Two-dimensional digital filters with sparse coefficients

Is sparsity an issue in 2-D digital filter design problems to explore and why is it important? How a 2-D filter can be designed to retain a desired coefficient sparsity for efficient implementation while achieving best possible performance subject to that sparsity constraint? These are the focus of this paper in which we present a two-phase design method for 2-D FIR digital filters in two most common design settings, namely, the least squares and minimax designs. Simulation studies are presented to illustrate each phase of the proposed design method and to evaluate the performance of the filters designed.