4
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: not found

      Biorthogonal wavelets and tight framelets from smoothed pseudo splines

      Read this article at

      ScienceOpenPublisherPMC
      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In order to get divergence free and curl free wavelets, one introduced the smoothed pseudo spline by using the convolution method. The smoothed pseudo splines can be considered as an extension of pseudo splines. In this paper, we first show that the shifts of a smoothed pseudo spline are linearly independent. The linear independence of the shifts of a pseudo spline is a necessary and sufficient condition for the construction of the biorthogonal wavelet system. Based on this result, we generalize the results of Riesz wavelets and derive biorthogonal wavelets from smoothed pseudo splines. Furthermore, by applying the unitary extension principle, we construct tight frame systems associated with smoothed pseudo splines with desired approximation order.

          Related collections

          Most cited references 19

          • Record: found
          • Abstract: not found
          • Article: not found

          Framelets: MRA-based constructions of wavelet frames

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Affine Systems inL2(Rd): The Analysis of the Analysis Operator

             Amos Ron,  Zuowei Shen (1997)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Fractional Splines and Wavelets

                Bookmark

                Author and article information

                Contributors
                zhjie@mail.nwpu.edu.cn
                Journal
                J Inequal Appl
                J Inequal Appl
                Journal of Inequalities and Applications
                Springer International Publishing (Cham )
                1025-5834
                1029-242X
                14 July 2017
                14 July 2017
                2017
                : 2017
                : 1
                Affiliations
                ISNI 0000 0001 0307 1240, GRID grid.440588.5, Department of Applied Mathematics, , Northwestern Polytechnical University, ; Xi’an, Shaanxi 710072 P.R. China
                Article
                1439
                10.1186/s13660-017-1439-3
                5509888
                © The Author(s) 2017

                Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                Funding
                Funded by: the nutural science basis research program of shaan xi province
                Award ID: 2014JQ1038
                Categories
                Research
                Custom metadata
                © The Author(s) 2017

                Comments

                Comment on this article