Minimum mean square error design of stack filters

This paper addresses the problem of designing optimal stack filters under the most commonly used error criterion in filter design, namely, the minimum mean square error (MSE) between the desired signal and the estimated signal. It is shown that the MSE can be expressed as a linear combination of the responses of positive Boolean filters to different binary input vectors. As a result, a stack filter which is optimal for signal estimation in the MSE sense can be determined as the solution of a linear program