Application of compactly supported wavelets to image compression

Multilevel unitary wavelet transform methods for image compression are described. The sub-band decomposition preserves geometric image structure within each sub-band or level. This yields a multilevel image representation. The use of orthonormal bases of compactly supported wavelets to represent a discrete signal in 2 dimensions yields a localized representation of coefficient energy. Subsequent coding of the multiresolution representation is achieved through techniques such as scalar/vector quantization, hierarchical quantization, entropy coding, and non-linear prediction to achieve compression. Performance advantages over the Discrete Cosine Transform are discussed. These include reduction of errors and artifacts typical of Fourier-based spectral methods, such as frequency-domain quantization noise and the Gibbs phenomenon. The wavelet method also eliminates distortion arising from data blocking. The paper includes a quick review of past/present compression techniques, with special attention paid to the Haar transfOrm, the simplest wavelet transform, and conventional Fourier-based subband coding. Computational results are presented.