The optimal recovery of a function from an inaccurate information on its k-plane transform. (26th April 2016)

• Record Type: Journal Article
• Authors: Bagramyan, Tigran
• Is Part Of: Inverse problems. Volume 32:Number 6(2016:Jun.)
• Publication Date: 2016-04-26
• Subjects: Radon transfrom -- optimal recovery -- Laplace operator -- x-ray transform -- k-plane transform -- extremal problems -- approximations; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/6/065004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the optimal recovery of the β th degree of the Laplacian value on a function from the information on its k -plane transform, measured with an error. We present the error of the optimal recovery and the set of optimal methods on classes with the bounded α th degree of the Laplacian, where 0 ≤ β < α . As a consequence, we give one inequality for the norms of the degree of the Laplace operator and the k -plane transform. Particular cases include new inversion methods and inequalities for the classical Radon and x-ray transforms.