Weighted Median Filter:
It is same as median filter, only difference is the mask is not empty. It will having some weight (or values) and averaged.
The steps to perform weighted median filtering are as follows:
1) Assume a 3x3 weighted mask.
2) Place the mask at the left hand corner.
3) After convolution (multiplication), Arrange the 9 pixels in ascending or descending order.
4) Chose the median from these nine values.
5) Place this median at the centre.
6) Move the mask through out the image