Empirical mode decomposition revisited by multicomponent non-smooth convex optimization

This work deals with the decomposition of a signal into a collection of intrinsic mode functions. More specifically, we aim to revisit Empirical Mode Decomposition (EMD) based on a sifting process step, which highly depends on the choice of an interpolation method, the number of inner iterations, and that does not have any convergence guarantees. The proposed alternative to the sifting process is based on non-smooth convex optimization allowing to integrate flexibility in the criterion we aim to minimize. We discuss the choice of the criterion, we describe the proposed algorithm and its convergence guarantees, we propose an extension to deal with multivariate signals, and we figure out the effectiveness of the proposed method compared to the state-of-the-art.