This thesis addresses the core challenges of modeling temporal characteristics of nonstationary signals, which often contain both smooth oscillations and abrupt changes. Through his doctoral research Mojtaba Nazari developed four novel variational decomposition algorithms that jointly extract AM-FM modes and discontinuities in univariate and multivariate signals, overcoming limitations of traditional methods.

Extending beyond temporal modeling, the thesis introduces a generalized framework—Multiscale Dynamic Graph Signal Analysis—to model multiscale topological structures (or interdependencies) of multivariate signals by integrating signal decomposition with graph learning and connectivity extraction techniques. Extensive evaluations on diverse real-world datasets, including biomedical and geophysical signals, demonstrate the proposed methods’ robust accuracy and scalability across multiple domains.

The PhD study was completed at the Department of Electrical and Computer Engineering, Faculty of Technical Sciences, Aarhus University.

This summary was prepared by the PhD student.

Time: Friday, 15 August 2025 at 10:00 am,
Place: Building 5123, room 313, Electrical and Computer Engineering (ECE), Aarhus University, Helsingforsgade 10, 8200 Aarhus
Title of PhD thesis: Modeling Temporal Characteristics and Topological Structures in Data-driven Signal Decomposition Methods
Contact information: Mojtaba Nazari, e-mail: m.nazari@ece.au.dk, tel.: +45 91974954
Members of the assessment committee:
Professor Morten Mørup, Section for Cognitive Systems, DTU Computer, Technical University of Denmark, Denmark
Professor Marta Molinas, Department of Engineering Cybernetics, Faculty of Information Technology and Electrical Engineering, NNU, Norway
Associate Professor Christian Fischer Pedersen (chair), Department of Electrical and Computer Engineering, Aarhus University
Main supervisor: Associate Professor Naveed ur Rehman, Department of Electrical and Computer Engineering, Aarhus University, Denmark
Co-supervisor: Clinical Associate Professor Anders Rosendal Korshøj, Department of Clinical Medicine - Brain and Spine Surgery, Aarhus University, Denmark
Language: The PhD dissertation will be defended in English

The defence is public.

The PhD thesis is available for reading at the Graduate School of Technical Sciences/GSTS, Ny Munkegade 120, building 1521, 8000 Aarhus C.