Inversion Formula for Shearlet Transform in Arbitrary Space Dimensions. (1st November 2016)

• Record Type: Journal Article
• Authors: Jiang, Shenming; Jiang, Zetao
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 11(2016)
• Page Start: 1438
• Page End: 1463
• Publication Date: 2016-11-01
• Subjects: Inversion formula -- shearlet group -- shearlet transform; 42C15 -- 94A12; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1212208
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study the convergence of the inverse shearlet transform in arbitrary space dimensions. For every pair of admissible shearlets, we show that although the integral involved in the inversion formula from the continuous shearlet transform is convergent in the L 2 sense, it is not true in general whenever pointwise convergence is considered. We give some sufficient conditions for the pointwise convergence to hold. Moreover, for any pair of admissible shearlets we show that the Riemannian sums defined by the inverse shearlet transform are convergent to the original function as the sampling density tends to infinity.