A Mathematical Introduction To Compressive Sensing Pdf

Research

Objective

Find, exploit, and create synergies between

Classical Approximation Theory
Sparse and Structured Recovery
(Deep) Learning
Scientific Computing
Applications in Engineering and Bioinformatics

Activities

Reading seminar on Data Science and Compressive Sensing (link)

Group

Students: Chunyang Liao; Bolong Ma; Srinivas Subramanian
Prospective - apply via the standard departmental process (link)
Postdocs: Josiah Park
Prospective - apply via mathjobs.org

Publications

Author profiles on Google Scholar and MathSciNet.

Books

		S. F., Mathematical pictures at a Data Science exhibition. Cambridge University Press. In production.
		S. F., H. Rauhut, A mathematical introduction to compressive sensing. Applied and Numerical Harmonic Analysis, Birkhäuser. List of errata

Survey

S. F., Flavors of compressive sensing. (doi) (pdf) (reproducible)
Approximation Theory XV: San Antonio 2016, Springer Proceedings in Mathematics & Statistics, vol 201, 61--104.

Preprints

S. F., C. Liao, Optimal recovery from inaccurate data in Hilbert spaces: regularize, but what of the parameter? (pdf) (reproducible)
S. F., C. Liao, S. Shahrampour, Y. Wang, Learning from non-random data in Hilbert spaces: an optimal recovery perspective. (pdf) (reproducible)

Selected Publications

S. F., J. B. Lasserre, Determining projection constants of univariate polynomial spaces.
Journal of Approximation Theory, 235, 74--91, 2018. (doi) (pdf)
R. Baraniuk, S. F., D. Needell, Y. Plan, M. Wootters, Exponential decay of reconstruction error from binary measurements of sparse signals.
IEEE Transactions on Information Theory, 63/6, 3368--3385, 2017. (doi) (pdf)
D. Koslicki, S. F., G. Rosen, Quikr: a method for rapid reconstruction of bacterial communities via compressive sensing. (doi) (pdf)
Bioinformatics, 29/17, 2096--2102, 2013.
S. F., Hard thresholding pursuit: an algorithm for compressive sensing. (doi) (pdf)
SIAM Journal on Numerical Analysis, 49/6, 2543--2563, 2011.
S. F., A. Pajor, H. Rauhut, T. Ullrich, The Gelfand widths of $\ell_p$-balls for $0 < p \le 1$. (doi) (pdf)
Journal of Complexity, 26/6, 629--640, 2010.

Complete papers inventory

Teaching

Current courses

Mathematical Foundations for Data Science (syllabus) (webpage)

Some lecture notes

Foundations and Methods of Approximation (updates required, restricted access) (notes) (codes)
Topics in Mathematical Data Science (supplanted soon, restricted access) (pdf) (codes) (old pdf)
Matrix Analysis (a few lectures missing) (pdf)
Mathematics of Genome Analysis (very incomplete, restricted access) (pdf)
Problem Solving Competitions (selected topics) (pdf)
Compressed Sensing (supplanted by the book written with H. Rauhut) (pdf)
Numerical Mathematics (some updates required) (pdf)

Software

Go to my Github page for download.

MinProj: This is a MATLAB package that computes exact projection constants and minimal projections in coordinate spaces and matrix spaces by solving linear programs, as well as approximate projection constants and minimal projections in polynomial spaces by solving linear or semidefinite programs. It relies on the external packages CVX and Chebfun.
Basc: This is a MATLAB package that computes Best Approximations by Splines under Constraints relative to various norms. Relying on the external packages CVX and Chebfun, it is based on a reformulation of constrained approximation problems as semidefinite programs. (demo)
SplineDim: This is a collection of SAGE routines designed to generate formulas for the dimension of multivariate spline spaces over specific partitions. It is based on Hilbert series computations. The core of the code was written by P. Clarke.
Quikr and WGSQuikr: These computational packages determine the composition of bacteria in an environmental sample analyzed by 16S rRNA amplicon and whole-genome shotgun sequencing technologies. The packages were assembled by D. Koslicki, who also set up this Galaxy server.
HTP: These are three MATLAB routines to be used when trying to recover a sparse vector x or a row-sparse matrix X from the incomplete linear measurements y=Ax or Y=AX. They are implementations of the HTP, FHTP, and SHTP algorithms.
Allometry: This is a collection of MATLAB routines to be used for the computation of exact constants in Banach space geometry.

Vita

Full curriculum vitae available in pdf. Biographical sketch available in txt.

Education

2001-05: PhD, University of Cambridge.
2000-01: Part III of Math Tripos (Distinction), University of Cambridge.
1998-01: Masters of Engineering, Ecole Centrale Paris.

Professional experience

2019-now: Professor of Mathematics, Texas A&M University.
2015-19: Associate Professor of Mathematics, Texas A&M University.
2013-15: Assistant Professor of Mathematics, University of Georgia.
2010-13: Assistant Professor of Mathematics, Drexel University.
2009-10: Postdoctoral Researcher, University of Paris 6.
2006-09: Postdoctoral Researcher, Vanderbilt University.

Visiting positions

January-June 2019: University of Wisconsin-Madison.
June 2018: LAAS-CNRS, Toulouse.
December 2017: Hong Kong University of Science and Technology.
May-June 2015: University of South Florida.
July-August 2009: University of Bonn.

Honors and Awards

2019: Recipient of a Presidential Impact Fellowship, Texas A&M University.
2012: Recipient of the Antelo Devereux Award for Young Faculty, Drexel University.
2010: Journal of Complexity Best Paper Award.

Former Advisees

Mahmood Ettehad (Grad student, Aug 2016-Jul 2020, now postdoc at the IMA, University of Minnesota).
Richard G. Lynch (Postdoc, Aug 2016-Jun 2019, now Instructional Assistant Professor at Texas A&M University).
Jean-Luc Bouchot (Postdoc, Nov 2012-Aug 2014, now Assistant Professor at Beijing Institute of Technology).
David Koslicki (Postdoc, Jan-Sep 2012, now Associate Professor at Pennsylvania State University).
Michael Minner (Grad Student, Sep 2012-Mar 2016, now at Sandia National Lab).

Editorial Boards

Journal of Approximation Theory (Aug 2017-now).
Sampling Theory, Signal Processing, and Data Analysis (Jun 2020-now).
Journal of Numerical Mathematics (May 2021-now).

Contact

Consultation hours: M 9-9:30am, Tu 5-5:30pm, W 11-11:30am, and by appointment.

Office location: 502D Blocker Building
Ireland Street
College Station
Texas

Mailing address: Texas A&M University
Department of Mathematics
3368 TAMU
College Station, TX 77843-3368

E-mail: foucart@tamu.edu or simon.foucart@centraliens.net
Zoom: tamu.zoom.us/my/foucart