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Publications


Books

S. Foucart, H. Rauhut, A mathematical introduction to compressive sensing.
Applied and Numerical Harmonic Analysis, Birkhaüser.

Papers

All preprints are pdf files. Numbers in smaller font refer to proceeding papers.

[23] P. Clarke, S. Foucart, Symbolic spline computations.
Submitted.
Preprint
[22] J.-L. Bouchot, S. Foucart, P. Hitczenko, Hard thresholding pursuit algorithms: number of iterations.
Submitted.
Preprint / Reproducibles
[21] D. Koslicki, S. Foucart, G. Rosen, Quikr: a method for rapid reconstruction of bacterial communities via compressive sensing.
To appear, Bioinformatics.
Article / Preprint
[20] F. Balabdaoui, S. Foucart, J. Wellner, On the Hermite spline conjecture and its connection to k-monotone densities.
Preprint
[19] S. Foucart, Stability and robustness of $\ell_1$-minimizations with Weibull matrices and redundant dictionaries.
In press, Linear Algebra and its Applications.
Article / Preprint
[18] S. Foucart, T. Sorokina, Generating dimension formulas for multivariate splines.
Albanian Journal of Mathematics, 7/1, 24--35, 2013.
Article / Preprint
An earlier version was entitled On the dimension of multivariate spline spaces, especially on Alfeld splits.
[17] S. Foucart, Stability and robustness of weak orthogonal matching pursuits.
Recent Advances in Harmonic Analysis and Applications, Springer Proceedings in Mathematics & Statistics, vol. 25, 395--405.
Proceedings / Preprint
[16] S. Foucart, Recovering jointly sparse vectors via hard thresholding pursuit.
Proceedings of SampTA 2011, Singapore.
Proceedings / Preprint
[15] A. Cohen, R. DeVore, S. Foucart, H. Rauhut, Recovery of functions of many variables via compressive sensing.
Proceedings of SampTA 2011, Singapore.
Proceedings / Preprint
[14] S. Foucart, Hard thresholding pursuit: an algorithm for compressive sensing.
SIAM Journal on Numerical Analysis, 49/6, 2543--2563, 2011.
Article / Preprint
[13] S. Foucart, Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants.
Approximation Theory XIII: San Antonio 2010, Springer Proceedings in Mathematics, vol. 13, 65--77.
Proceedings / Preprint
[12] S. Foucart, A. Pajor, H. Rauhut, T. Ullrich, The Gelfand widths of $\ell_p$-balls for $0 < p \le 1$.
Journal of Complexity, 26/6, 629--640, 2010.
Article / Preprint
[11] S. Foucart, R. Gribonval, Real versus complex null space properties for sparse vector recovery.
Comptes Rendus de l'Academie des Sciences, 348/15-16, 863--865, 2010.
Article / Preprint
[10] S. Foucart, A note on guaranteed sparse recovery via $\ell_1$-minimization.
Applied and Computational Harmonic Analysis, 29/1, 97--103, 2010.
Article / Preprint
[9] S. Foucart, M.-J. Lai, Sparse recovery with pre-Gaussian random matrices.
Studia Mathematica, 200, 91--102, 2010.
Article / Preprint
[8] S. Foucart, Allometry constants of finite-dimensional spaces: theory and computations.
Numerische Mathematik, 112/4, 535--564, 2009.
Article / Preprint
[7] S. Foucart, M.-J. Lai, Sparsest solutions of underdetermined linear systems via $\ell_q$-minimization for $0 < q \le 1$.
Applied and Computational Harmonic Analysis, 26/3, 395--407, 2009.
Article / Preprint
[6] S. Foucart, Open questions around the spline orthoprojector.
East Journal on Approximations, 14/2, 241--253, 2008.
Preprint
[5] S. Foucart, Some comments on the comparison between condition numbers and projection constants.
Approximation Theory XII: San Antonio 2007, M. Neamtu and L. L. Schumaker (eds.), Nashboro Press, 2008, 143--156.
Preprint
[4] S. Foucart, Yu. Kryakin, A. Shadrin, On the exact constant in Jackson-Stechkin inequality for the uniform metric.
Constructive Approximation, 29/2, 157--179, 2009.
Article / Preprint
[3] S. Foucart, On the value of the max-norm of the orthogonal projector onto splines with multiple knots.
Journal of Approximation Theory, 140/2, 154--177, 2006.
Article / Preprint
[2] S. Foucart, Interlacing property for B-splines.
Journal of Approximation Theory, 135/1, 1--21, 2005.
Article / Preprint
[1] S. Foucart, On the best conditioned bases of quadratic polynomials.
Journal of Approximation Theory, 130/1, 46--56, 2004.
Article / Preprint
[PhD thesis] Small-normed projections onto polynomial and spline spaces.
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Last modified: June 25, 2013.