Codes and Expansions (CodEx) Seminar
Alexander Powell (Vanderbilt University)
Dynamical Duals and Error Diffusion
Dynamical sampling addresses the problem of recovering a signal from space-time samples of an evolution process. Many problems in dynamical sampling can be conveniently formulated in terms of frame theory. A frame is said to be dynamical if the frame vectors are generated by the iterates of a linear operator. Aceska and Kim proved that if a frame is dynamical then its canonical dual frame is also dynamical. However, not all frames are dynamical. Given a frame which is not necessarily dynamical, we study the dynamical structure of its dual frames. We prove that every redundant finite frame has infinitely many dual frames that are dynamical. We then show an application of dynamical dual frames to error diffusion algorithms for quantizing finite frame expansions. This is joint work with Jon Ashbrock.