Time: Monday, April 10, 2017, 1:00pm @ MTH3206

Speaker: Sui Tang (JHU)

Title: Universal spatiotemporal sampling sets for discrete spatially invariant evolution processes

Abstract: Let (I, +) be a finite abelian group and A be a circular convolution operator. The problem under consideration is how to construct minimal Ω ⊂ I and li such that Y = {ei, Aei, · · · , Aliei: i ∈ Ω} is a frame for l2(I),where {ei: i ∈ I} is the canonical basis of l2(I). This problem is motivated by the spatiotemporal sampling problem in discrete spatially invariant evolution processes. We will show that the cardinality of Ω should be at least equal to the largest geometric multiplicity of eigenvalues of A, and consider the universal spatiotemporal sampling sets (Ω, li) for convolution operators where only requires the information about the geometric multiplicity of eigenvalues. We will give an algebraic characterization for such sampling sets and show how this problem is linked with sparse signal processing theory and polynomial interpolation theory.