Riesz transforms in image processing and optics

Presenter: Swanhild Bernstein, TU Bergakademie Freiberg, Germany

Joint work with Bettina Heise, Martin Reinhardt

Riesz transforms play an essential role in image processing and optics. On one hand the are the building blocks of monogenic signals and on the other hand the also can be used as an substitue (in some sense) of derivatives in imaging and image processing. In this talk we would like to highlight the role of the Riesz transforms, fractional Riesz transforms and some fractional-type monogenic signals. These generalizations are based on quaternionic and Clifford calculus.