, Volume 2, Issue 4, pp 421-436

Gaussian wavelet transform: Two alternative fast implementations for images

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Abstract

A series of schemes for pyramid multiresolution image coding has been proposed, all of them based on sets of orthogonal functions. Several of them are implementable in the spatial domain (such as wavelets), whereas others are more suitable for Fourier domain implementation (as for instance the cortex transform). Gabor functions have many important advantages, allowing easy and fast implementations in either domain, but are usually discarded by their lack of orthogonality which causes incomplete transforms. In this paper we quantify such effect, showing a Gaussian Wavelet Transform, GWT, withquasiorthogonal Gabor functions, which allows robust and efficient coding. Our particular GWT is based on a human visual model. Its incompleteness causes small amounts of reconstruction errors (due to small indentations in the MTF), which, however, are irrelevant under criteria based on visual perception.