Mathematical Foundations of Data Analysis II

Organizers: Dr. Boqiang Huang, Dr. Jehan Rihani

Schedule:

Lectures:

Thursday, 16:00 - 17:30 Lecture Room 2.03 in the Math.-Institute
Friday, 12:00-13:30 162, Seminar room 3 in the Math.-Institute

Tutorial:

Tuesday, 10-11.30 Seminar room 3 in the Math.-Institute

Contents:

This is part II of the lecture series Mathematical Foundations of Data Analysis''. Part I has
been given in SS 2016. The series aims to give a comprehensive introduction of state-of-the-art
data analysis methods together with their mathematical motivations, theories, and algorithm
realizations in MATLAB.
In part II, we shall extend our knowledge-base and math toolbox studied in part I to problems
and applications on multi-dimensional (multi-D) data. In details:
Section 1, time-frequency representations (on multi-variate data and vector-valued data)
1.1 (Fast) Fourier transforms
1.2 (Fast) wavelet transforms
1.3 empirical mode decompositions
Section 2, data approximation and compression (main focus on images)
2.1 Data approximation based on time-frequency representation methods
2.2 Quantization methods
2.3 Entropy coding and decoding methods

Literature:

1. S. Mallat, A wavelet tour of signal processing, third edition: The sparse way, Academic Press,
2008.
2. C.K. Chui, Q. Jiang, Applied mathematics: Data compression, spectral methods, Fourier
analysis, wavelets, and applications, Atlantis Press, 2013.
3. I. Daubechies, J. Lu, H.-T. Wu, Synchrosqueezed wavelet transforms: An empirical mode
decomposition-like tool, Applied and Computational Harmonic Analysis, vol. 30, pp. 243-261,2011.
4. N.E. Huang, S.S.P. Shen, Hilbert-Huang transform and its applications, World Scientic Publishing,
Singapore, 2005.
5. B. Huang, A. Kunoth, An optimization-based empirical mode decomposition scheme, Journal
of Computational and Applied Mathematics, vol. 240, pp. 174-183, 2013.