A Fast Parallel Implementation of the Wavelet Packet

Adaptive signal representations such as those determined by best-basis type algorithms have found extensive application in image processing, although their use in real-time applications may be limited by the complexity of the algorithm. In contrast to the wavelet transform which can be computed in O(n) time, the full wavelet packet expansion required for the standard best basis search takes O(n log n) time to compute. In the parallel world, however, both transforms take O(log n) to compute when the number of processors equal the number of data elements, making the wavelet packet expansion attractive to implement. This note describes near real-time performance obtained with a parallel implementation of best basis algorithms for Wavelet Packet bases. The platform for our implementation is a DECmpp 12000/Sx 2000, a parallel machine identical to the MasPar MP-2. The DECmpp is a single instruction, multiple data (SIMD) system; such systems support a data parallel programming model, a model well suited to the task at hand. We have implemented the 1D and the 2D WPT on this machine and our results show a signiicant speedup over the sequential counterparts. In the 1D case we almost attain the theoretical speedup, while in the 2D case we increase execution speed by about two orders of magnitude. The current implementation of the 1D transform is limited to signals of length 2048, and the 2D transform is limited to images of size: 3232, 6464, and 128128. We are currently working on extending our transform to handle signals and images of larger size.