Stochastic Median Filter

\label{stochastic-median-filter}
In 1\label{in-1}
In 2\label{in-2} In 3\label{in-3} In 4\label{in-4} In 5\label{in-5} In 6\label{in-6} In 7\label{in-7} In 8\label{in-8} In 9\label{in-9}
Figure 4.10: Implementation of comparison network to get the median value
Noise reduction based on the Median filter is a non–linear digital filtering approach, often used to remove certain types of random noise, especially salt and pepper noise. This technique is widely used
Figure 4.11: Stochastic implementation of a node in the comparison network used for median filter
since it reduces noise and preserve edges [10]. The main idea is to replace each pixel with the median of neighboring pixels in the image. To define the neighbors, a window of dimension m × n which shifts
, pixel by pixel, over the entire image. In this work, a window of dimension 3 × 3 will be considered as
case study.
It can be seen in Fig.4.10 [16] the implementation of comparison network to provide the median value in each sliding of the window. Each node can be considering as a sorting element which arranges two input i and j in ascending order. As the stochastic implementation, Fig.4.11 carries out this element with three MUX and one Stochastic tanh function. The first multiplexer and tanh component play
the role of comparator which generate a signal ≈ 1 when Pini > Pinj , ≈ 0 when Pini < Pinj , and
0.5 elsewhere [16]. Consequently, this element will stochastically provides an ascending order of two
inputs.
The simulation results of noise reduction based on the median filter using the conventional and stochas- tic approaches are shown in Fig.4.12. In this work, the sequence of length 1024 bits is used to stochas- tically stand for each scaled pixel value. It can be seen in this figure that the quality of the processed images is better than the original one with a considerable noise reduction. Moreover, stochastic ap- proach with a simplicity in hardware design provides a good result as conventional one. Furthermore, when consider the influence of the length of bit sequence on simulation result, it can be shown in Fig.4.12c, Fig.4.12d, Fig.4.12e, and Fig.4.12f that the length 1024 bits gives a better output ( reduces more noises) in comparison with those of other lengths. This fact can be explained due to the following feature [16]: the variation of the error in case of the binary radix format is independent of the number of bits, while that of stochastic number is inversely proportional to the bit sequence length.