A noncausal 1-D median hybrid filter

A new class of nonlinear filters, the so-called class of Multi-Directional Infinite Impulse Response Median Hybrid Filters (MIMH), is presented and analyzed. The input signal is processed twice using a Linear Shift-Invariant (LSI) Infinite Impulse Response (IIR) filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering (a LSI IIR filtering module) and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties (including impulse removal, step preservation, and noise suppression)