Compton cameras are becoming a subject of increasing interest in medical imaging due to their potential applications. Compton cameras are used to obtain an image by employing the gamma-rays which interact within the device. For the image to be accurate, knowledge of the incident energy of the gamma-ray is often required by the reconstruction algorithms. However, in a conventional two-layer Compton camera this incident energy can only be estimated, provided that the requirement of photoabsorption in the second plane may not be fulfilled for all signal events. To overcome this, a possible solution is to add a third plane to the Compton camera, in which case we refer to the device as a “three-layer Compton telescope”. Thus the incident energy can be directly obtained from the gamma-rays which interact in the three planes; but then, in the image reconstruction process asssociated with such device, a System Matrix which accounts for these new signal events is needed. Furthermore, Sensitivity Matrix corrections are relevant in Compton camera imaging and should be properly estimated. A common way to achieve these requirements is to compute both the Sensitivity and System Matrices by Monte Carlo methods. The slowness of this method is typically solved by precalculating both matrices once, prior to the reconstruction process.
The IRIS group (Image Reconstruction, Instrumentation and Simulations for medical imaging applications) of IFIC-Valencia is developing a three-layer Compton telescope based on continuous LaBr3 crystals coupled to SiPMs. Hence, given the high granularity of our prototype, a Monte Carlo precalculation of the Sensitivity and System Matrices would imply high computational burdens. For this reason, the group has proposed an analytical model, which allows computing the probability of detection of those events which give rise to signal in the telescope in order to estimate on the fly the Sensitivity and System Matrices. Currently, the model is in its last stage of validation for a two-layer Compton telescope. Nevertheless, such validation must be extended to characterize entirely the three-layer Compton telescope that is being developed at the group. The process is not trivial, provided the different topology of the events which give rise to signal or background, and the decrease of the efficiency.
In this work we present the first preliminary tests on the validation of the proposed model for a three-layer Compton telescope. This is achieved by comparing the analytical predictions of elements of the Sensitivity and System Matrices with the results of Monte Carlo simulations. The performance of the model is tested by obtaining images of monochromatic, point-like sources from simulated data. In addition, a preliminary study on the background/signal ratio for a three-layer Compton telescope is reported, emphasizing those events which most contribute to image degradation.