Jeff Blanchard's Research Page

Research

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 was previously supported by the National Science Foundation under the following awards:
- RUI: Efficient Algorithms for Compressed Sensing and Matrix Completion, NSF DMS 1620390.
- 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.

Publications:

Journal Publications

Conjugate Gradient Iterative Hard Thresholding for Structured Sparsity, IEEE Open Journal of Signal Processing, Vol. 3, 16 pages, September 2022. (journal version is open access)
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)
On Rank Awareness, Thresholding, and MUSIC for Joint Sparse Recovery (with Caleb Leedy and Yimin Wu), Applied and Computational Harmonic Analysis, 48(1): 482-495, January 2020. (preprint)
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, January 2015. (preprint version), (supplementary material)
CGIHT: Conjugate Gradient Iterative Hard Thresholding for Compressed Sensing and Matrix Completion (with Jared Tanner and Ke Wei), Information and Inference: a journal of the IMA, 4(4): 289-327, December 2015. (journal version is open access)
Selecting Multiple Order Statistics with a Graphics Processing Unit (with Erik Opavsky and Emircan Uysaler), ACM Transactions on Parallel Computing, 3(2), Article 10, Pages 10:1-10:23, July 2016. (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.
  - Selecting Multiple Order Statistics with a Graphics Processing Unit
    Jeffrey D. Blanchard, Erik Opavsky, Emircan Uysaler
    ACM Transactions on Parallel Computing (TOPC), 2016
    
    frames are not supported
- Associated Software: GGMS: Grinnell GPU Multi-Selection
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, 22(2): 254-282, 2015 (Wiley Early View, July 2014), (preprint version)
Toward Deterministic Compressed Sensing, Proceedings of the National Academy of Sciences, 110(4), Early Edition, January 2013, (preprint version)
GPU Accelerated Greedy Algorithms for Compressed Sensing (with Jared Tanner), Mathematical Programming Computation, 5(3): 267-304, 2013, (preprint version)
- Associated Software: GAGA: GPU Accelerated Greedy Algorithms for Compressed Sensing
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.
  - Fast k-selection algorithms for graphics processing units, Tolu Alabi, Jeffrey D. Blanchard, Bradley Gordon, Russel Steinbach
    Journal of Experimental Algorithmics (JEA), 2012
    
    frames are not supported
- 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)
Matricial Filters and Crystallographic Composite Dilation Wavelets (with Ilya A. Krishtal), Mathematics of Computation, 81, 905-922, 2012 (published online July 2011) (preprint version)
Phase Transitions for Greedy Sparse Approximation Algorithms (with Coralia Cartis, Jared Tanner, and Andrew Thompson) Applied and Computational Harmonic Analysis, 30(2), 188-203, 2011 (preprint version)
On 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)

Proceedings

Large Scale Iterative Hard Thresholding on a Graphical Processing Unit, (with Jared Tanner) Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, September 2010.
Pushing the RIP Phase Transition in Compressed Sensing, (with Andrew Thompson) Proceedings of the European Signal Processing Conference, August 2010. (preprint version)
Phase Transitions for Restricted Isometry Properties, (with Coralia Cartis and Jared Tanner) Proceedings of Signal Processing with Adaptive Sparse Structured Representations, April 2009

Thesis

Existence and Accuracy Results for Composite Dilation Wavelets, Washington University in St. Louis, 2007. Chapter 2 of this thesis has been improved in the papers beginning Minimally Supported Frequency above.

Software

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.)
- GGMS: Grinnell GPU Multi-Selection (v2.0.0) A version with a single reduction phase and device wide sorting; also includes library specific versions of the algorithm.
- GGMS: Grinnell GPU Multi-Selection (v1.0.0) The original package which only uses the Thrust library.
- 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.

Selected Conferences:

International Congress on Industrial and Applied Mathematics (ICIAM 2015), Symposium: Mathematics of Information and Low Dimensional Models (Session 1), (Session 2), (Session 3), Beijing, China, August 2015
International Symposium on Mathematical Programming, Pittsburgh, PA, July 2015
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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