Fast gamma-ray interaction-position estimation using k-d tree search.

We have developed a fast gamma-ray interaction-position estimation method using k-d tree search, which can be combined with various kinds of closeness metrics such as Euclidean distance, maximum likelihood estimation, etc. Compared with traditional search strategies, this method can achieve both speed and accuracy at the same time using the k-d tree data structure. The k-d tree search method has a time complexity of O(log(2)(N)), where N is the number of entries in the reference data set, which means large reference datasets can be used to efficiently estimate each event's interaction position. This method's accuracy was found to be equal to that of the exhaustive search method, yielding the highest achievable accuracy. Most importantly, this method has no restriction on the data structure of the reference dataset and can still work with complicated mean-detector-response functions (MURFs), meaning that it is more robust than other popular methods such as contracting-grid-search (CG) or vector-search (VS) methods that could yield locally optimal instead of globally optimal results.