Orthogonally compensated W-multiresolution analysis and signal processing

The concept of a W-matrix is used to give an elementary interpretation of a biorthogonal wavelet decomposition of signals. The authors also give a method to modify the decomposition to give an orthogonal projection on the space spanned by the scaling vectors. Roughly speaking, their treatment is a finite-length analog of the well-known theory of multiresolution analysis of Meyer and Mallat. Their approach differs in that it deals directly with the discrete case, it takes care of the boundary elements without explicit padding,and it uses a notion similar to that of semiorthogonality introduced by Chui. Their algorithm has flexibility in the choice of filter coefficients. The decomposition, orthogonalization, and restoration algorithms are computationally fast