Bound Ratio Minimization of Filter Bank Frames

This paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction (PR) filter banks (FBs). For a given analysis PRFB, a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel. The redesign minimizes the frame bound ratio of the FB while maintaining its original properties and performance. The obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing. The optimal solution is applied to subband noise suppression and tree structured FB gain optimization, resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement. Effectiveness of the optimal solution is demonstrated by extensive numerical examples.