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Nonlinear filter plays an important role in the field of image
processing due to their ability to perform noise cancellation
effectively. The median filter is one of the best known
nonlinear filters. In median filtering, a pixel is replaced
with the median within a window even if the pixel is not
corrupted. Some filters based on a detection-estimation
strategy are proposed to solve this problem. Even though
the performance of the detection-estimation style filters
are better than the conventional filters, the filtering result
of these detection-estimation style filters still can be
affected by the corrupted elements in the input
vector. In this paper, a novel nonlinear filter is
proposed to solve this problem. The new filter, called the
error- trimmed median filter, trims the corrupted elements
in an input vector before feeding it into the median filter.
In this way the filtering capability of the filter is
increased significantly. To detect the corrupted elements in the
input vector the technique of the adaptive fuzzy linear
regression is used. The adaptive fuzzy linear regression is
a new method proposed in this paper to approximate the optimal
solution of the fuzzy linear regression. The computer
simulations based on the MSE and MAE error criterion show that
the filtering capability of the error-trimmed median filter
is good even when the noise ratio is high.
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