Most of the crystal identification (CI) or Depth-Of-Interac- tion (DOI) measurement schemes for phoswich detectors are based on pulse shape discrimination [7], [18]. This approach is very sensitive to noise and mostly limited to photopeak sig- nals for efficient discrimination. To overcome this problem, a fully digital method, based on an adaptive filtering scheme, has been proposed [19]. This method, which is better known as Au- toRegressive model with eXogenous variable (ARX), is able to discriminate crystals even with low-energy Compton events. Al- though this method is very accurate, it is computationally expen- sive and not really tailored for real-time processing. Simplified versions of the ARX technique with recursive algorithms, such as Least Mean Square (LMS) or Recursive Least Square (RLS) [14], and non recursive algorithms, such as Wiener [13] estima- tion, are more appropriate for real time digital processing. Prior to the real-time implementation of the algorithm, an analysis of the DAQ chain characteristics in the pole-zero domain (Z-trans- form) must be done. This analysis consists in building a model by replacing each part of the front-end electronic (Fig. 9) by fil- ters in the Z-domain as depicted in Fig. 10.
In this modeled Z-domain chain [20], the crystal model is considered as an unknown, because it is included in a phoswich detector, and is replaced with an adaptive filter (detailed below). Since the crystal is coupled to the APD, it is impossible to di- rectly extract the DAQ model and this one must be derived from acquired events using the system identification toolbox from