A SHIFT-INVARIANT DISCRETE WAVELET TRANSFORM

This correspondence presents a unifying approach to the derivation and implementation of a shift-invariant wavelet transform of one-and two- dimensional (1-D and 2-D) discrete signals, Starting with Mallat's mul tiresolution wavelet representation (MRWAR), the correspondence presen ts an analytical process through which a shift-invariant, orthogonal, discrete wavelet transform called the multiscale wavelet representatio n (MSWAR) is obtained, The coefficients in MSWAR are shown to be inclu sive of those in MRWAR with the implication that the derived represent ation is invertible. The computational complexity of MSWAR is quantifi ed in terms of the required convolutions, and its implementation is sh own to be equivalent to the filter upsampling technique.