Order statistics-based unbiased homomorphic system to reduce multiplicative noise

In this paper, we propose an order statistics-based unbiased homomorphic system to reduce multiplicative noise. The design of such a system is based on the probability density function (PDF) of the noise. First, we generalize the order statistics-based nonlinear filter called the sampled function weighted order (SFWO) filter proposed in [1] to reduce additive noise, to the case when the additive noise is not symmetric. This generalized SFWO (GSFWO) filter is then used in a homomorphic system to reduce multiplicative noise corrupting a signal. It is shown that the output from this GSFWO filter-based homomorphic system will be biased and hence, a bias compensation technique is applied to the output to get the unbiased estimate. A study of the qualitative and quantitative performance of the proposed GSFWO filter-based unbiased homomorphic system in reducing multiplicative noise is carried out and compared to that of some of the existing ones. It is found that the proposed GSFWO filter-based system consistently outperforms the others irrespective of the type of the PDF of the multiplicative noise.