Exact inversion of an integral transform arising in passive detection of gamma-ray sources with a Compton camera

Fatma Terzioglu

doi:10.1117/12.2534439

28 May 2019 Exact inversion of an integral transform arising in passive detection of gamma-ray sources with a Compton camera

Fatma Terzioglu

Author Affiliations +

Proceedings Volume 11072, 15th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine; 1107217 (2019) https://doi.org/10.1117/12.2534439
Event: Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 2019, Philadelphia, United States

Abstract

In this paper, we address exact inversion of the integral transform, called Compton (or cone) transform, that maps a function on R3 to its integrals over conical surfaces. Compton transform arises in passive detection of gammaray sources with a Compton camera which has promising applications in medical and industrial imaging as well as in homeland security imaging and astronomy. We present a two-step method that uses the full set of available projections for inverting the Compton transform: first the recovery of the Radon transform from the Compton transform, and then the Radon transform inversion. The first step can be done in various ways by means of the generalization of a previously obtained result relating the Compton and Radon transforms. This leads to a variety of Compton inversion formulas that are independent of the geometry of detectors as long as a generous admissibility condition is met. We formulate one inversion formula that is simpler and performs well in the case of noisy data, which is demonstrated by a numerical simulation.

Citation Download Citation

Fatma Terzioglu "Exact inversion of an integral transform arising in passive detection of gamma-ray sources with a Compton camera", Proc. SPIE 11072, 15th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 1107217 (28 May 2019); https://doi.org/10.1117/12.2534439

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