## 1 Introduction
[31] and inspired the development of several PEM systems such as Clear-PEM [32], composed of a dual-plate detector head composed of LSO (Lutetium oxyorthosilicate) crystals and designed to allow the breast and axilla region field of view (FOV); dual-head planar PEM [33], which has a parallel dual-planar detector geometry composed of LSO crystals and designed for greater flexibility in positioning the object into the FOV; the LBNL-PEM (Lawrence Berkeley National Laboratory-PEM) [34], which has a rectangular geometry, with four detector plates composed of LSO crystals surrounding the breast, and has depth of interaction (DOI) measurements capabilities; the Naviscan PEM flex system [35], which is a specially designed system with two opposite detector heads to fit on a stereotactic mammography unit, with the aim of allowing emission and transmission scans at the same time; the Elmammo (Shimadzu) dbPET (dedicated breast PET) system [36], developed by Shimadzu Co. and designed with three contiguous rings allowing a larger FOV and confirmed high resolution images with four layers of DOI measurement capability; and the Jefferson laboratory PEM system [37], designed to be mounted on a stereotactic biopsy table to perform PEM-guided biopsies. We have developed a highly sensitive PEMGRAPH (Mirai Imaging Inc., Fukushima, Japan) that consists of a dedicated dual-head PEM system with Pr:LuAG (Praseodymium-dopped Lutetium Aluminum Garnet) crystal and was designed for breast cancer diagnosis [38]. The Pr:LuAG scintillator, with its high light yield, short decay time and good energy resolution, is preferred for angular coverage, while BaSO\({}_{4}\) (Barium sulfate) is utilized as a reflector with the crystal to efficiently reflect scintillation photons from Pr:LuAG. PEMGRAPH showed a high spatial resolution of 2.0 mm (FWHM) in the plane parallel to the detectors [39] and a higher detection sensitivity for breast cancer compared with whole-body PET [40]. Our developed system was found to have higher spatial resolution and higher sensitivity when compared to other commercial PEM devices. Recently, [PERSON] et al. [41] reported that the \({}^{16}\)O(p,2p2n)\({}^{13}\)N reaction has a relatively low threshold energy and it could be potentially used for proton range verification. As a result, the \({}^{13}\)N creation may be extracted by computing the gradient between early and late PET scans, and it is found to be highly connected with the Bragg peak. In our recent work, we have employed the Monte Carlo technique to study the generation of the \({}^{13}\)N radioisotope and its potential use to estimate the Bragg peak location in a simulated water-gel phantom [42]. In the present work, we have introduced an analysis scheme based on our recent experimentally obtained results from a cyclotron and the PEMGRAPH system for the three-dimensional (3D) visualization of positron emitting radioisotopes (particularly \({}^{13}\)N). The present analysis scheme uses data obtained from the PEMGRAPH system from a proton irradiated phantom to provide the 3D distribution of positron emitting radioisotopes by using the spectral analysis (SA) approach. All necessary computer programs and raw data used in the present analysis scheme were made open source under the GPLv3 license, which allows users to freely modify, compile and distribute data without any restrictions. To the best of our knowledge, this is the first time such an extensive algorithmic scheme is being proposed, and this will be useful to enhance the effectiveness of proton range monitoring and verification.