Learnable Empirical Mode Decomposition based on Mathematical Morphology - Morphologie mathématique (CMM) Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Imaging Sciences Année : 2022

Learnable Empirical Mode Decomposition based on Mathematical Morphology

Résumé

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) by considering a convex sum of envelopes instead of the 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.
Fichier principal
Vignette du fichier
ArticleEMD.pdf (1019.98 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03221652 , version 1 (09-05-2021)
hal-03221652 , version 2 (21-07-2021)
hal-03221652 , version 3 (26-08-2021)

Identifiants

Citer

Santiago Velasco-Forero, Romain Pagès, Jesus Angulo. Learnable Empirical Mode Decomposition based on Mathematical Morphology. SIAM Journal on Imaging Sciences, 2022, 15 (1), ⟨10.1137/21M1417867⟩. ⟨hal-03221652v3⟩
4805 Consultations
516 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More