Jared W. Tanner Oxford University Email: [email protected] Institute Web: people.maths.ox.ac.uk/tanner/

Positions Professor of the Mathematics of Information, Oxford Univ., Mathematics, 08/12-current Professor of the Mathematics of Information, Univ. of Edinburgh, Mathematics, 01/11-08/12 Reader in , Univ. of Edinburgh, Mathematics, 07/09-12/10 Lecturer in Applied Mathematics, Univ. of Edinburgh, Mathematics, 07/07-06/09 Assistant Professor (Warnock endowed chair), Univ. of Utah, Mathematics, 07/06-08/10 NSF Mathematical Sciences Postdoctoral Fellow, Stanford Univ., Statistics, 06/04-07/06 Visiting Assistant Research Professor, Univ. of California, at Davis, Mathematics, 07/02-06/04.

Education Ph.D. in Applied Mathematics, Univ. of California, Los Angeles, June 2002 (Advisor: Eitan Tadmor) : Adaptive High Resolution Recovery of Piecewise Smooth Data From its Spectral Information B.S. in Physics, minors in Chemistry and Mathematics, Univ. of Utah, July 1997

Journal Publications

1. CGIHT: Conjugate Gradient Iterative Hard Thresholding for compressed sensing and comple- tion; Information and Inference: A J. of the IMA, in press. (with Jeffrey D. Blanchard and Ke Wei) 2. Low rank matrix completion by alternating steepest descent methods; Applied and Computational Har- monic Analysis, in press. (with Ke Wei) 3. Conjugate Gradient Iterative Hard Thersholding: observed noise stability for compressed sensing; IEEE Transactions on Signal Processing, Vol. 63(2) (2015) 528-537. (with Jeffrey D. Blanchard and Ke Wei) 4. Performance comparison of greedy algorithms in compressed sensing; Numerical Linear Algebra with Applications, accepted. (with Jeffrey D. Blanchard) 5. Bounds of restricted isometry constants in extreme asymptotics: formulae for Gaussian matrices; Lin- ear Algebra and its Applications, Vol. 441(1) (2014) 88-109. (with Bubacarr Bah) 6. Normalized iterative hard thresholding or matrix completion; SIAM J. on Scientific Computing, Vol. 35(5) (2013) S104-S125. (with Ke Wei) 7. Vanishingly sparse matrices and expander graphs, with application to compressed sensing; IEEE Trans- actions on , Vol. 59(11) (2013) 7491-7508. (with Bubacarr Bah) 8. GPU accelerated greedy algorithms for compressed sensing; Mathematical Programming Computation, Vol. 5(3) (2013) 267-304. (with Jeffrey D. Blanchard) 9. Improved bounds on restricted isometry constants for Gaussian matrices; SIAM Journal on Matrix Analysis, Vol. 31(5) (2010) 2882-2898. (with Bubacarr Bah) 10. Coarse quantization for random interleaved sampling of bandlimited signals; Mathematical Modelling and Numerical Analysis, Vol. 46(3) (2012) 605-618. (with Alexander M. Powell, Yang Wang, and Ozgur Yilmaz) 11. Phase transitions for greedy sparse approximation algorithms; Applied and Computational Harmonic Analysis, Vol. 30(2) (2011) 188-203. (with Jeffrey D. Blanchard, Coralia Cartis, and Andrew Thomp- son) 12. Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing; Philosophical Transactions of The Royal Society A, Vol. 367(1906) (2010) 4273-4293. (with David L. Donoho). 13. Precise undersampling theorems; Proceedings of the IEEE, Vol. 98(6) (2010) 913-924. (with David L. Donoho) 14. Decay properties for restricted isometry constants; IEEE Signal Processing Letters, Vol. 16(7) (2009) 572-575. (with Jeffrey D. Blanchard and Coralia Cartis) 15. Compressed Sensing: How sharp is the RIP; SIAM Review, Vol. 53(1) (2011) 105-125. (with Jeffrey D. Blanchard and Coralia Cartis) 16. Counting the faces of randomly-projected hypercubes and orthants, with applications; Discrete and Computational Geometry, Vol. 43(3) (2010) 522-541. (with David L. Donoho) 17. Exponential bounds implying construction of compressed sensing matrices, error-correcting codes and neighborly polytopes by random sampling; IEEE Transactions on Information Theory, Vol. 56(4) (2010) 2002-2016. (with David L. Donoho) 18. Identification of Matrices having a Sparse Representation; IEEE Transactions on Signal Processing, Vol. 56(11) (2008) 5376-5388. (with Gotz E. Pfander and Holger Rauhut) 19. Counting faces of randomly-projected polytopes when the projection radically lowers dimension; Journal of the AMS, Vol.22(1) (2009) 1-53. (with David L. Donoho) 20. Neighborliness of Randomly-Projected Simplices in High Dimensions; Proceedings of the National Academy of Sciences, Vol. 102(27) (2005) 9452-9457. (with David L. Donoho) 21. Sparse Nonnegative Solutions of Underdetermined Linear Equations by Linear Programming; Proceed- ings of the National Academy of Sciences, Vol. 102(27) (2005) 9446-9451. (with David L. Donoho) 22. Robust reprojection methods for the resolution of Gibbs phenomenon; Applied and Computational Harmonic Analysis, Vol. 20(1) (2006) 3-25. (with Anne Gelb) 23. Fast reconstruction methods for bandlimited functions from periodic nonuniform sampling; SIAM J. on Numerical Analysis, Vol. 44(3) (2006) 1073-1094. (with Thomas Strohmer) 24. Optimal Filter and Mollifier for Piecewise Smooth Spectral Data; Mathematics of Computation, Vol. 75(254) (2006) 767-790. 25. Adaptive Filters for Piecewise Smooth Spectral Data; IMA Journal of Numerical Analysis, Vol. 25(4) (2005) 635-647. (with Eitan Tadmor) 26. Implementations of Shannon’s sampling theorem, a time-frequency approach; Sampling Theory in Signal and Image Processing, Vol. 4(1) (2005) 1-17. (with Thomas Strohmer) 27. Adaptive Mollifiers - High Resolution Recover of Piecewise Smooth Data from its Spectral Information; Foundations of Computational Mathematics, Vol. 2(2) (2002) 155-189. (with Eitan Tadmor) 28. Iterative Reconstruction of Fluorine-18 SPECT Using Geometric Point Response Correction; Journal of Nuclear Medicine, Vol. 39(1) (1998) 124-130. (with Gengsheng L. Zeng, Grant T. Gullberg, Chuanyong Bai, Paul E. Christian, Frederick Trisjono, Edward V.R. Di Bella, and Hugh T. Morgan)

