2023/12/25 by James W. Webber, Webber, James W., Sean Holman +3
Computer Science · Medicine · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2312.15635
openalex publication_date 2023/12/25 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/28
We present a novel analysis of a Radon transform, R, which maps an L2 function of compact support to its integrals over smooth surfaces of revolution with centers on an embedded hypersurface in ℝn. Using microlocal analysis, we derive necessary and sufficient conditions relating to R for the Bolker condition to hold, which has implications regarding the existence and location of image artifacts. We present a general inversion framework based on Volterra equation theory and known results on the spherical Radon transform, and we prove injectivity results for R. Several example applications of our theory are discussed in the context of, e.g., Compton Scatter Tomography (CST) and Ultrasound Reflection Tomography (URT). In addition, using the proposed inversion framework, we validate our microlocal theory via simulation, and present simulated image reconstructions of image phantoms with added noise.