The spherical empirical mode decomposition algorithm is an adaptation in the spherical space of the 2D empirical mode decomposition in Euclidian space. This algorithm is a signal analysis method for any spherical data, such as orbital measurements. The two primary advantages of this innovation are the absence of edge effects in the results, and the computational efficiency of the processing.
The 2D empirical mode decomposition in Euclidian space requires significant edge treatment of the grid. In addition, the selection of projection during the generation of the input grid must produce a true equidistant point set. The edge effects of the decomposition in Euclidian space were addressed by wrapping the data around the grid on all edges of the grid, thereby increasing the size of the input grid. The increase in the size of the input grid increases the computational efforts of the original method. Even with edge treatment strategies, the projection method from spherical to a rectangular grid will produce adverse boundary effects.
The spherical empirical mode decomposition algorithm removes the adverse edge effects and increases the computational efficiency of the current approach. The rectangular grid is replaced by a geodesic discrete global grid, an icosahedral Snyder equal-area spherical grid. The rectangular scanning pattern for the morphological reconstruction is replaced by a spiral scanning pattern. The Euclidian distance for the radial basis function component is replaced by the orthodromic distance — the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere. The algorithm operates on discrete spherical data. It performs the sifting process of the 2D empirical mode decomposition, but with the updated component. The algorithm can be implemented on any digital computer system and for any operating system, in any scientific programming language.
This work was done by Nicolas Gagarin of Starodub, Inc. for Goddard Space Flight Center. GSC-16697-1