Optimal signal reconstruction based on time-varying weighted empirical mode decomposition

- Optimal signal reconstruction via the EMD-based framework is addressed.
- A new algorithm, termed, time-varying weighted EMD (TVW-EMD) is proposed.
- A formulation of reconstructing original signal through the EMD followed by time-varying weightings of the oscillation modes is derived in the minimum mean-square error (MMSE) sense.
- The effectiveness of the proposed new algorithm is supported by computer simulations including real biomedical signals.

Empirical mode decomposition (EMD) is a tool developed for analyzing nonlinear and non-stationary signals. It is capable of splitting any signal into a set of oscillation modes known as intrinsic mode functions and a residual function. Although the EMD satisfies the perfect signal reconstruction property by superimposing all the oscillation modes, it is not based on any optimality criterion. The lack of optimality limits the signal recovery performance of the EMD in the presence of disturbances such as noise and interference. In this paper, we propose a new algorithm, termed, time-varying weighted EMD, which gives the best estimate of a given signal in the minimum mean-square error sense. The main idea of the proposed algorithm is to reconstruct the original signal through the EMD followed by time-varying weightings of the oscillation modes. Simulations including two real-life signals are performed to show the superiority of the proposed algorithm.

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