Optimal Basis Pursuit Based on Jaya Optimization for Adaptive Fourier Decomposition

The Adaptive Fourier Decomposition (AFD) is a novel signal decomposition algorithm that can describe an analytical signal through a linear combination of adaptive basis functions. At every decomposition step of the AFD, the basis function is determined by making a search in an over-complete dictionary. The decomposition continues until the difference between the energies of the original and reconstructed signals is to be less than a predefined tolerance. To reach the most accurate description of the signal, the AFD requires a large number of decomposition levels and a long duration because of using a sufficiently small tolerance and searching in a large dictionary. To make the AFD more practicable, we propose to combine it with Jaya algorithm for determining basis functions. The proposed approach does not require any dictionary and a tolerance for stopping decomposition. Furthermore, it enables to determine the decomposition level of the AFD automatically.