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The Berkeley Wavelet Transform: A Biologically Inspired Orthogonal Wavelet Transform

benjamin.willmore{at}dpag.ox.ac.uk Department of Physiology, Anatomy, and Genetics, University of Oxford, Parks Road, Oxford OX1 3PT, U.K.

Ryan J. Prenger

prenger{at}berkeley.edu Physics Department, University of California, Berkeley, CA 94720, U.S.A.

Michael C.-K. Wu

wafting{at}berkeley.edu Biophysics Graduate Group, University of California, Berkeley, CA 94720, U.S.A.

Jack L. Gallant

gallant{at}berkeley.edu Department of Psychology and Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94720, U.S.A.

We describe the Berkeley wavelet transform (BWT), a two-dimen-sional 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 constant 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 localized 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 that 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.