Celebratio Mathematica

R. Balan and I. Daubechies: “Optimal stochastic encoding and approximation schemes using Weyl–Heisenberg sets,” Chapter 11, pp. 259–320 in Advances in Gabor analysis. Edited by H. G. Feichtinger and T. Strohmer. Applied and Numerical Harmonic Analysis. Birkhäuser (Boston), 2003. MR 1955939 Zbl 1033.94001 incollection

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“Applied harmonic analysis and sparse approximation: Abstracts from the workshop held June 10–16, 2012.” Edited by I. Daubechies, G. Kutyniok, H. Rauhut, and T. Strohmer. Oberwolfach Rep. 9 : 2 (2012), pp. 1759–1843. MR 3156721 Zbl 1349.00127 article

Applied harmonic analysis and sparse approximation are highly active research areas with a lot of recent exciting developments. Their methods have become crucial for a wide range of applications in technology and science, such as signal and image processing. Understanding of the underlying mathematics has grown vastly. Interestingly, there are a lot of connections to other fields, such as convex optimization, probability theory and Banach space geometry. Yet, many problems in these areas remain unsolved or even unattacked. The workshop intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations.

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“Applied harmonic analysis and sparse approximation: Abstracts from the workshop held August 16–22, 2015.” Edited by I. Daubechies, G. Kutyniok, H. Rauhut, and T. Strohmer. Oberwolfach Rep. 12 : 3 (2015), pp. 2189–2263. MR 3444265 Zbl 1380.00060 article

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations.

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“Applied harmonic analysis and sparse approximation: Abstracts from the workshop held March 25–31, 2018.” Edited by I. Daubechies, G. Kutyniok, H. Rauhut, and T. Strohmer. Oberwolfach Rep. 15 : 1 (2018), pp. 723–792. Zbl 1409.00083 article

Massive data sets have their own architecture. Each data source has an inherent structure, which we should attempt to detect in order to utilize it for applications, such as denoising, clustering, anomaly detection, knowledge extraction, or classification. Harmonic analysis revolves around creating new structures for decomposition, rearrangement and reconstruction of operators and functions — in other words inventing and exploring new architectures for information and inference. Two previous very successful workshops on applied harmonic analysis and sparse approximation have taken place in 2012 and in 2015. This workshop was the an evolution and continuation of these workshops and intended to bring together world leading experts in applied harmonic analysis, data analysis, optimization, statistics, and machine learning to report on recent developments, and to foster new developments and collaborations.

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