Recursive LMS L-filters for noise removal in images

The problem of designing the weights for recursive L-filters optimized by the least mean square (LMS) algorithm is addressed. The coefficients derived for nonrecursive filtering are not optimal for recursive implementation, where the estimate of current pixel depends on the past outputs of the filter. To combat this, analogous to the design of adaptive IIR filters, the optimization scheme referred to as equation-error formulation is employed. The recursive filter performs better in suppressing noise than its nonrecursive counterpart.