Wavelet decomposition and reconstruction using arbitrary kernels: a new approach

In a previous paper, we presented a method to design perfect reconstruction filters using arbitrary lowpass filter kernels and presented fast filters with compression performance surpassing the well-known 9/7 biorthogonal filters. This paper improves the results obtained by Polyak and Pearlman (see Proc. IEEE International Conference on Image Processing, Santa Barbara, CA, vol.1, p.660-63, 1997), presenting filters comparable in compression performance and faster than the biorthogonal 10/18 filters. Furthermore, we combine our approach with the lifting and prediction schemes similar to the ones discussed by Said and Pearlman (see IEEE Trans. on Image Processing, vol.5, p.1303-10, 1996) in deriving the SS-P filters and later extended by Sweldens (see Appl. Comput. Harm. Anal., vol.3, no.2, p.186-200, 1996), thus obtaining integer to integer transforms whose performance is comparable to one of the S+P filters. At this stage, our algorithms are, however considerably slower. In any case it seems that the flexibility of our method shows some promise to serve as a basis for finding new integer to integer filters