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 arepromising 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