On the relationship between quasi-affine systems and the à trous algorithm.
We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasi-affine counterparts associated with a fairly general class of scaling functions that includes the class of compactly supported...