An improved variational mode decomposition method for internal waves separation

This paper proposes to revisit the 2-D Variational Mode Decomposition (2-D-VMD) in order to separate the incident and reflected waves in experimental images of internal waves velocity field. 2-D-VMD aims at splitting an image into a sequence of oscillating components which are centered around specific spatial frequencies. In this work we develop a proximal algorithm with local convergence guarantees, allowing more flexibility in order to deal with modes having different spectral properties and to add some optional constraints modeling prior informations. Our method is compared with the standard 2-D-VMD and with a Hilbert based strategy usually employed for processing internal waves images.