toward Deterministic Compressed Sensing, Proceedings of the National Academy of Sciences, 110(4), Early Edition, January 2013,
- GPU Accelerate Greedy Algorithms for Compressed Sensing
(with Jared Tanner), Mathematical Programming Computation, 5(3): 267-304, 2013, (preprint version)
- Fast K-selection Algorithms for Graphics Processing Units
(with Tolu Alabi, Bradley Gordon, and Russel Steinbach), ACM Journal of Experimental Algorithmics, 17(2), Article 4.2, Pages 4.2:1-4.2:29, 2012. (no preprint version due to ACM Authorizer)
- ACM Authorizer Service: this link will take you to the definitive published version of the paper free of charge.
- Associated Software: GGKS: Grinnell GPU k-Selection
- Recovery Guarantees for Rank Aware Pursuits (with Mike E. Davies), IEEE Signal Processing Letters, 19(7), 427-430, July 2012, (preprint version)
- Associated Video of Mike Davies' Presentation on these results from the SMALL Workshop, January 2011.
- Crystallographic Haar-type Composite Dilation Wavelets (with
Kyle R. Steffen), Wavelets and Multiscale Analysis: Theory and
Appilcations, Birkhauser, Cohen and Zayed eds., 2011 (preprint version)
Wavelets (with Ilya A. Krishtal), Mathematics of
Computation, 81, 905-922, 2012 (published online July 2011) (preprint version)
Transitions for Greedy Sparse Approximation
Algorithms (with Coralia Cartis, Jared Tanner, and Andrew
Applied and Computational Harmonic Analysis, 30(2), 188-203, 2011 (preprint version)
Support Sizes of Restricted Isometry Constants, (with Andrew
Thompson) Applied and Computational Harmonic Analysis, 29(3)
382-390, 2010 (preprint version)
- Compressed Sensing: How Sharp is the Restricted Isometry Property?, (with Coralia Cartis and Jared Tanner), SIAM Review, 53(1), 105-125, 2011 (preprint version)
- Extended technical report (formerly titled The restricted isometry property and l^q-regualrization: phase transitions for sparse approximation)
- Decay Properties of Restricted Isometry Constants, (with Coralia Cartis and Jared Tanner), IEEE Signal Processing Letters, 16(7), 572-575, 2009 (preprint version)
- Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets, Journal of Geometric Analysis, 19(1), 19-35, 2009 (preprint version)
- Minimally Supported Frequency Composite Dilation Wavelets, Journal of Fourier Analysis and Applications, 15(6), 796-815, 2009 (preprint version)
Copyrights for the preprint versions are identical to those of the published version. Submitted papers may change copyright holder without notice.
- 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. (This link takes you to the Google Code page.)
- GGMS: Grinnell GPU Multi-Selection (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 GGMS Google Code page redirects you back here since they no longer permit downloads. A GGMS github repository is also available. 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.)
- FOCM 2014, Workshop: Computational Harmonic Analysis, Montevideo, Uruguay, December 2014
- SIAM Annual Meeting, Symposium: Mathematics of Information and Low Dimensional Models, Chicago, IL, July 2014
- ISIT 2014, IEEE International Symposium on Information Theory, Honolulu, HI, July 2014
- PP14, SIAM Parallel Processing for High Performance Computing, Portland, OR, February 2014
- CIPMA 2013: New Trends in Applied Harmonic Analysis, Mar del Plata, Argentina, August 2013
- Iowa-Nebraska Functional Analysis Seminar, Des Moines, IA, November 2012
- SIAM Annual Meeting, Minneapolis, MN, July 2012
- SIAM Southeastern Atlantic Sectional Conference: Minisymposium on Applied Harmonic Analysis, Huntsville, AL, March 2012
- PP12, SIAM Parallel Processing for High Performance Computing, Savannah, GA, February 2012
- MathFest Invited Paper Session: Polyhedra are Everywhere, Lexington, KY, August 2011
- 24th Biennial Conference on Numerical Analysis, Glasgow, Scotland, July 2011
- SPARS11, Workshop on Signal Processing with Adaptive Sparse Structured Representations, Edinburgh, Scotland, June 2011
- Scottish Parallel Computational Mathematics (SPARC-M), St. Andrews, Scotland, November 2010
- International Conference on Numerical Analysis and Applied Mathematics, Rodos, Greece, September 2010
- European Signal Processing Conference, Aalborg, Denmark, August 2010
- SIAM Annual Meeting, Symposium on Compressed Sensing, Pittsburgh, PA, July 2010
- PCMI Summer Program on Image Processing, Park City, Utah, June/July 2010
- 13th International Conference on Approximation Theory, San Antonio, TX, March 2010
- SMALL Meeting, Villars, Switzerland, February 2010
- MathFest and Project NExT Workshop, Portland, OR, August 2009
- 20 Years of Wavelets, Chicago, IL, May 2009
- SPARS'09, Workshop on Signal Processing with Adaptive Sparse Structured Representations, Saint-Malo, France, April, 2009
- AMS-MAA Joint Mathematics Meeting, Washington, D.C., January 2009
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