The solution of minimization problem 1 is the output value for location . denotes the 1D filtering window. are the position indices in a 2D profile. and are both indices in the filtering window. Both and are temporary variables. is the length of the filtering window. Simply speaking, for each point in the 2D data, the median filter substitutes it with the median of neighbor points included by the window with size . The process of corresponds to finding the median in the window constructed by .

2020-02-10