Optimal design of two-channel biorthogonal filter banks

A method for the design of signal-adapted 2-channel biorthogonal filter banks of finite length is presented. The design problem is formulated as a constrained optimization problem and is solved by converting it into an iterative line-search problem through a first-order parameterization of the perfect reconstruction constraint. It is shown that for filter banks with analysis and synthesis lowpass filters of different lengths, a refinement of the algorithm is possible that leads to a solution in a very small neighborhood of a local minimizer, which satisfies the PR constraint precisely.