Recursive wavelet filters for video coding

Recursive wavelet filters and an alternative algorithm for implementing wavelet transform are presented in this paper. The recursive filters use previously calculated (past) wavelet coefficients as inputs to calculate the current wavelet coefficient, and provide the same transform results as convolutional FIR and lifting wavelet filters. The coefficients of the recursive filters are derived from those of conventional FIR wavelet filters. The wavelet transform with recursive filters requires a smaller amount of memory and is easy to implement in hardware. Another important advantage of the recursive filters is that perfect reconstruction can be easily achieved using recursive wavelet filters if a sequence of pixels to be transformed is extended by boundary pixel repetition. Boundary pixel repetition can be more efficient than the widely used method of symmetric extension for image and video coding.