Books and edited volumes

1. The Princeton Companion to Applied Mathematcs; Edited by Nick Higham, 1016pp, (with other asso- ciate editors Mark R. Dennis, Paul Glendinning, Paul A. Martin, and Fadil Santosa)

Refereed Proceedings

1. Large scale iterative hard thresholding on a graphical processing unit; American Institute of Physics Conference Proceedings, Vol. 1281, pp. 1730-1734, September 2010. (with Jeffrey D. Blanchard) 2. Phase transitions for restricted isometry properties; Proceedings of Signal Processing with Adaptive Sparse Structured Representations, April 2009. (with Jeffrey D. Blanchard and Coralia Cartis) 3. Fast reconstruction algorithms for periodic nonuniform sampling with applications to time-interleaved ADCs; Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, April 2007. (with Thomas Strohmer) 4. Thresholds for the Recovery of Sparse Solutions via L1 Minimization; Proceedings of the Conference on Information Sciences and Systems, March 2006. (with David L. Donoho) 5. An Adaptive Order Godunov Type Central Scheme; ”Hyperbolic Problems: Theory, Numerics, Appli- cations”, Proceedings of the 9th International Conference in Pasadena, March 2002 (T. Hou and E. Tadmor, eds.), Springer, 2003, 871-880. (with Eitan Tadmor)

