Optimization Design of Two-Channel Biorthogonal Graph Filter Banks

Narang and Ortega have constructed a two-channel biorthogonal graph filter bank with compact support. The design method does not consider the spectral response of the kernels. In this letter, we employ optimization approach to design the spectral kernels. The analysis and synthesis kernels are, respectively, optimized with constrained optimization problems, in which the reconstruction error and spectral selectivity are controlled simultaneously. The optimization problems are semidefinite programming (SDP), which can be solved effectively. Numerical examples and comparison are included to show that the proposed approach is more flexible in making trade-off between the spectral selectivity and reconstruction error over the existing method.