Matrix Spectral Factorization for Alpert Multiwavelet Filter Bank

Multiwavelets can be orthogonal, symmetric, smooth, and with short support, all at the same time. However, the design of multifilters with these properties remains a challenging problem. Obtaining multifilters by using matrix spectral factorization (MSF) is still quite unknown in the signal processing community. There are a number of numerical approaches to MSF, but they usually cannot handle the case when the determinant of the matrix product filter has zeros on the unit circle (i.e. singularity), which is precisely of greatest interest in the construction of multiwavelets. We describe a novel design of Alpert's multiwavelet filter using Bauer's method for MSF of a product multifilter. We apply the proposed multifilter for image denoising of gray images and compare with the orthogonal GHM and CL multifilters.