Adaptive LMS L-filters for smoothing noisy images

Several adaptive LMS L-filters, both constrained and unconstrained ones, are developed for noise suppression in images and being compared in this paper. First, the location-invariant LMS L-filter for a nonconstant signal corrupted by zero-mean additive white noise is derived. Subsequently, the normalized and the sign LMS L-filters are studied. It is shown that both these filters turn to be identical for a certain choice of the adaptation step-size. A modified LMS L-filter with nonhomogeneous step-sizes is also proposed in order to accelerate the rate of convergence of the adaptive L-filter. Finally, a signal-dependent adaptive filter structure is developed to allow a separate treatment of the pixels that are close to the edges from the pixels that belong to homogeneous image regions.