Two-dimensional FIR signal adapted filter banks: Optimality and design

The effect of different subsampling matrices with the same sampling density, on the optimality of two-dimensional filter banks is studied in this paper. It is seen that, in the case of two channel filter banks, there can be three distinct filter banks for an input power spectral density, with each one optimum for the corresponding subsampling matrix. For most of the natural images, the quincunx filter bank is optimum. In addition to this, a suboptimal solution that extends one-dimensional (1D) signal adapted filter bank design procedure, to two-dimensional (2D) nonseparable and separable signal adapted filter banks, using iterative greedy algorithm, is proposed. The nonseparable filter bank is designed for both four channel and two channel quincunx filter banks. A cascade structure is used for the factorization of 2D paraunitary polyphase matrix in the nonseparable case and a 2D separable FIR PU polyphase matrix is used in the separable case. The simulated FIR responses match the ideal responses very closely.