Empirical mode decomposition revisited by multicomponent non-smooth convex optimization

An unconstrained optimization approach to empirical mode decomposition

“…The construction of the modes makes our method complete because their sum retrieves the original signal, in contrast to [11] where the reconstruction is not guaranteed. Computational cost is similar to EMD's.…”

“…A multicomponent non-smooth convex optimization approach to EMD was introduced by Pustelnik et al in [10], and it was more deeply explained in [11]. The optimization problem to be solved is the following:…”

“…Because of that, it is not possible to reproduce the simulations from [10,11] since the parameters they reported were for the constrained problem. The default setting is: p = 2, q = 2, r = 1 and second order for the derivative.…”

Application of improved bi-dimensional empirical mode decomposition (BEMD) based on Perona–Malik to identify copper anomaly association in the southwestern Fujian (China)

“…Bi-dimensional empirical mode decomposition (BEMD) was developed as a two-dimensional version of EMD. Through BEMD two-dimensional signals or data can be decomposed into a series of bi-intrinsic mode functions (BIMFs) (Bhuiyan et al, 2008a,b;Huang et al, 2010;Chen et al, 2014;Pustelnik et al, 2014).…”

A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

“…This ability turns out to be of primary importance in terms of computational complexity in the context of some large-scale problems (see e.g. [1,[6][7][8][9][10][11]). Block-coordinate versions of various proximal algorithms have been recently proposed, such as the forward-backward algorithm [12][13][14][15][16][17][18][19], the Alternating Direction Method of Mutipliers [20,21], and the Douglas-Rachford algorithm [12], where some of the block indices in {1, .…”