Prologue

We met for the entrance ceremony for the same major. The Courant Institute is responsible for New York University’s undergraduate programs in computer science and mathematics. For some reason we sat together and talked on and off.

When everything was over, we continued to sit and talk. She said; I am taking special interest in Gitta Kutyniok courses on Harmonic Analysis and Signal Processing Seminar jointly with the Numerical Analysis and Scientific Computing especially the first one on Anisotropic Multiscale Systems on Bounded Domains.

“I nodded my head and said, “Ugh, uh huh”.

It must have given her enough time to catch her breath because she continued.

“Many important problems are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic structures is obviously the more important the higher the number of spatial variables is, principal difficulties arise already in two spatial dimensions. Since it was shown that the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. I think I can really sink my teeth into that, how about you?”

Chapter 1 »