HR job title
- Professor
- Contact Info
- 1 979 845 7554
Foucart, Simon Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
I have research interests in compressive sensing; Approximation Theory (especially Spline Functions and Minimal Projections);
computational mathematics; bioinformatics; and data science.
computational mathematics; bioinformatics; and data science.
- Overview
- Publications
- Research
- Teaching
- Background
- Contact
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Overview
Publications
selected publications
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academic article
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Foucart, S., Tadmor, E., & Zhong, M.
(2023).
On the Sparsity of LASSO Minimizers in Sparse Data Recovery. 57(2), 901-919.
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Foucart, S., & Liao, C.
(2023).
Optimal Recovery from Inaccurate Data in Hilbert Spaces: Regularize, But What of the Parameter?. 57(2), 489-520.
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Foucart, S.
(2023).
The sparsity of LASSO-type minimizers. Applied and Computational Harmonic Analysis.
62, 441-452.
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Foucart, S., Liao, C., Shahrampour, S., & Wang, Y.
(2022).
Learning from non-random data in Hilbert spaces: an optimal recovery perspective. 20(1), 5.
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Deregowska, B., Fickus, M., Foucart, S., & Lewandowska, B.
(2022).
On the value of the fifth maximal projection constant. Journal of Functional Analysis.
283(10), 109634-109634.
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Foucart, S.
(2021).
Facilitating OWL norm minimizations. Optimization Letters.
15(1), 263-269.
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Foucart, S.
(2021).
Instances of computational optimal recovery: Refined approximability models. Journal of Complexity.
62, 101503-101503.
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Ettehad, M., & Foucart, S.
(2021).
Instances of Computational Optimal Recovery: Dealing with Observation Errors*. 9(4), 1438-1456.
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Foucart, S., & Li, J.
(2018).
Sparse Recovery from Inaccurate Saturated Measurements. 158(1), 49-66.
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Deregowska, B., Foucart, S., Lewandowska, B., & Skrzypek, L.
(2018).
On the norms and minimal properties of de la Vallee Poussin's type operators. 185(4), 601-619.
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Foucart, S., & Lasserre, J. B.
(2018).
Determining projection constants of univariate polynomial spaces. Journal of Approximation Theory.
235, 74-91.
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Foucart, S., & Lecue, G.
(2017).
An IHT Algorithm for Sparse Recovery From Subexponential Measurements. IEEE Signal Processing Letters.
24(9), 1280-1283.
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Baraniuk, R. G., Foucart, S., Needell, D., Plan, Y., & Wootters, M.
(2017).
Exponential Decay of Reconstruction Error From Binary Measurements of Sparse Signals. IEEE TRANSACTIONS ON INFORMATION THEORY.
63(6), 3368-3385.
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Foucart, S., & Powers, V.
(2017).
Basc: constrained approximation by semidefinite programming. IMA Journal of Numerical Analysis.
37(2), 1066-1085.
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Foucart, S., & Skrzypek, L.
(2017).
On maximal relative projection constants. Journal of Mathematical Analysis and Applications.
447(1), 309-328.
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Foucart, S., & Needham, T.
(2017).
Sparse recovery from saturated measurements (R). Information and Inference.
6(2), 196-212.
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Foucart, S.
(2016).
Computation of Minimal Projections and Extensions. Numerical Functional Analysis and Optimization.
37(2), 159-185.
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Foucart, S.
(2016).
Dictionary-Sparse Recovery via Thresholding-Based Algorithms. Journal of Fourier Analysis and Applications.
22(1), 6-19.
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Bouchot, J., Foucart, S., & Hitczenko, P.
(2016).
Hard thresholding pursuit algorithms: Number of iterations. Applied and Computational Harmonic Analysis.
41(2), 412-435.
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Foucart, S., Minner, M. F., & Needham, T.
(2015).
Sparse disjointed recovery from noninflating measurements. Applied and Computational Harmonic Analysis.
39(3), 558-567.
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Foucart, S., & Koslicki, D.
(2014).
Sparse Recovery by Means of Nonnegative Least Squares. IEEE Signal Processing Letters.
21(4), 498-502.
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Foucart, S.
(2014).
Stability and robustness of l(1)-minimizations with Weibull matrices and redundant dictionaries. Linear Algebra and Its Applications.
441, 4-21.
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Koslicki, D., Foucart, S., & Rosen, G.
(2014).
