Random Fourier Series vs. Random Wavelet Series

Explore the contrasting properties of random Fourier series and random wavelet series in this 32-minute lecture by Stéphane Jaffard from Université Paris Est Créteil, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the key factors behind the immense success of wavelet bases, including Stéphane Mallat's multiresolution analysis framework and Ingrid Daubechies' compactly supported wavelets. Examine Yves Meyer's characterization of function spaces through wavelet coefficients and its practical applications in statistics, signal processing, and image processing. Understand the numerical robustness of wavelet-based function reconstruction compared to Fourier series. Discover surprising consequences of these properties, highlighting the significant differences in regularity between random wavelet series and random Fourier series.