Fast computation of the 2D discrete wavelet transform
Frederick M. Waltz · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
Interest in the discrete wavelet transform has grown explosively in the last five years, even though the underlying concepts are decades old and nearly identical transform techniques were being applied in industry 10 years ago. The most important aspect of the new work is the development of the underlying theory. Most if not all of the current applications of wavelets are software based, implying either slow execution times or very expensive computers. This paper shows the feasibility of using moderately-priced commercially-available image processing boards to carry out multi-band 2-dimensional (2D) wavelet transforms at real-time (30 images/sec) or faster-than-real-time rates. Implementations for both real and complex wavelets are shown. Word length and kernel size limitations are discussed, along with methods to overcome them. One-dimensional wavelets are mentioned as a special case of 2D wavelets. Because of the high speed and moderate cost of these implementations, much wider application of wavelets to industrial problems is now possible.