A novel envelope model based on convex constrained optimization

The theoretical analysis for an iterative envelope algorithm

“…These points (α i , β i ) satisfying (17) are illustrated as the shaded region M in Fig. 13(c), where α i and β i are respectively the horizontal and vertical axes.…”

“…The study on envelope is an active field in time-frequency and non-stationary signal processing. In that year or later [16] was published, some new approaches appeared [9,10,17]. It is meaningful to summarize or compare those new algorithms.…”

Optimal Averages for Nonlinear Signal Decompositions - Another Alternative for Empirical Mode Decomposition

“…al. [9,27] proposed a non-smooth convex optimization approach to calculate multi-components of the signal so that each one can be considered as an IMF. In their optimization model, a constrain is used to enforce near orthogonality among the components.…”

“…This is a feature shared by the original EMD method and the non-smooth optimization approach taken by Pustelnik et. al [9,27]. On the other hand, many existing alternatives, such as the methods studied in [4,7,8,29,15], use pre-defined functions as bases for IMFs.…”

“…And we like to stress that this is a distinguished feature in our framework in response to the nature of nonlinear and non-stationary signals. To the best of our knowledge, in other existing optimization based decompositions, such as the ones in [7,8,29,15,9,27], the objective functions are globally defined. Third, considering the possibility that the intrinsic components in a signal may not be orthogonal to each other, we do not use any conditions to achieve near orthogonality in the decomposition.…”