Applied Mathematics Seminar

Speaker:  Dr. Yi Wang,   Professor and Chair at Auburn University at Montgomery (AUM). 

Title: Sparse representation with non-linear Fourier atoms

Abstract: In this talk, we study the sparse representation of a finite energy signal with intrinsic mode functions in a dictionary consisting of non-linear Fourier atoms. Each non-linear Fourier atom is a mono-component with a physically meaningful non-negative instantaneous frequency. The sparse representation is obtained adaptively by an orthogonal matching pursuit using a two-level greedy search. It is demonstrated that the representation has efficient energy decay in error compared to the Fourier expansion and wavelet expansion.

Keywords: sparse representation, non-liner Fourier atom, orthogonal matching pursuit, trust-region-reflective search.