An Efficient Design Method for Optimal Weighted Median Filtering

Earlier research has shown that the problem of optimal weighted median filtering with structural constraints can be formulated as a nonconvex nonlinear programming problem in general. However, its high computational complexity and poor performance due to its nonconvex nature prohibit it from practical applications. In this paper, we shall show that the design problem can be formulated as a convex quadratic programming problem. The new algorithm is very efficient in the sense of computational complexity. The algorithm is also efficient in the sense of its capability to approach the global minimum. Using the algorithm optimal 1-D weighted median filters preserving pulses of length 3, 4 and 5 are tabulated.