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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 01630563 |
| DOI: | 10.1080/01630563.2016.1193026 |
