An optimization algorithm for recursive weighted median filters with real-valued weights

A generalized recursive weighted median (RWM) filter structure admitting negative weights is introduced. Much like the sample median is analogous to the sample mean, the proposed class of RWM filters is analogous to the class of infinite impulse response (IIR) linear filters. RWM filters provide advantages over linear IIR filters, offering near perfect “stop-band” characteristics and robustness against noise. A novel “recursive decoupling” adaptive optimization algorithm for the design of these RWM filters is also introduced. In the optimization algorithm, the previous outputs used to compute the recursive WM filter output are replaced by previous desired outputs. This structure avoids the feedback inherent in the recursive operation and therefore leads to a much simpler derivation of the gradient in the steepest descent algorithm used to update the filter coefficients