Recursive weighted median filters admitting negative weights and their optimization

A recursive weighted median (RWM) filter structure admitting negative weigh ts is introduced. Much like the sample median is analogous to the sample me an, 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 "stopband" characteristics and r obustness against noise. Unlike linear IIR filters, RWM filters are always stable under the bounded-input bounded-output criterion, regardless of the values taken by the feedback filter weights, RWM filters also offer a numbe r of advantages over their nonrecursive counterparts, including a significa nt reduction in computational complexity, increased robustness to noise, an d the ability to model "resonant" or vibratory behavior. A no, el "recursiv e decoupling" adaptive optimization algorithm for the design of this class of recursive RWM filters is also introduced. Several properties of RWM filt ers are presented, and a number of simulations are included to illustrate t he advantages of RWM filters over their nonrecursive e counterparts and IIR linear filters.