The Berkeley Wavelet Transform: A Biologically Inspired Orthogonal Wavelet Transform
Authors:
- 1 June 2008
- journal article
- Published by MIT Press in Neural Computation
- Vol. 20 (6) , 1537-1564
Abstract
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 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, ...Keywords
This publication has 35 references indexed in Scilit:
- COMPLETE FUNCTIONAL CHARACTERIZATION OF SENSORY NEURONS BY SYSTEM IDENTIFICATIONAnnual Review of Neuroscience, 2006
- Methods for first-order kernel estimation: simple-cell receptive fields from responses to natural scenesNetwork: Computation in Neural Systems, 2003
- Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuliNetwork: Computation in Neural Systems, 2001
- Responses of neurons in primary and inferior temporal visual cortices to natural scenesProceedings Of The Royal Society B-Biological Sciences, 1997
- Emergence of simple-cell receptive field properties by learning a sparse code for natural imagesNature, 1996
- The generalized Gabor scheme of image representation in biological and machine visionIEEE Transactions on Pattern Analysis and Machine Intelligence, 1988
- Relations between the statistics of natural images and the response properties of cortical cellsJournal of the Optical Society of America A, 1987
- The cortex transform: Rapid computation of simulated neural imagesComputer Vision, Graphics, and Image Processing, 1987
- Phase Relationships Between Adjacent Simple Cells in the Visual CortexScience, 1981
- Mathematical description of the responses of simple cortical cells*Journal of the Optical Society of America, 1980