Willmore, Ben; Prenger, Ryan J.; Wu, Michael C.-K.; Gallant, Jack L. The Berkeley wavelet transform: A biologically inspired orthogonal wavelet transform. (English) Zbl 1136.92310 Neural Comput. 20, No. 6, 1537-1564 (2008). Summary: 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, 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. MSC: 92C20 Neural biology 65T60 Numerical methods for wavelets 94A12 Signal theory (characterization, reconstruction, filtering, etc.) PDFBibTeX XMLCite \textit{B. Willmore} et al., Neural Comput. 20, No. 6, 1537--1564 (2008; Zbl 1136.92310) Full Text: DOI Link References: [1] DOI: 10.1364/JOSAA.2.000284 · doi:10.1364/JOSAA.2.000284 [2] DOI: 10.1117/12.976485 · doi:10.1117/12.976485 [3] DOI: 10.1098/rspb.1997.0246 · doi:10.1098/rspb.1997.0246 [4] DOI: 10.1016/S0042-6989(97)00121-1 · doi:10.1016/S0042-6989(97)00121-1 [5] Daubechies I., Commun. Pur. Appl. Math. 41 pp 906– (1988) [6] DOI: 10.1016/0042-6989(80)90065-6 · doi:10.1016/0042-6989(80)90065-6 [7] DOI: 10.1080/09548980500464030 · doi:10.1080/09548980500464030 [8] DOI: 10.1016/0042-6989(82)90113-4 · doi:10.1016/0042-6989(82)90113-4 [9] DOI: 10.1364/JOSAA.4.002379 · doi:10.1364/JOSAA.4.002379 [10] DOI: 10.1162/neco.1994.6.4.559 · doi:10.1162/neco.1994.6.4.559 [11] Gabor D., J. Inst. Electr. Eng. 93 pp 429– (1946) [12] DOI: 10.1007/BF01456326 · JFM 41.0469.03 · doi:10.1007/BF01456326 [13] Jones J. P., J. Neurophysiol. 58 (6) pp 1233– (1987) [14] DOI: 10.1364/JOSA.70.001297 · doi:10.1364/JOSA.70.001297 [15] DOI: 10.1113/jphysiol.1978.sp012489 · doi:10.1113/jphysiol.1978.sp012489 [16] DOI: 10.1113/jphysiol.1978.sp012488 · doi:10.1113/jphysiol.1978.sp012488 [17] DOI: 10.1038/381607a0 · doi:10.1038/381607a0 [18] DOI: 10.1126/science.7233231 · doi:10.1126/science.7233231 [19] DOI: 10.1109/TSMC.1983.6313086 · doi:10.1109/TSMC.1983.6313086 [20] DOI: 10.1109/34.3910 · Zbl 0645.92026 · doi:10.1109/34.3910 [21] DOI: 10.1117/12.304883 · doi:10.1117/12.304883 [22] Ringach D. L., J. Neurosci. 22 (13) pp 5639– (2002) [23] Rolls E. T., J. Neurophysiol. 73 (2) pp 713– (1995) [24] Smyth D., J. Neurosci. 23 (11) pp 4746– (2003) [25] DOI: 10.1088/0954-898X/12/3/304 · Zbl 0997.92005 · doi:10.1088/0954-898X/12/3/304 [26] DOI: 10.1088/0954-898X/2/4/004 · Zbl 0828.92009 · doi:10.1088/0954-898X/2/4/004 [27] DOI: 10.1126/science.287.5456.1273 · doi:10.1126/science.287.5456.1273 [28] DOI: 10.1016/S0734-189X(87)80184-6 · doi:10.1016/S0734-189X(87)80184-6 [29] DOI: 10.1109/10.16453 · doi:10.1109/10.16453 [30] Willmore B., Soc. Neurosci. Abstr. 618 pp 17– (2005) [31] DOI: 10.1088/0954-898X/14/3/309 · doi:10.1088/0954-898X/14/3/309 [32] DOI: 10.1080/713663277 · doi:10.1080/713663277 [33] DOI: 10.1146/annurev.neuro.29.051605.113024 · doi:10.1146/annurev.neuro.29.051605.113024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.