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We construct directional wavelet systems that will enable building efficientsignal representation schemes with good direction selectivity. In particular,we focus on wavelet bases with dyadic quincunx subsampling. In our previouswork, We show that the supports of orthonormal wavelets in our framework arediscontinuous in the frequency domain, yet this irregularity constraint can beavoided in frames, even with redundancy factor less than 2. In this paper, wefocus on the extension of orthonormal wavelets to biorthogonal wavelets andshow that the same obstruction of regularity as in orthonormal schemes existsin biorthogonal schemes. In addition, we provide a numerical algorithm forbiorthogonal wavelets construction where the dual wavelets can be optimized,though at the cost of deteriorating the primal wavelets due to the intrinsicirregularity of biorthogonal schemes.

Directional Wavelet Bases Constructions with Dyadic Quincunx Subsampling