Sampling for the V-line transform with vertex on a circle. (23rd June 2021)

• Record Type: Journal Article
• Authors: Nguyen, Duy N; Nguyen, Linh V
• Is Part Of: Inverse problems. Volume 37:Number 7(2021)
• Publication Date: 2021-06-23
• Subjects: sampling -- V-line transform -- Compton camera imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac03a2
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider a special V-line transform in the two dimensional space. It integrates a given function f over the V-lines whose vertices are on a circle centered at the origin and whose symmetric axes pass through the origin. We study the sampling problem of this V-line transform. Namely, we consider the problem of recovering the continuous data from its discrete samples. Under suitable conditions, we prove an error estimate of the recovery. The error estimate is explicitly expressed in terms of f . We then elaborate the required conditions for two sampling schemes: standard and interlaced ones. Finally, we analyze the number of sampling points needed for each case.