OPTIMAL STACK FILTERS UNDER RANK SELECTION AND STRUCTURAL CONSTRAINTS

A new expression for the moments about the origin of the output of sta ck filtered data is derived in this paper. This expression is based on the A and M vectors containing the well-known coefficients A(i) of st ack filters and numbers M(Phi, gamma, N, i) defined in this paper. The noise attenuation capability of any stack filter can now be calculate d using the A and M vector parameters in the new expression. The conne ction between the coefficients A(i) and so called rank selection proba bilities r(i) is reviewed and new constraints, called rank selection c onstraints, for stack filters are defined. The major contribution of t he paper is the development of an extension of the optimality theory f or stack filters presented by Yang et al. and Yin. This theory is base d on the expression for the moments about the origin of the output, an d combines the noise attenuation, rank selection constraints, and stru ctural constraints on the filter's behaviour. For self-dual stack filt ers it is proved that the optimal stack filter which achieves the best noise attenuation subject to rank selection and structural constraint s can usually be obtained in closed form. An algorithm for finding thi s form is given and several design examples in which this algorithm is used are presented in this paper.