LIFTPACK: A Software Package for Wavelet Transforms using Lifting
Abstract:
We present LIFTPACK: A software package written in C for fast calculation of 2D biorthogonal wavelet transforms using the lifting scheme. The lifting scheme is a new approach for the construction of biorthogonal wavelets entirely in the spatial domain, i.e., independent of the Fourier Transform. Constructing wavelets using lifting consists of three simple phases: the first step or Lazy wavelet splits the data into two subsets, even and odd, the second step calculates the wavelet coefficients (high pass) as the failure to predict the odd set based on the even, and finally the third step updates the even set using the wavelet coefficients to compute the scaling function coefficients (low pass). The predict phase ensures polynomial cancelation in the high pass (vanishing moments of the dual wavelet) and the update phase ensures preservation of moments in the low pass (vanishing moments of the primal wavelet). By varying the order, an entire family of transforms can be built. The lifting scheme ensures fast calculation of the forward and inverse wavelet transforms that only involve FIR filters. The transform works for images of arbitrary size with correct treatment of the boundaries. Also, all computations can be done in-place.
