An iterative technique to design 2D QMF banks under constraints by the method of Lagrange multipliers

In order to design 2D FIR filters for near-perfect reconstruction, we study an iterative technique for designing 2D QMF banks without loosening the constraint of filter size. This technique allows one to solve the problem of the nonlinearity of the reconstruction equations and offers the possibility of introducing constraints derived from these equations by the method of Lagrange multipliers. We provide the algorithm and results of this technique in the case of orthogonal and staggered sampling structures. The proposed method is efficient and permits one to obtain near-perfect reconstruction filter banks. These produce good reconstructed images in color television images.