In July 2024, the FWF-funded project „DISCO – Discrepancy and universal discretization of continuous frames“ started at the Acoustics Research Institute of the OeAW. In this project, Nicki Holighaus and his team, together with partners at the University of Vienna and Johannes Kepler University Linz study and develop novel, universal reduction schemes for highly redundant dictionaries of functions.

The mathematical terminology ‚continuous frames‘ is describes such dictionaries, which can be used to decompose complex functions (or data) into simple building blocks, so-called atoms. Such decompositions are used to illuminate the structure and properties of functions (or data) under scrutiny. However, continuous frames often consist of a continuum (mathematical: uncountably many) atoms. Hence, constructive reduction of the dictionary size is essential for practical use of continuous frames and the use for data analysis. Therefore, our team studies universal reduction schemes that can be used under mild and rather general conditions on the dictionary. To this end, we use so-called low discrepancy sets, a number-theoretic construction through which we can guarantee that the methods developed in this project are applicable to a large variety of continuous frames.

More information about the project can be found here.