The Finite Heisenberg-Weyl Groups in Image Processing

by Srdan Lazendic (Ghent University)

Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday March 8, 2019 at 14:30

The continuous Heisenberg-Weyl groups have a long history in physics and signal processing. However, their discrete variants haven’t received the deserved attention. When a signal is transformed by an element of the (much larger) discrete symplectic group, autocorrelations, which are mathematical tool for finding repeating patterns in a signal, can be calculated from trace inner products of covariance matrices with signed permutation matrices from the discrete Heisenberg-Weyl group. The mapping between a signal and its autocorrelation coefficients based on the Heisenberg-Weyl group is called the Weyl transform. This instance of the Weyl transform is a special case of a general framework for representation of operators in harmonic analysis. We will make it clear how those beautiful properties of the Weyl transform can be used for particular application in image processing and show the original results for image classification.