WPT based fast multiresolution transform

In this paper, we propose a fast multi-resolution transform using wavelet packet transform (WPT). This fast algorithm switches between a transform coder and a subband coder on user discretion. The proposed algorithm uses discrete approximate trigonometric expansions, which have previously been proposed for exploiting spatial and spectral correlation in multidimensional signals. Specifically, we describe an approach for fast implementation of the approximate Fourier expansion (AFE). This approach uses the discrete wavelet transform (DWT) as a tool to compute the approximate Fourier expansion (AFE). If no intermediate coefficients are dropped and no approximations are made, the proposed algorithm computes the exact result of the approximate Fourier expansion (AFE) of the signal, and its computational complexity is on the same order of the fast Fourier transform (FFT) algorithm. In this paper, we also show the capacity of the proposed algorithm for reducing noise while doing the approximation. Further, we discuss the possible implementation of the proposed algorithm using parallel processing resulting in faster implementation. The proposed algorithm provides an efficient complexity vs. accuracy tradeoff.