Multiresolution analysis on bounded domains for the design of biorthogonal wavelet bases

An axiomatic approach to biorthogonal multiresolution analyzes on bounded domains is presented. The intervalized multiresolution analysis (MRA) leads to a generalized framework within which one can construct biorthogonal wavelet transforms, including many constructions presented in the literature to date. The framework also leads naturally to algorithms for calculating and constraining pertinent properties of both the discrete filters and their corresponding continuous basis functions. Construction of wavelet analysis within the new framework is then illustrated with the design of a basis specifically tailored to reduce the boundary artifacts induced by some wavelet transforms used in image processing.