Learnable Empirical Mode Decomposition based on Mathematical Morphology

Abstract

Empirical mode decomposition (EMD) is a fully data driven method for multiscale decomposing signals into a set of components known as intrinsic mode functions. EMD is based on lower and upper envelopes of the signal in an iterated decomposition scheme. In this paper, we put forward a simple yet effective method to learn EMD from data by means of morphological operators. We propose an end-to-end framework by incorporating morphological EMD operators into deeply learned representations, trained using standard backpropagation principle and gradient descent-based optimization algorithms. Three generalizations of morphological EMD are proposed: a) by varying the family of structuring functions, b) by varying the pair of morphological operators used to calculate the envelopes, and c) the use of a convex sum of envelopes instead of the classical mean point used in classical EMD. We discuss in particular the invariances that are induced by the morphological EMD representation. Experimental results on supervised classification of hyperspectral images by 1D convolutional networks demonstrate the interest of our method.