Sampling for the V-line Transform with Vertex in a Circle

TL;DR

This paper introduces sampling schemes for a specialized V-line transform with centers on a circle, providing error estimates that relate to the function being transformed, advancing understanding of sampling in integral geometry.

Contribution

It proposes two novel sampling schemes for the V-line transform with centers on a circle and derives explicit error estimates for these schemes.

Findings

Standard and interlaced sampling schemes are developed.

Error estimates are explicitly expressed in terms of the function.

The schemes improve understanding of sampling in V-line transforms.

Abstract

In this paper, we consider a special V-line transform. It integrates a given function f over the V-lines whose centers are on a circle centered at the origin and the symmetric axes pass through the origin. We derive two sampling scheme of the transform: the standard and interlaced ones. We prove the an error estimate for the schemes, which is explicitly expressed in term of f.