General framework of the construction of biorthogonal wavelets based on Bernstein bases: Theory analysis and application in image compression

The authors present a general framework of the construction of biorthogonal wavelets based on Bernstein bases along with theory analysis and application. The presented framework possesses the largest possible regularity, the required vanishing moments and the passband flatness of frequency response of filters. Based on this concept, the authors establish explicit formulas for filters of biorthogonal wavelets with arbitrary odd lengths. Meanwhile, a new family of parametric filters with symmetry is constructed. The choice of filter bank in wavelet compression is a critical issue that affects image quality. In this study, an optimal model of FIR aiming at image compression is brought forward, and the optimal finite impulse response (FIR) filters can be obtained correspondingly through sequential quadratic programming (SQP) and genetic algorithm (GA). The authors demonstrate the performance of the new family of filters given in this study for image compression with very encouraging results.