Boundary filter design for multiwavelets

When designing boundary filters for multiwavelets, perfect reconstruction and moment conditions are two of the most important criteria to be considered. Since the filter coefficients of multiwavelets are expressed in the form of matrices, the moment conditions for multiwavelets do not relate to the filter coefficients in a simple way as for scalar wavelets. The authors first formulate the moment conditions of multiwavelets and then use them as the criteria for the optimisation of the boundary multifilters. They then apply the proposed optimisation scheme to the design of boundary multifilters for CL and GHM multiwavelets. The optimised boundary filters possess the desired perfect reconstruction property and vanishing moments that allow them to reduce the boundary artefact by up to 75% as compared with the traditional approach.