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Critically sampled graph wavelets converted from linear-phase biorthogonal wavelets

This paper presents a design method of critically sampled graph wavelet transforms (CSGWTs) utilizing real-valued biorthogonal linear-phase wavelets for regular signals. Their filter characteristics are equivalent to those of biorthogonal linear-phase wavelets and can be expressed by real-valued closed-form with the sum of sinusoidal waves in the graph spectral domain. The proposed CSGWTs satisfy the perfect reconstruction condition for graph signals. Since the proposed filters are smooth functions, they are well-behaved even if we use a lower-order polynomial approximation. The performance of the proposed CSGWTs is evaluated by comparison with existing CSGWTs.