Optimization design of 17/11 biorthogonal wavelet and its performance analysis for image compression

Many wavelet filter banks suitable for image coding, e.g. CDF-9/7, Winger-17/11 (W-17/11), Villasenor-6/10 and 10/18 (V-6/10 and V-10/18), have irrational coefficients, and thus require infinite computational precision to implement the corresponding Discrete Wavelet Transforms (DWT). Here a simple technique for parametrization construction of 17/11 biorthogonal wavelet family is presented: first, the associated synthesis filter is formulated as one trigonometric polynomial represented by two free parameters; then the perfect reconstruction condition of the filter bank is reduced to one system of linear equations; finally the analysis filter is obtained by solving this system of linear equations. Thus, the exact free parameter expressions for the 17/11 biorthogonal wavelet filter banks are derived. By adjusting the free parameters, one can easily construct any linear phase 17/11 filters (a pair) with desired features. As a case study, a previously unpublished 17/11 biorthogonal wavelet filter bank with rational coefficients is constructed, which has optimum coding gain. Extensive simulations show that the new filter bank has the compression performance comparable to that of W-17/11 and V-10/18 for image transform coding, while surpasses the CDF-9/7 and V-6/10 far away.