2017/11/23 by Yang Zhang, Zhang, Yang
Computer Science · Mathematics · Medicine · #35R30 #44A12 #65R32 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Medical Imaging Techniques and Applications #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1711.08575
openalex publication_date 2017/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the integral transform over a general family of broken rays in ℝ2. It is natural for broken rays to have conjugate points, for example, when they are reflected from a curved boundary. If there are conjugate points, we show that the singularities cannot be recovered from local data and therefore artifacts arise in the reconstruction. We apply these conclusions to two examples, the V-line Radon transform and the parallel ray transform. In each example, a detailed discussion of the local and global recovery of singularities is given and we perform numerical experiments to illustrate the results.