Algebraic design of discrete multiwavelet transforms

An algebraic approach to the design of different kinds of discrete wavelet transforms (orthogonal and biorthogonal single-/multiwavelet transforms, multiwavelet-like transforms) is taken. The different transforms are analysed with respect to computational efforts, approximation properties and symmetry. The design of the orthogonal and biorthogonal single-/multiwavelets requires the solution of a system of linear and nonlinear equations. Only the biorthogonal case enables symmetric coefficients. The basis matrix of the multiwavelet-like transform is easy to compute, orthogonal and ultimately symmetric. Modifications of this multiwavelet-like transform are given with respect to practical applications.<>