WGSQuikr: fast whole-genome shotgun metagenomic classification. PLoS ONE.
9(3), e91784-e91784.
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Koslicki, D., Foucart, S., & Rosen, G.
(2013).
Quikr: a method for rapid reconstruction of bacterial communities via compressive sensing. Bioinformatics.
29(17), 2096-2102.
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FOUCART, S., & SOROKINA, T.
(2013).
GENERATING DIMENSION FORMULAS FOR MULTIVARIATE SPLINES. Albanian Journal of Mathematics.
7(1), 25-35.
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Foucart, S.
(2011).
HARD THRESHOLDING PURSUIT: AN ALGORITHM FOR COMPRESSIVE SENSING. SIAM Journal on Numerical Analysis.
49(6), 2543-2563.
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Foucart, S., & Lai, M.
(2010).
Sparse recovery with pre-Gaussian random matrices. Studia Mathematica.
200(1), 91-102.
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Foucart, S.
(2010).
A note on guaranteed sparse recovery via l(1)-minimization. Applied and Computational Harmonic Analysis.
29(1), 97-103.
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Foucart, S., & Gribonval, R.
(2010).
Real versus complex null space properties for sparse vector recovery. COMPTES RENDUS MATHEMATIQUE.
348(15-16), 863-865.
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Foucart, S., Pajor, A., Rauhut, H., & Ullrich, T.
(2010).
The Gelfand widths of l(p)-balls for 0 < p <= 1. Journal of Complexity.
26(6), 629-640.
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Foucart, S.
(2009).
Allometry constants of finite-dimensional spaces: theory and computations. Numerische Mathematik.
112(4), 535-564.
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Foucart, S., Kryakin, Y., & Shadrin, A.
(2009).
On the Exact Constant in the Jackson-Stechkin Inequality for the Uniform Metric. Constructive Approximation.
29(2), 157-179.
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Foucart, S., & Lai, M.
(2009).
Sparsest solutions of underdetermined linear systems via l(q)-minimization for 0 < q <= 1. Applied and Computational Harmonic Analysis.
26(3), 395-407.
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Foucart, S.
(2008).
Open questions around the spline orthoprojector. East Journal on Approximations.
14(2), 241-253.
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Foucart, S.
(2006).
On the value of the max-norm of the orthogonal projector onto splines with multiple knots. Journal of Approximation Theory.
140(2), 154-177.
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Foucart, S.
(2005).
Interlacing property for B-splines. Journal of Approximation Theory.
135(1), 1-21.
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Foucart, S.
(2004).
On the best conditioned bases of quadratic polynomials. Journal of Approximation Theory.
130(1), 46-56.
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Roussel, A. J., & Constable, P. D.
(1999).
Fluid and electrolyte therapy - Preface. Veterinary Clinics of North America - Food Animal Practice.
15(3), XI-XI.
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Foucart, S., Tadmor, E., & Zhong, M.
(2023).
On the Sparsity of LASSO Minimizers in Sparse Data Recovery. 57(2), 901-919.
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book
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Foucart, S.
(2022).
Mathematical Pictures at a Data Science Exhibition. Cambridge University Press (CUP).
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Foucart, S., & Rauhut, H.
(2013).
A Mathematical Introduction to Compressive Sensing. Springer Nature.
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Foucart, S.
(2022).
Mathematical Pictures at a Data Science Exhibition. Cambridge University Press (CUP).
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conference paper
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Foucart, S.
(2017).
Complexity of multivariate problems based on binary information. 227-230.
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Foucart, S., Needell, D., Plan, Y., & Wootters, M.
(2017).
De-biasing low-rank projection for matrix completion. Proceedings of SPIE.
1039417.
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Foucart, S.
(2017).
Flavors of Compressive Sensing. Springer Proceedings in Mathematics and Statistics.
61-104.
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Foucart, S.
(2012).
Sparse Recovery Algorithms: Sufficient Conditions in Terms of Restricted Isometry Constants. Springer Proceedings in Mathematics.
65-77.
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Foucart, S.
(2012).
Stability and Robustness of Weak Orthogonal Matching Pursuits. Springer Proceedings in Mathematics and Statistics.
395-405.
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Foucart, S.
(2017).
Complexity of multivariate problems based on binary information. 227-230.
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institutional repository document
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Foucart, S.
(2022).
