Balanced spatial and frequency localised 2-D nonseparable wavelet filters

A filter cannot have simultaneous localization in the spatial domain and the frequency domain by virtue of the uncertainty principle: there is a trade-off between spatial and frequency localizations. The design of two-dimensional wavelet filters on the quincunx sampling lattice is considered in this paper. The filters are optimized with respect to the Balanced-Localization (BL) metric. The BL metric represents a balance between the spatial localization and frequency localization of a filter. An efficient technique is proposed for designing a class of biorthogonal wavelet filters with prescribed regularity. © 2001 IEEE.