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On the matrix completion problem for multivariate filter bank construction

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Abstract

We survey the main techniques for the construction of multivariate filter banks and present new results about special matrices of order four and eight suitable for their construction.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, P.R. China

    Qiuhui Chen

  2. Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, New York, 12222, USA

    Charles A. Micchelli

  3. Department of Mathematics, Syracuse University, Syracuse, NY, 13244-1150, USA

    Yuesheng Xu

  4. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Yuesheng Xu

Authors
  1. Qiuhui Chen
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  2. Charles A. Micchelli
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  3. Yuesheng Xu
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Correspondence to Yuesheng Xu.

Additional information

Communicated by J. Carnicer and J.M. Peña

Qiuhui Chen: Supported in part by NSFC under grant 10201034 and project-sponsored by SRF for ROCS, SEM.

Charles A. Micchelli: Supported in part by the US National Science Foundation under grant CCR-0407476.

Yuesheng Xu: All correspondence to this author. Supported in part by the US National Science Foundation under grant CCR-0407476, by the Natural Science Foundation of China under grant 10371122 and by the Chinese Academy of Sciences under the program “One Hundred Distinguished Chinese Young Scientists”.

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Chen, Q., Micchelli, C.A. & Xu, Y. On the matrix completion problem for multivariate filter bank construction. Adv Comput Math 26, 173–204 (2007). https://doi.org/10.1007/s10444-005-7535-9

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