Full Recovery from Point Values: an Optimal Algorithm for Chebyshev Approximability Prior
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Foucart, S.
(2022).
The Sparsity of LASSO-type Minimizers
-
Dergowska, B., Fickus, M., Foucart, S., & Lewandowska, B.
(2022).
On the value of the fifth maximal projection constant
-
Foucart, S., & Liao, C.
(2021).
Optimal Recovery from Inaccurate Data in Hilbert Spaces: Regularize, but what of the Parameter?
-
Foucart, S., Tadmor, E., & Zhong, M.
(2020).
On the sparsity of LASSO minimizers in sparse data recovery
-
Ettehad, M., & Foucart, S.
(2020).
Instances of Computational Optimal Recovery: Dealing with Observation Errors
-
Foucart, S., & Koslicki, D.
(2020).
Finer Metagenomic Reconstruction via Biodiversity Optimization
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Foucart, S., & Koslicki, D.
(2020).
Finer Metagenomic Reconstruction via Biodiversity Optimization
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Foucart, S., & Koslicki, D.
(2020).
Finer Metagenomic Reconstruction via Biodiversity Optimization
-
Ettehad, M., & Foucart, S.
(2020).
Instances of Computational Optimal Recovery: Dealing with Observation Errors
-
Foucart, S.
(2020).
Instances of Computational Optimal Recovery: Refined Approximability Models
-
Foucart, S., Liao, C., Shahrampour, S., & Wang, Y.
(2020).
Learning from Non-Random Data in Hilbert Spaces: An Optimal Recovery Perspective
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Foucart, S., & Lasserre, J.
(2019).
Computation of Chebyshev Polynomials for Union of Intervals
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Foucart, S., Gribonval, R., Jacques, L., & Rauhut, H.
(2019).
Jointly Low-Rank and Bisparse Recovery: Questions and Partial Answers
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Daubechies, I., DeVore, R., Foucart, S., Hanin, B., & Petrova, G.
(2019).
Nonlinear Approximation and (Deep) ReLU Networks
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Foucart, S., & Jacques, L.
(2019).
One-Bit Sensing of Low-Rank and Bisparse Matrices
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Foucart, S., Needell, D., Pathak, R., Plan, Y., & Wootters, M.
(2019).
Weighted matrix completion from non-random, non-uniform sampling patterns
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Ettehad, M., & Foucart, S.
(2018).
Approximability Models and Optimal System Identification
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Foucart, S., & Lasserre, J.
(2018).
Determining Projection Constants of Univariate Polynomial Spaces
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Foucart, S., & Subramanian, S.
(2018).
Iterative Hard Thresholding for Low-Rank Recovery from Rank-One Projections
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Baraniuk, R., Foucart, S., Needell, D., Plan, Y., & Wootters, M.
(2016).
One-Bit Compressive Sensing of Dictionary-Sparse Signals
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Baraniuk, R., Foucart, S., Needell, D., Plan, Y., & Wootters, M.
(2014).
Exponential decay of reconstruction error from binary measurements of sparse signals
-
Foucart, S., Pajor, A., Rauhut, H., & Ullrich, T.
(2010).
The Gelfand widths of $ell_p$-balls for $0
-
Foucart, S., Kryakin, Y. u., & Shadrin, A.
(2006).
On the exact constant in Jackson-Stechkin inequality for the uniform metric
-
Foucart, S.
(2022).
Full Recovery from Point Values: an Optimal Algorithm for Chebyshev Approximability Prior
Research
principal investigator on
Teaching
teaching activities
- MATH323 Hnr-linear Algebra Instructor
- MATH491 Research Instructor
- MATH601 Meth Appl Math I Instructor
- MATH664 Seminar Applied Math Instructor
- MATH667 Found And Mtds Approx Instructor
- MATH677 Math Foundations Data Science Instructor
- MATH680 Topics Mathematical Data Sci Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
Background
education and training
- Ph.D. in Mathematics, University of Cambridge - (Cambridge, United Kingdom) 2005
- M.E., Ecole Centrale de Lyon - (Écully, Rhone-Alpes, France) 2001
- B.S. in Mathematics, Sorbonne University - (Paris, France) 1999
awards and honors
- Antelo Devereux Award, conferred by Drexel University - (Philadelphia, Pennsylvania, United States), 2012
Contact
first name
- Simon
has last name
- Foucart
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77845-3368
USA
Other
- foucart@tamu.edu