Three-Dimensional Image Reconstruction from Compton Camera Data
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© 2016 Society for Industrial and Applied Mathematics. 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 three dimensions (the much simpler two-dimensional case was considered in a previous publication). An admissibility condition on detectors geometry is formulated, under which all these inversion techniques will work.
author list (cited authors)
Kuchment, P., & Terzioglu, F.