Multivariate Symmetric Interpolating Dual Multiwavelet Frames

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Multivariate Symmetric Interpolating Dual Multiwavelet Frames. / Krivoshein, Aleksandr .

In: Symmetry, Vol. 14, No. 7, 1425, 11.07.2022.

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

BibTeX

@article{74798488a4eb4e4ebff3a2bc32b20a77,

title = "Multivariate Symmetric Interpolating Dual Multiwavelet Frames",

abstract = "The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented. ",

keywords = "symmetry group, multivariate multiwavelet frames, matrix mask, interpolating refinable function vector, symmetry group, multivariate multiwavelet frames, matrix mask, interpolating refinable function vector",

author = "Aleksandr Krivoshein",

note = "Publisher Copyright: {\textcopyright} 2022 by the author.",

year = "2022",

month = jul,

day = "11",

doi = "https://doi.org/10.3390/sym14071425",

language = "English",

volume = "14",

journal = "Symmetry",

issn = "2073-8994",

publisher = "MDPI AG",

number = "7",

}

RIS

TY - JOUR

T1 - Multivariate Symmetric Interpolating Dual Multiwavelet Frames

AU - Krivoshein, Aleksandr

PY - 2022/7/11

Y1 - 2022/7/11

N2 - The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented.

AB - The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented.

KW - symmetry group

KW - multivariate multiwavelet frames

KW - matrix mask

KW - interpolating refinable function vector

KW - symmetry group

KW - multivariate multiwavelet frames

KW - matrix mask

KW - interpolating refinable function vector

UR - http://www.scopus.com/inward/record.url?scp=85137352143&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e43005a6-a921-3cae-b3c8-40b43f4ab111/

U2 - https://doi.org/10.3390/sym14071425

DO - https://doi.org/10.3390/sym14071425

M3 - Article

VL - 14

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 7

M1 - 1425

ER -

ID: 98563138