An Efficient Method for Ellipse Reconstruction Using the Hough Transform for Cherenkov Cone Detection

With the availability of silicon photo diode arrays new imaging concepts such as the detection of Cherenkov light emitted from energetic Compton electrons generated after gamma ray interaction in thick radiators become feasible with the advantage of very fast timing. In simulations it had been shown that under conditions, where the multiple scattering of an electron track perpendicular to the read-out plane is sufficiently reduced, the position and the depth of interaction still are preserved in the detected photon pattern. However, the angular distribution of Compton electrons generated from gamma rays necessitates the reconstruction of ellipses. The widely used Hough transform for fast image reconstruction requires the use of a 5-dimensional parameter space, with the consequence of impractical exponential increase in computing time and loss of sensitivity. Here it is shown that the use of a priori knowledge reduces the reconstruction to the circular problem with the direct result of the depth of interaction and a simple geometrical calculation for positional and angular determination. It is found that for electrons with an energy of 4 MeV stopped in PMMA a precision of 4% for the depth of interaction (DOI) compared to the complementary thickness CD of the radiator (CD = thickness of the radiator minus DOI) can be obtained. For the directional resolution (relative angular resolution) the same value is obtained, yielding finally a position resolution similar to DOI since the Cherenkov angle to be used is close to 45 degrees. Applications of the method will be found in imaging of high energy therapeutic radio nuclides, industrial imaging and homeland security.