Minimax Design of Two-channel Biorthogonal Graph Filter Banks Using Sequential Linear Programming

Biorthogonal graph filter banks (GFBs) are foundational building blocks for graph signal processing, but their design remains challenging for achieving both low reconstruction error and high spectral selectivity. This work proposes a systematic design framework to address this issue. We first formulate the design problem under a minimax criterion, where a scaling factor is used to balance the reconstruction error and spectral response error. Moreover, a Chebyshev-based spectral transformation is applied in the formulation to mitigate the numerical instability inherent to high-degree polynomial approximation. Next, by linearizing the reconstruction error function via first-order Taylor expansion, we propose a sequential linear programming (SLP) algorithm that iteratively solves the target design problem. In this way, the biorthogonal GFBs with high reconstruction accuracy and sharp spectral selectivity can be efficiently designed. Extensive experiments, including comparisons with  state-of-the-art methods, validate the versatility of the proposed method. The applicability of the optimized biorthogonal GFBs to nonlinear approximation of images is additionally explored.