Sparse Representation with Nonlinear Fourier Atoms

Abstract

In this paper, we study the sparse representation of a finite energy signal with intrinsic mode functions in a dictionary consisting of nonlinear Fourier atoms. Each nonlinear Fourier atom is a mono-component with a physically meaningful nonnegative 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.