Optimal soft morphological filtering under breakdown probability constraints

A robust filtering method with good detail preservation properties is a desideratum in many signal processing applications. Unfortunately, it is typically difficult to design a filter having these two properties simultaneously. This paper gives a method to optimize filters by giving different penalties for deviations from the robustness and from the detail preservation requirements. It is illustrated that by relaxing the robustness requirement a little, the optimal filter can obtain significantly improved detail preservation properties