On The Design Of Rationalised Bi-orthogonal Wavelet Using Reversible Logic

This paper presents a novel approach to obtain rational bi-orthogonal wavelet filter coefficients based on Perfect Reconstruction (PR) in Half-Band Polynomial (HBP) by removing Vanishing Moments (VM). A delta-error approach is adopted to design wavelet filter coefficients that reduce the error using an iterative method. This error equation is formulated in terms of generalized HBP, where the odd values are equated to zero and the filter coefficients are constrained with complete dyadic conditions. This produces a generalized design for bi-orthogonal filter with perfect reconstruction. Furthermore, in order to realize power-efficient designs, we propose a reversible logic based implementation for the proposed bi-orthogonal wavelet filter bank. The implementation efficiency is measured in terms of Gate Count (GC), Quantum Cost (QC), Ancilla Input (AI) and Garbage Output (GO). The proposed Design 2 is able to reduce (GC, QC, AI, GO) by (34.3%, 31.6%, 33.9%, 31.1%) when compared to existing design. The effectiveness of the proposed wavelet Filter Banks (FBs) is verified using an image compression application. The experimental results show that, the proposed rationalised wavelet FBs are able to achieve an average increase of 16% in PSNR when compared to existing designs.