Optimal stack filters under rank selection and structural constraints

Abstract A new expression for the moments about the origin of the output of stack 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 stack filters and numbers M ( Φ , γ , N , i ) defined in this paper. The noise attenuation capability of any stack filter can now be calculated using the A and M vector parameters in the new expression. The connection between the coefficients A i and so called rank selection probabilities r i is reviewed and new constraints, called rank selection constraints, for stack filters are defined. The major contribution of the paper is the development of an extension of the optimality theory for stack filters presented by Yang et al. and Yin. This theory is based on the expression for the moments about the origin of the output, and combines the noise attenuation, rank selection constraints, and structural constraints on the filter's behaviour. For self-dual stack filters it is proved that the optimal stack filter which achieves the best noise attenuation subject to rank selection and structural constraints can usually be obtained in closed form. An algorithm for finding this form is given and several design examples in which this algorithm is used are presented in this paper.