Three-Dimensional Image Reconstruction from Compton Camera Data

abstract

• 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 3 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.

authors

• Kuchment, Peter

published proceedings

• SIAM JOURNAL ON IMAGING SCIENCES

author list (cited authors)

• Kuchment, P., & Terzioglu, F.

citation count

• 27

complete list of authors

• Kuchment, Peter||Terzioglu, Fatma

publication date

• January 2016

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

keywords

• Compton Camera Imaging
• Cone Transform
• Integral Geometry
• Inversion
• Radon Transform

Digital Object Identifier (DOI)

• 10.1137/16M107476X

start page

• 1708

end page

• 1725

volume

• 9

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2F16m107476x