Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes

The idea of empirical mode decomposition (EMD) was proposed by N. E Huang as an iterative method of decomposition of a nonlinear and nonstationary function into the sum of components called internal modes. First, EMD was presented as a method for analyzing one-dimensional time series. The method made it possible to extract rapidly oscillating signal components with zero averages superimposed on slow oscillations. In this paper, we describe an algorithm for empirical decomposition of a two-dimensional time series using a $B$-spline in an EMD iterative process.