Biorthogonal Quincunx Coifman Wavelets

We de ne and construct a new family of compactly supported, nonseparable two-dimensional wavelets, \biorthogonal quincunx Coifman wavelets" (BQCWs), from their one-dimensional counterparts using the McClellan transformation. The resulting lter banks possess many interesting properties such as perfect reconstruction, vanishing moments, symmetry, diamondshaped passbands, and dyadic fractional lter coe cients. We derive explicit formulas for the frequency responses of these lter banks. Both the analysis and synthesis lowpass lters converge to an ideal diamondshaped halfband lowpass lter as the order of the corresponding BQCW system tends to in nity. Hence, they are promising in image and multidimensional signal processing applications. In addition, the synthesis scaling function in a BQCW system of any order is interpolating (or cardinal), which has been known as a desired merit in numerical analysis.