An Optimization Algorithm Based on Median Filtering for Nonlinear Image Processing
Rui Lü · 2004
This paper introduces a recursive weighted median filter admitting negative weights which provides several advantages over the infinite impulse response linear filters, finite impulse response linear filters and non-recursive weighted median filters and offers robustness to noise levels and near perfect stop-band characteristics that is very useful in practice. The paper also presents an adaptive optimization algorithm for design of recursive weighted median filters. This algorithm is developed under the mean absolute error criterion. In this framework, the previous outputs used to compute the RWM filter output are replaced by previous desired outputs. Thus, the RWM filter is approximated by a two-input, single output filter that depends on the input samples and on delayed samples of the desired response. Such a structure is free of the feedback inherent in the recursive operation,therefore,leading to a much simpler derivation of the gradient in the steepest descent algorithm used to update the filter coefficients. Proposed in the paper algorithm of adaptive recursive weighted median filtering lowers the complexity comparable to that of the LMS algorithm.