Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames.
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| Title: | Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames. |
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| Authors: | Cui, Lihong1 (AUTHOR) lhongcui@163.com, Zhu, Ning2 (AUTHOR), Wang, Youquan1 (AUTHOR), Sun, Jianjun3 (AUTHOR), Cen, Yigang4 (AUTHOR) |
| Source: | Numerical Functional Analysis & Optimization. 2016, Vol. 37 Issue 9, p1089-1106. 18p. |
| Subjects: | Wavelets (Mathematics), Multiresolution time-domain method, Frames (Vector analysis), Color image processing, Mathematical optimization |
| Abstract: | In this article, we introduce and study the matrix-valued tight wavelet frames for analyzing matrix-valued signal based on matrix-valued multiresolution analysis (MMRA). We put our emphasis on the existence of the MMRA-based matrix-valued tight wavelet frames by establishing the correspondence with their the unitary extension principle (UEP). Here in particular we introduce the square brackets product and the quasi-interpolatory operator, which makes the certificating process for UEP become relatively simple. Some interesting byproducts, such as features on the quasi-interpolatory operator 𝒫nin the matrix-valued function space case, are the critical foundation for our main work. [ABSTRACT FROM AUTHOR] |
| Copyright of Numerical Functional Analysis & Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 117954843 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cui%2C+Lihong%22">Cui, Lihong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lhongcui@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhu%2C+Ning%22">Zhu, Ning</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Youquan%22">Wang, Youquan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sun%2C+Jianjun%22">Sun, Jianjun</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cen%2C+Yigang%22">Cen, Yigang</searchLink><relatesTo>4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Numerical+Functional+Analysis+%26+Optimization%22">Numerical Functional Analysis & Optimization</searchLink>. 2016, Vol. 37 Issue 9, p1089-1106. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Wavelets+%28Mathematics%29%22">Wavelets (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Multiresolution+time-domain+method%22">Multiresolution time-domain method</searchLink><br /><searchLink fieldCode="DE" term="%22Frames+%28Vector+analysis%29%22">Frames (Vector analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Color+image+processing%22">Color image processing</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, we introduce and study the matrix-valued tight wavelet frames for analyzing matrix-valued signal based on matrix-valued multiresolution analysis (MMRA). We put our emphasis on the existence of the MMRA-based matrix-valued tight wavelet frames by establishing the correspondence with their the unitary extension principle (UEP). Here in particular we introduce the square brackets product and the quasi-interpolatory operator, which makes the certificating process for UEP become relatively simple. Some interesting byproducts, such as features on the quasi-interpolatory operator 𝒫nin the matrix-valued function space case, are the critical foundation for our main work. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Numerical Functional Analysis & Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/01630563.2016.1193026 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1089 Subjects: – SubjectFull: Wavelets (Mathematics) Type: general – SubjectFull: Multiresolution time-domain method Type: general – SubjectFull: Frames (Vector analysis) Type: general – SubjectFull: Color image processing Type: general – SubjectFull: Mathematical optimization Type: general Titles: – TitleFull: Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cui, Lihong – PersonEntity: Name: NameFull: Zhu, Ning – PersonEntity: Name: NameFull: Wang, Youquan – PersonEntity: Name: NameFull: Sun, Jianjun – PersonEntity: Name: NameFull: Cen, Yigang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: 2016 Type: published Y: 2016 Identifiers: – Type: issn-print Value: 01630563 Numbering: – Type: volume Value: 37 – Type: issue Value: 9 Titles: – TitleFull: Numerical Functional Analysis & Optimization Type: main |
| ResultId | 1 |
