2016/04/11 by Peter Kuchment, Kuchment, Peter, Fatma Terzioglu +1
Engineering · Medicine · #44A12 #53C65 #92C55 #Advanced X-ray and CT Imaging #Data Analysis #Digital Radiography and Breast Imaging #FOS: Physical sciences #I.2.1 #I.4.5 #Medical Imaging Techniques and Applications #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1604.03805
openalex publication_date 2016/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we address analytically and numerically the inversion of the integral transform (cone or Compton transform) that maps a function on ℝ3 to its integrals over conical surfaces. It arises in a variety of imaging techniques, e.g. in astronomy, optical imaging, and homeland security imaging, especially when the so called Compton cameras are involved. Several inversion formulas are developed and implemented numerically in 3D (the much simpler 2D case was considered in a previous publication). An admissibility condition on detectors geometry is formulated, under which all these inversion techniques will work.