Abstract :
Wavelet theory and its relatives (subband coding, filter banks and multiresolution analysis) have become hot this last decade. Like the sinusoids in Fourier analysis, wavelets form bases that can decompose (analyze) and reconstruct (synthesize) signals and images. As a by-product, we obtain the accompanying processing (filtering, compression, denoising, etc.). But unlike the sinusoids, there seems to be an inexhaustible variety of different wavelet types: orthogonal, biorthogonal, spline, smooth, rough, short, long and so forth. We construct the simplest wavelet algorithm possible, called the fast Haar transform (FHT). We then indicate how this may be generalized to other fast wavelet algorithms
Keywords :
data compression; image coding; image reconstruction; signal reconstruction; signal synthesis; transform coding; wavelet transforms; Fourier analysis; biorthogonal; denoising; fast Haar transform; fast wavelet algorithms; filter banks; filtering; image analysis; image compression; multiresolution analysis; orthogonal; signal analysis; signal compression; signal reconstruction; signal synthesis; sinusoids; subband coding; wavelet theory; Filter bank; Filtering; Image analysis; Image coding; Image reconstruction; Multiresolution analysis; Noise reduction; Signal analysis; Signal synthesis; Wavelet analysis;
