Standard

On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. / Makarov, A. A.; Makarova, S. V. .

In: Numerical Analysis and Applications, Vol. 14, No. 3, 08.2021, p. 258-268.

Research output: Contribution to journal › Article › peer-review

Harvard

Makarov, AA & Makarova, SV 2021, 'On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid', Numerical Analysis and Applications, vol. 14, no. 3, pp. 258-268. https://doi.org/10.1134/s199542392103006x

APA

Makarov, A. A., & Makarova, S. V. (2021). On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. Numerical Analysis and Applications, 14(3), 258-268. https://doi.org/10.1134/s199542392103006x

Vancouver

Makarov AA, Makarova SV. On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. Numerical Analysis and Applications. 2021 Aug;14(3):258-268. https://doi.org/10.1134/s199542392103006x

Author

Makarov, A. A. ; Makarova, S. V. . / On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. In: Numerical Analysis and Applications. 2021 ; Vol. 14, No. 3. pp. 258-268.

BibTeX

@article{b3b085007ea444a292cb160add5557d0,
title = "On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid",
abstract = "Abstract: An explicit representation of filter banks is obtained for constructing wavelet transforms of spaces of linear minimal splines on nonuniform grids on a segment. Decomposition and reconstruction operators are constructed, and it is proved that they are mutually inverse. Some interrelations between the corresponding filters are established. The approach to constructing spline wavelet decompositions used in the present paper is based on using the approximating relations as initial structures for constructing spaces of minimal splines and the calibration relations to prove that the corresponding spaces are embedded An advantage of the approach is the possibility of using nonuniform grids and arbitrary nonpolynomial spline wavelets without using the formalism of Hilbert spaces.",
keywords = "B-spline, filter banks, minimal spline, spline wavelet, wavelet transform, ALGORITHMS",
author = "Makarov, {A. A.} and Makarova, {S. V.}",
note = "Makarov, A.A., Makarova, S.V. On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. Numer. Analys. Appl. 14, 258–268 (2021). https://doi.org/10.1134/S199542392103006X",
year = "2021",
month = aug,
doi = "10.1134/s199542392103006x",
language = "English",
volume = "14",
pages = "258--268",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "3",

}

RIS

TY - JOUR

T1 - On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid

AU - Makarov, A. A.

AU - Makarova, S. V.

N1 - Makarov, A.A., Makarova, S.V. On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid. Numer. Analys. Appl. 14, 258–268 (2021). https://doi.org/10.1134/S199542392103006X

PY - 2021/8

Y1 - 2021/8

N2 - Abstract: An explicit representation of filter banks is obtained for constructing wavelet transforms of spaces of linear minimal splines on nonuniform grids on a segment. Decomposition and reconstruction operators are constructed, and it is proved that they are mutually inverse. Some interrelations between the corresponding filters are established. The approach to constructing spline wavelet decompositions used in the present paper is based on using the approximating relations as initial structures for constructing spaces of minimal splines and the calibration relations to prove that the corresponding spaces are embedded An advantage of the approach is the possibility of using nonuniform grids and arbitrary nonpolynomial spline wavelets without using the formalism of Hilbert spaces.

AB - Abstract: An explicit representation of filter banks is obtained for constructing wavelet transforms of spaces of linear minimal splines on nonuniform grids on a segment. Decomposition and reconstruction operators are constructed, and it is proved that they are mutually inverse. Some interrelations between the corresponding filters are established. The approach to constructing spline wavelet decompositions used in the present paper is based on using the approximating relations as initial structures for constructing spaces of minimal splines and the calibration relations to prove that the corresponding spaces are embedded An advantage of the approach is the possibility of using nonuniform grids and arbitrary nonpolynomial spline wavelets without using the formalism of Hilbert spaces.

KW - B-spline

KW - filter banks

KW - minimal spline

KW - spline wavelet

KW - wavelet transform

KW - ALGORITHMS

UR - http://www.scopus.com/inward/record.url?scp=85113932165&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/48e7840a-27ca-3a99-bdb6-40fd4ec10244/

U2 - 10.1134/s199542392103006x

DO - 10.1134/s199542392103006x

M3 - Article

AN - SCOPUS:85113932165

VL - 14

SP - 258

EP - 268

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 3

ER -

ID: 85563445