Professur für Angewandte Mathematik

On Tuesday July 1st, 2025 we welcome Dr. Frank Filbir to our faculty colloquium!

Title of his presentation: Phase Retrieval in Action – Image Reconstruction from Spectrogram Measurements

We meet at 4.15 p.m. for a cup of coffee on the red sofa near office IM 130. to chat with our guest.  

Frank’s talk will begin at 5:00 p.m. in room IM HS 11. 

You may find the abstract at: 

https://www.fim.uni-passau.de/fileadmin/dokumente/fakultaeten/fim/lehrstuhl/graf/Filbir_neu_Koll_Einl_1.7.25.pdf

After the colloquium, we’ll be going to a restaurant. Everyone will cover their own expenses. You’re very welcome to join us!

Wir feiern unseren neuen festen Standort in der Dr.-Hans-Kapfinger-Str. 30 mit einem Abend der offenen Tür.

Nach über zehn Jahren Pop-Up-Museum haben wir jetzt eine feste Heimat im Raum HK30 010. Alle sind eingeladen, mitzufeiern! Wir freuen uns auf Sie!

www.mathe-museum.uni-passau.de

Das Paper "Rebricking frames and bases" von Thomas Fink, Brigitte Forster und Florian Heinrich ist "online first" im Journal of Mathematical Analysis and Applications erschienen:

https://doi.org/10.1016/j.jmaa.2024.129051

Abstract:

In 1949, Denis Gabor introduced the ``complex signal'' (nowadays called ``analytic signal'') by combining a real function f with its Hilbert transform Hf to a complex function f+iHf. His aim was to extract phase information, an idea that has inspired techniques as the monogenic signal and the complex dual tree wavelet transform. In this manuscript, we consider two questions: When do two real-valued bases or frames {fn:n∈ℕ} and {gn:n∈ℕ} form a complex basis or frame of the form {fn+ign:n∈ℕ}? And for which bounded linear operators A forms {fn+iAfn:n∈ℕ} a complex-valued orthonormal basis, Riesz basis or frame, when {fn:n∈ℕ} is a real-valued orthonormal basis, Riesz basis or frame? We call this approach \emph{rebricking}. It is well-known that the analytic signals don't span the complex vector space L2(ℝ;ℂ), hence H is not a rebricking operator. We give a full characterization of rebricking operators for bases, in particular orthonormal and Riesz bases, Parseval frames, and frames in general. We also examine the special case of finite dimensional vector spaces and show that we can use any real, invertible matrix for rebricking if we allow for permutations in the imaginary part.

Viel Spass beim Lesen!