The Berkeley Wavelet Transform: A biologically-inspired orthogonal wavelet transform

摘要

We describe the Berkeley Wavelet Transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets, at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single DC term), the wavelets form a complete, orthonormal basis in two dimensions.The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localised in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial-frequency and orientation bandwidths which are comparable with biological values.Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis, and is therefore inexpensive to compute, manipulate and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.