Directionally selective fractional wavelet transform using a 2-d non-separable unbalanced lifting structure

Authors:
Furkan Keskin;A. Enis $#199;etin
Affiliations:
Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara, Turkey;Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara, Turkey
Venue:
MUSCLE'11 Proceedings of the 2011 international conference on Computational Intelligence for Multimedia Understanding
Year:
2011

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Abstract

In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1 [n] and x2 [n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q=1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained.