Biorthogonal quincunx Coifman wavelets
We define 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 filter banks possess many interesting properties such as perfect reconstruction, vanishing moments, symmetry, diamond-shaped passbands, and dyadic fractional filter coefficients. We derive explicit formulas for the frequency responses of these filter banks. Both the analysis and synthesis lowpass filters converge to an ideal diamond-shaped halfband lowpass filter as the order of the corresponding BQCW system tends to infinity. 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.