Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets

  • N. K. Bose
  • S. Lertrattanapanich
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


Filter Bank Mother Wavelet Polynomial Matrix Convolutional Code Multiresolution Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 2004

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  • N. K. Bose
  • S. Lertrattanapanich

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