Articles under review

1. Expander `0-decoding. (with Rodrigo Mendoza-Smith)

Prizes, Honors, and Awards - Selected Philip Leverhulme Prize, 2009-2012 Awarded annually to 25 UK researchers under the age of 35, 5 awards in mathematics triannually. Sloan Research Fellow in Science and Technology, 2007-2009 Awarded annually to approx. 20 Fellows in Mathematics from junior faculty in the USA and Canada Monroe H. Martin Prize (Applied Mathematics), IPST - U. of Maryland, 2005 Awarded every five years to two junior faculty for a single authored paper of significant merit NSF Postdoctoral Fellowship in the Mathematical Sciences, 06/04-06/06 Awarded to approximately 35 researchers annually, fully supporting 2 years of research, $108,000 Fox Prize (Numerical Analysis), Institute for Mathematics and its applications, First Place, 2003 Awarded bi-annually to six or seven researchers in Numerical Analysis, under 31 years of age

Editorial Duties Information and Inference: A Journal of the IMA, Founding Editor in Chief, 2011+ Founded upon request, other EICs are Robert Calderbank, David L. Donoho, and John Shawe-Taylor. Applied and Computational Harmonic Analysis, 2012+ SIAM book series “Fundamentals of Algorithms”, editorial board, 2011-2014. Multiscale Modeling and Simulation (SIAM), Associate Editor, 2011+ IEEE Signal Processing Letters, Associate Editor, 2009-2012. IEEE Selected Topics in Signal Processing, Guest Editor, Special issue on Compressive Sensing, Vol. 4(2), 2010.

Leadership Activities Siam membership committee, 2015+ Session Organizer for Foundations of Computational Mathematics 2014 signal processing section. Minisymposium organizer for Inverse Problems (IPTA) 2014 Organizing committee for IMA conference on the mathematical challenges of big data, December 2014. Organizer (with F. Kirwan) of Prospects in Mathematics, 2014 This meeting serves to recruit PhD students across the UK, funded by the LMS and IMA.. Intived by the Council for the Mathematical Sciences to be one of five UK mathematicians to present a topic of mathematical innovation to members of Parliament, Westminster Hall, as part of the National Science and Engineering Week. March 15th 2012. In 2007-11 I have given six short courses (50 hours in 5 countries) on compressed sensing (by invitation): IPAM (Los Angeles), RICAM (Linz), PCMI (Park City), UCL (London), SOCN (K.U. Leuven), IHP (Paris). Organizer (with F. Kirwan) of Prospects in Mathematics, 2014 This meeting serves to recruit PhD students across the UK, funded by the LMS, IMA, and ICMS. Vice President, SIAM UKIE, 2010-12 Session Organizer for Foundations of Computational Mathematics 2011 signal processing section. Chair Organizing committee for SPARS 2011, held at the Univ. of Edinburgh. This is the premier annual meeting on sparse approximation, attended by 170 participants. SPARS conference steering committee member 2011+ Organizer (with I. Gordon) of Prospects in Mathematics, 2010 This meeting serves to recruit PhD students across the UK, funded by the LMS, IMA, and ICMS. Organizer for Scottish Computational Mathematics Symposium, Edinburgh Scotland, 2009. Minisymposium organizer for Warwick Scientific Computing Capstone Conference 2009. Invitor of invited speakers for European Meeting of Statisticians 2009. Special sessions organizer for Sampling Theory and Applications 2009. Technical Program Committee for SPARS09, about 80 participants. Member of the Scientific Committee for the Smith Institute (Oxford) Knowledge Transfer Network for Industrial Maths, since 2007. Organiser for UK Sparse Approximation day meeting November 3rd, International Centre for Mathematical Sciences - Edinburgh. Seven invited speakers, anticipated 35 participants. Chair Organising committee for the 2007 AMS Von Neumann Symposium - Sparse Representations and High Dimensional Geometry. 86 participants, in excess of $40,000 raised from four institutions (NSF, SIAM, AMS, MAA) to fund plenary speakers, invited speakers, and graduate students. Organising committee for three mini-symposium on Compressed Sensing at the 2007 International Congress on Industrial and Applied Mathematics, 12 speakers. Organising committee for IPAM short course May 30 - June 1, 2007 Sparse Representations and High Dimensional Geometry. Eight speakers and 54 participants, over 80% of participants (many international) fully funded.

