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 and the filter coefficients are constrained with complete dyadic conditions. This produces a generalised design for bi-orthogonal filter with perfect reconstruction. Futhermore, in order to realise power-efficient designs, we propose a reversible logic based implementation for the proposed bi-orthogonal wavelet filter bank. The effectiveness of the proposed wavelet Filter Banks (FBs) is verified using an image compression application. The proposed rationalised wavelet FBs achieve an average increase of 16% in PSNR when compared to existing designs.