Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets

The recent developments in the theory of multivariate polynomial matrix factorization have proven to be promising for potential applications. Attention is given here to the relevance of the described algebraic results to multidimensional filter bank design and, consequently, also to first generation discrete wavelet construction. The recent use of such wavelets in image sequence superresolution (high resolution) is then described in the context of the conversion of the high resolution nonuniformly sampled raster generated from an acquired sequence of low resolution frames to the desired uniformly sampled high resolution grid. In the future, the multivariate polynomial matrix factorization results can be profitably adapted to the problem of multidimensional convolutional code construction, and the construction (by filter banks) and subsequent deployment of second generation wavelets (which adapt to irregular sampled data) are expected to provide improved superresolution.