Grants (grants under £5000 excluded): Industrial CASE doctoral studentship with SELEX-ES, July 2015, £129,000, Principal Investigator. Algorithms for Data Simplicity 2012-13. EPSRC, £39,695, Principle Investigator. Conference funding for SPARS 2011, ICMS £20,000, Principal Investigator. nVIDIA Academic Partnership grant 2010, £6, 500, Principal Investigator. Conference funding for Prospects in Mathematics 2010, LMS £5,000, Principal Investigator. Philip Leverhulme Prize in Mathematics 2008-11, £70, 000, Principal Investigator. EU FP7 Medium-scale research project 2008-11, Univ. of Edinburgh portion £330, 000, core member. Visiting Professorship for Hans Feichtinger (Univ. of Vienna) 2008, Leverhulme Trust. £18, 786, Principal Investigator. High-Dimensional Nonparametric Density Estimation for the Analysis of Images and Shapes 2008-11. National Science Foundation (NSF), $474,000, Co-Principle Investigator. Von Neumann Symposim “Sparse Respresentations and High Dimensional Geometry” 2007, American Mathematical Society $30,000, Principal Investigator. Von Neumann Symposim additional funding, NSF, $10,000, Principal Investigator. Sloan Research Fellowship in Science and Technology 2007-11, $45,000, Principal Investigator. Analog-to-Information 2005. Defense Advanced Research Program Agency, $45, 000, Consultant.

Supervisions Postdoc supervisor for Jeffrey Blanchard, 2007-09, Univ. of Utah continued at Univ. of Edinburgh for 2010 as NSF International Postdoc, currently Assistant Professor Grinnell College, Iowa. PhD supervisor for Bubacarr Bah, 2008-2012, Univ. of Edinburgh (Thesis title: Restriced Isometry Constants in Compressed Sensing), currently postdoc at University of Texas, Austin. PhD co-supervisor for Andrew Thompson, 2008-2012, Univ. of Edinburgh (Thesis title: Quantative Analysis of Algorithms for Compressed Signal Recovery), currently departmental lecturer at Oxford University mathematics institute. PhD supervisor for Ke Wei, 2010-current, Univ. of Oxford Postdoc supervisor for Martin Lotz, 2010-2012, Univ. of Edinburgh funded through Leverhulme Trust Early Career Fellowship. currently Lecturer at the University of Manchester. PhD supervisor for Rodrigo Mendoza-Smith, 2013-current, Univ. of Oxford. PhD co-supervisor (with Dr. Harrington) for Bernadette Stolz, 2015-current, University of Oxford.

Industry/Government Interactions SELEX Galileo - part of a multi-national defence company, with the Edinburgh branch specialising in all areas of imaging and radar. Co-supervised student (Andrew Thompson) participated in an six month internship. The project has continued with commissioning of a prototype Compressed Sensing camera and support of a CASE studentship for algorithm design. Consultant 2009-current. HRL Laboratories - a major research consortium (including Boeing and General Motors) specialising in microelectronics, sensors, materials, information processing, and applied electromagnetics. As part of a Defence Advances Research Program Agency (DARPA) initiative Analog-to-Information I aided research team of eight members at HRL to use Compressed Sensing and assisted in its development for the next generation analog-to-digital converters. Consultant 2005-2007. Calgary Scientific - a high tech company (with over 30 employees) developing mathematical algorithms and software for seismic and medical imaging. Between 2004 and 2008 I was on the Scientific Advisory board. In this capacity I oversee the research direction of senior (PhD.) researchers, review patents, and assist in algorithm development.

