Optimal design of three‐dimensional FIR digital filters. Design method by linear programming and reduction of computations by exploiting symmetries

Recently, the signal processing by the three‐dimensional digital filter is considered in such applications as dynamic image processing, medical image processing, robot vision, and analysis of seismic or meteorological data. This paper proposes a method of optimum design for the three‐dimensional FIR digital filter using linear programming. the optimum design of the three‐dimensional digital filter, including the design by linear programming, requires in general a large computational complexity. From such a viewpoint, this paper discusses the reduction of computational complexity utilizing the symmetry in the frequency response, and the result is actually applied to the design by linear programming. As a result, it is shown, for the case of the spherical lowpass filter, that the computation time is reduced by one order of magnitude by utilizing the symmetry.