Adaptive LMS L-filters for noise suppression in images

Several adaptive least mean squares (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. It is demonstrated that the location-invariant LMS L-filter can be described in terms of the generalized linearly constrained adaptive processing structure proposed by Griffiths and Jim. Subsequently, the normalized and the signed error LMS L-filters are studied. 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.