The Fast Iterative Truncated Mean Order Statistics Filter

Mean filter is the most basic linear filter method. It is optimal for suppressing Gaussian noise. Since the output of mean filter is the average value of a domain, not the value of a pixel, it is easy to destruction the image details at the same time to attenuate the noise. Me-dian filter is the most typical nonlinear filter technology and widely used in signal and image processing. It yields good impulsive noise suppression and edge preservation characteris-tics. However, its performance is poorer than mean filter in attenuating additive short-tailed noise. Besides, it relies on sorting operation which is time-consuming and intractable for multivariate data. In summary, both of the two filters have advantages and disadvantages, and are adapted to different types of noise. However, in practical application, it is difficult to know the distribution of noise which interferences on the original signal in advance. As a result, it is particularly important to put forward a type of filter to attenuate different kinds of noise.Based on the theory of mean filter, median filter and order statistics filter, this thesis proposes a filter algorithm which owns merits of both the mean and median filter and is easy to realize. The proposed iterative truncated mean (ITM) filter provided an iterative algorithm which truncated the samples iteratively, then used the average of truncated date as filter outputs to approach the median. This thesis proves the convergence of{T(k)} and outputs yt1, yt2 of ITM filter, when the size of filter window is even. Based on this, this thesis puts forward an approximation method to seek any r-th order statistics, named the iterative truncated mean order statistics (ITM-OS) filter. Meanwhile, this thesis gives the proper stopping criteria for ITM-OS filter. Set the input data set inside the filter window be x, the conception of ITM-OS filter is to expand x to a new data set xp, making the r-th order statistics of x become the median of xp. Then the median of xp which obtained by the ITM filter is just the r-th order statistics of x. Hence, this iterative algorithm can seek for arbitrary order statistic data without data sorting. It provides a convenient for filters which are based on data sorting. In addition, iterative trimmed and truncated mean order statistics (ITTM-OS) filter is proposed, which is optimal to attenuate the mixed additive noise and exclusive noise. Finally, this thesis generalizes the fast algorithm which estimates the median to the continuous functions on a bounded interval. It gives a kind of approximation algorithm for seeking the median of continuous function.