Existence of Matrix-Valued Multiresolution Analysis-Based Matrix-Valued Tight Wavelet Frames. (1st September 2016)

• Record Type: Journal Article
• Authors: Cui, Lihong; Zhu, Ning; Wang, Youquan; Sun, Jianjun; Cen, Yigang
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 9(2016)
• Page Start: 1089
• Page End: 1106
• Publication Date: 2016-09-01
• Subjects: Matrix-valued tight wavelet frames -- unitary extension principle -- MMRA -- quasi-interpolatory operator; 42C15 -- 42C40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1193026
• Languages: English
• ISSNs: 0163-0563

Abstract

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 𝒫 n in the matrix-valued function space case, are the critical foundation for our main work.