An adaptive and Sparse Decomposition for Analytic Signals in Hardy-2 Space

In this paper, an adaptive algorithm is proposed to decompose analytic signals of Hardy-2 space in a sparse way. The limitation of previous related studies such as AFD and Matching Pursuit always find local optimal solutions by greedy-flavor iteration. These solutions also rely on initial values. Our new algorithm utilizes l-1 minimization or Basis Pursuit strategy with a redundant dictionary consists of reproducing kernels. We prove that the design matrix has singular values which tend to zero rapidly given that the parameters are selected in some special meaner. These theoretical results lay the foundation for sparse representations of analytic signals. Two numerical examples are discussed to illustrate the algorithm.