A direct method for the design of 2-D nonseparable filter banks

A direct approach for the design of 2-D nonseparable diamond-shaped filter banks is proposed. The design goal is achieved by formulating the problem as an iterative quadratic programming problem in which the perfect reconstruction condition is incorporated into a weighted least squares type objective function while satisfactory stopband attenuation is assured by imposing a set of constraints on the amplitude of the lowpass analysis filter in the stopband. Analytical formulas for the exact and efficient evaluation of the objective function are derived, and an analysis on the local convergence of the proposed algorithm is given. The paper concludes with two design examples that illustrate the proposed design method.