Plenary Conference/Workshop Lectures Workshop on Sensing and Analysis of High-Dimensional Data, Durham USA, July 27-29, 2015. Workshop on Sensing and Analysis of High-Dimensional Data, London UK, September 4-5, 2014. Workshop on Statistical Issues in Compressive Sensing, G¨ottingen Germany, November 11-13, 2013. 25th Biennial Conference on Numerical Analysis, Glasgow UK, June 25-28, 2013. SIAM Conference on Applied Linear Algebra, Valencia Spain, June 18-22, 2012. South African Symposium on Numerical and Applied Mathematics, Stellenbosch, Mar. 23-25, 2011. Modern Trends in Optimization and its Application, UCLA, Oct. 11-15, 2010. 2nd Int. Conf. on Numerical Linear Algebra and Optimization, Birmingham UK, Sept. 13-15, 2010. INSPIRE Conference on Information Representation and Estimation, London UK, Sept. 6-8, 2010. Generalized Functions 2010, Novi Sad Serbia, June 3-6, 2010. 2nd Joint Conf. on the Belgian Math. Society and LMS, Leuven Belgium, Dec. 4-5, 2010. Statistique Fonctionnelle et Operatorielle, Dijon France, June. 18-19, 2009. Workshop on Sparsity and Compressive Sensing, Antalya Turkey, Apr. 11, 2009. Sparsity in and Statistics, London England, Apr. 1-3, 2009. Scottish Computational Mathematics Symposium, Edinburgh Scotland, Sep. 10, 2008. New Directions in Tomographic Image Reconstruction, Manchester England, June 30 - July 1, 2008. Nonlinear Approximation Techniques Using L1, Texas USA, May 16-18, 2008. Nonlinear and Adaptive Approximation in High Dimensions, Bad Honnef Germany, Dec. 10-15, 2007. Twentieth Annual Pacific Northwest Numerical Analysis Seminar, British Columbia, Sept. 30, 2006. Sampling Theory and Application, Samsun Turkey, July 10-15, 2005.

Colloquium and Seminar Talks - beginning with most recent Univ. of Bath, Strathclyde Univ., Cardiff Univ., Bristol Univ., Univ. of Manchester, Univ. of Glasgow, Univ. College London, Queen Mary Univ. London, Imperial College London, Univ. of Edinburgh, International Univ. Bremen, Harvard Univ., Arizona State Univ., Brown Univ., Univ. of Maryland College Park, Univ. of Cambridge, Univ. of Oxford, Paris VI, Warwick Univ., Stanford Univ., Univ. of Calgary, Univ. of British Columbia, Simon Frasier Univ., Univ. of Utah, Univ. of Wisconsin Madison, Univ. of California Davis, Rice Univ., California Institute of Technology, Univ. of South Carolina, Univ. of Novi Sad (Serbia), Univ. of Vienna, Lawrence Livermore National Labs, Univ. of California Los Angeles.

Long Term Programs Mathematics of Information, Institute for Mathematics and its Applications, University of Minnesota, September 15 - December 15, 2011. Long Term Visitor. Statistical Theory and Methods for Complex, High-Dimensional Data, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, January - June, 2008. Visiting Fellow. Modern Methods of Time-Frequency Analysis, Erwin Schrodinger Institute, University of Vienna, April - July, 2005. Visiting Fellow. Multiscale Geometry and Analysis in High Dimensions, Institute for Pure & Applied Mathematics, UCLA, September - December, 2004. Core participant.

Departmental / Administrative Service Graduate studies committee, Mathematics Institute, 2014+, University of Oxford MSc. in Modern Applications of Mathematics, external examiner, 2013 - current, University of Bath. Steering committee, EPSRC Centre for doctoral training in Industrially Focused Mathematical Modelling (InFoMM), Mathematics Institute, 2013+, University of Oxford Mathematics Institute Strategy Group, 2013+, University of Oxford Colloquium organiser, Mathematics Institute, 2012+, University of Oxford MSc. in Mathematical Modelling and Scientific Computing, Examiner 2012 - 2015, University of Oxford. College of Science and Eng. Research Training Committee member, 2010 - 2012, Univ. of Edinburgh. Tasked with founding an MSc in Scientific Computing. Full responsibility for all aspects: curriculum, university approval, budget, advertising. Mathematics Postgraduate (Ph.D.) Admissions Officer, Univ. of Edinburgh, 2009 - 2012 Hiring committee, Pure Mathematics Lectureship, Univ. of Edinburgh 2009 Hiring committee, Sir Edmund Whittaker Chair, Univ. of Edinburgh 2009