Singularities of the X-ray transform and limited data tomography in R2 and R3
SIAM Journal on Mathematical Analysis
On the V-line radon transform and its imaging applications
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
A series formula for inversion of the V-line Radon transform in a disc
Computers & Mathematics with Applications
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Several novel imaging modalities proposed during the last couple of years are based on a mathematical model, which uses the V-line Radon transform (VRT). This transform, sometimes called broken-ray Radon transform, integrates a function along V-shaped piecewise linear trajectories composed of two intervals in the plane with a common endpoint. Image reconstruction problems in these modalities require inversion of the VRT. While there are ample results about inversion of the regular Radon transform integrating along straight lines, very little is known for the case of the V-line Radon transform. In this paper, we derive an exact inversion formula for the VRT of functions supported in a disc of arbitrary radius. The formula uses a two-dimensional restriction of VRT data, namely the incident ray is normal to the boundary of the disc, and the breaking angle is fixed. Our method is based on the classical filtered back-projection inversion formula of the Radon transform, and has similar features in terms of stability, speed, and accuracy.