【115/5/7】15:20-16:10 Prof. Gi-Ren Liu(Department of Mathematics, National Cheng Kung University)
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| Time | 2026-5-7 15:20-16:10 |
| Venue | 31106, Department of Mathematics |
| Speaker | Prof. Gi-Ren Liu(Department of Mathematics, National Cheng Kung University) |
| Title | Probabilistic Analysis of Scattering Transform and Scalogram Ridges |
| Abstract | This talk presents a line of research that bridges practical signal analysis with the probabilistic analysis of wavelet-based time–frequency methods. I will begin by illustrating how the scattering transform, constructed from cascades of modulus wavelet transforms, can be used to extract robust multi-scale features from EEG signals for sleep stage classification. This application motivates a theoretical investigation of how such representations behave in the presence of noise. In particular, I will present central and non-central limit theorems associated with time–frequency representations, together with results on their rates of convergence. Finally, I will discuss recent work on the probabilistic analysis of scalogram ridges. In this study, ridges—defined as local maxima of the complex modulus of the analytic wavelet transform across scales—are modeled as a potentially set-valued random process. I will explain key properties of these ridges, including uniqueness, continuity, and robustness with respect to noise, and discuss how deviations from the ideal (noise-free) case depend on the signal-to-noise ratio. Overall, this talk aims to provide a unified perspective on how modern time–frequency analysis methods connect algorithmic design, real-world data analysis, and theoretical understanding. |
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