Multiwavelet prefilters: Orthogonal prefilters preserving approximation order p less than or equal to 3

In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space {dollar}Vsb0.{dollar} We desire this association or prefiltering to preserve polynomial data up to the approximation order of the scaling vector {dollar}Phi{dollar} as well as preserve the energy of the signal. In this thesis, we show existence of and a general construction for orthogonal (paraunitary) FIR prefilters that preserve the approximation order of a given arbitrary compactly supported orthonormal generator {dollar}Phi{dollar} with approximation order {dollar}ple3.{dollar} Because the scaling vector in the theory of multiwavelets is an orthonormal generator, as examples we give several orthogonal FIR prefilters for the DGHM scaling vector with approximation order {dollar}p=2,{dollar} the scaling vector of Legendre polynomials and a piecewise quadratic scaling vector both with approximation order {dollar}p=3.{dollar} In addition, we give experimental results comparing the orthogonal prefilters to the interpolation prefilter for the DGHM scaling vector on three standard test images.