Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames |
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| Authors: | Lihong Cui Ning Zhu Youquan Wang Jianjun Sun Yigang Cen |
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| Institution: | 1. School of Science, Beijing University of Chemical Technology, Beijing, Chinalhongcui@163.com;3. School of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Beijing, China;4. School of Science, Beijing University of Chemical Technology, Beijing, China;5. College of Chemical Engineering, Beijing University of Chemical Technology, Beijing, China;6. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China |
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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 𝒫n in the matrix-valued function space case, are the critical foundation for our main work. |
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| Keywords: | Matrix-valued tight wavelet frames unitary extension principle MMRA quasi-interpolatory operator |
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