Page personnelle d'Irène Waldspurger

Irène Waldspurger

I am a CNRS researcher at CEREMADE (Université Paris-Dauphine).

Before that, I was a postdoctoral fellow at MIT Institute for Data, Systems, and Society, working with Philippe Rigollet in the Center for Statistics.

Even before that, I was a PhD student in the DATA team (École normale supérieure, computer science department), under the supervision of Stéphane Mallat. I was at the same time a teaching assistant in the department of mathematics.

Contact: waldspurger (at) ceremade (dot) dauphine (dot) fr

Research

I am interested in inverse problems, especially in phase retrieval, both on the theoretical side (uniquess and stability of the reconstruction) and on the algorithmic side.

I am also interested in machine learning. I notably studied some mathematical properties of the scattering transform.

Curriculum vitae

PhD thesis

Publications

Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs : F. Rakoto Endor, I. Waldspurger (preprint, 2024)
[arXiv pdf]
Projected gradient descent accumulates at Bouligand stationary points : G. Olikier, I. Waldspurger (preprint, 2024)
[arXiv pdf]
Lecture notes on non-convex algorithms for low-rank matrix recovery : I. Waldspurger (Preprint, 2021)
[arXiv pdf]
This text is an intermediate between lecture notes and a review article. It is derived from the lecture notes I wrote in French for my Claude-Antoine Peccot lecture at Collège de France :
Séance 1 Séance 2 Séance 3 Séance 4
Rank optimality for the Burer-Monteiro factorization : I. Waldspurger, A. Waters (SIAM Journal on Optimization, 2020, 30(3), pages 2577-2602)
[arXiv pdf]
Exponential decay of scattering coefficients : I. Waldspurger (Draft)
[Technical report : arXiv pdf]
[Another version, for the SampTA 2017 conference : pdf]
Phase retrieval with random Gaussian sensing vectors by alternating projections : I. Waldspurger (IEEE Transactions on Information Theory, 2018, 64(5), pages 3301-3312)
[Long version : arXiv pdf] [Short version : arXiv pdf] [Code]
Phase retrieval for imaging problems : F. Fogel, I. Waldspurger, A. d'Aspremont (Mathematical Programming computation, 2016, pages 1-25)
[arXiv pdf]
Wavelet methods for shape perception in electro-sensing : H. Ammari, S. Mallat, I. Waldspurger, H. Wang (Contemporary mathematics, 660, 2016, pages 1-21)
[arXiv pdf]
Phase retrieval for wavelet transforms : I. Waldspurger (IEEE Transactions on Information Theory, 63(5), 2017, pages 2993-3009)
[arXiv pdf code and examples]
Phase retrieval for the Cauchy wavelet transform : S. Mallat, I. Waldspurger (Journal of Fourier Analysis and Applications, 21(6), 2015, pages 1251-1309)
[arXiv pdf audio examples]
Phase recovery, MaxCut and complex semidefinite programming : I. Waldspurger, A. d'Aspremont, S. Mallat (Mathematical Programming, 149(1-2), 2015, pages 47-81)
[arXiv pdf code]
(Last code update: December 2015)

Vulgarisation

Notes d'un exposé au séminaire de vulgarisation Mathematic Park,
sur la minimisation de fonctions convexes à gradient lipschitzien
Un article dans Images des mathématiques,
sur la reconstruction de phase
Connexité des ensembles de Julia. RMS, 123, 2013.