A new enhanced morphological filter and signal recovery

We present a new approach to noise reduction based on mathematical morphology. The proposed algorithm performs an adaptive, nonlinear, and recursive filtering. The results show that a deterministic or a stochastic signal corrupted by an additive noise of general nature is recovered using the new nonlinear filter. The new filter is able to remove a correlated noise, or a signal-dependent noise from the desired signal. This filter is also capable of recovering desired signals even in low signal-to-noise ratios and it is versatile enough to combat heavy tail Cauchy noise. We also provide the pertinent probability density function for the output of the main part of the new filter.