An iterative algorithm for the design of 2-D nonseparable diamond-shaped filter banks

An iterative method for the design of two-dimensional (2-D) nonseparable diamond-shaped filter banks is proposed. Matrix techniques are used to re-formulate a least-squares objective function as a standard fourth-order function of the filter coefficients. A linearization procedure is then applied to obtain a modified quadratic objective function. As a result, the major step in the iterative algorithm proposed is to minimize a standard unconstrained quadratic function, which can be done with high computation efficiency. Compared with other existing design methods, our method is a direct approach that entails more flexibility in achieving design specifications and improved computational efficiency, as is demonstrated by design examples.