A new complex approach towards approximate inverse and generalized Radon transform. Issue 9 (2nd September 2018)

• Record Type: Journal Article
• Authors: Li, Wei; Wang, Jinping
• Is Part Of: Complex variables and elliptic equations. Volume 63:Issue 9(2018)
• Page Start: 1258
• Page End: 1270
• Publication Date: 2018-09-02
• Subjects: Residue theorem -- Sobolev spaces -- generalized Radon transform -- integral equation; 30E25 -- 65R32 -- 65F22; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2017.1357706
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract: In this paper, we first consider the framework of Sobolev spaces and derive analytically a reconstruction algorithm by means of the residue theorem of complex analysis, the approximate inverse, Gaussian mollifier and integral equations. And we successfully extend Natterer's results to the generalized Radon transform with non-uniform attenuation. Finally, we investigate the smoothing properties of the generalized Radon transform.