Prompt gamma ray (PG) imaging based on Compton camera (CC) is promising to realize in vivo verification during the proton therapy. However, the finite spatial and energy resolution of current CC, as well as the Doppler broaden effect, degrade the quality and resolution of PG images. In addition, due to the inherent geometrical complexity of Compton camera data, PG imaging can be time-consuming and difficult to reconstruct in real-time, while using standard techniques such as filtered back-projection or maximum likelihood-expectation maximization. In this paper, we propose three modifications of origin ensembles with resolution recovery (OE-RR) algorithm based on Markov chains to accelerate the convergence to equilibrium of OE-RR algorithm and improve the image quality. For evaluation, we performed a Monte Carlo simulation of a three-stage CZT Compton camera with resolution loss to detect the PG produced by a proton beam in a water phantom, and evaluate image quality of the gamma rays emitted during proton irradiation. The results show that our ordered OE-RR algorithm realized a good resolution recovery and accurate estimation of the position, including the peak and the distal falloff of the PG emission with remarkably faster reconstruction, thus demonstrating the feasibility of this new method in non-idealized PG-based proton range verification.

This paper describes a new geometric algorithm to determine the largest feasible cutter size for 2-D milling operations to be performed using a single cutter. First is given a general definition of the problem as the task of covering a target region without interfering with an obstruction region. This definition encompasses the task of milling a general 2-D profile that includes both open and closed edges. Discussed next are three alternative definitions of what it means for a cutter to be feasible, with explanations of which of these definitions is most appropriate for the above problem. Then, a geometric algorithm is presented for finding the maximal cutter for 2-D milling operations, and the algorithm is shown to be correct.

Different cutter path patterns have been shown to be efficient for different types of pocket geometries. However, for certain types of complex pockets, no single type of pattern produces efficient cutter paths throughout the pocket. In this paper, different cutter path patterns are systematically analysed and several existing heuristics for selecting cutter path patterns are discussed. Based on observations, a new cutter path generation algorithm is described in this paper. This algorithm generates cutter path by using different patterns in different regions of the geometry and seamlessly morphing them together. In case of complex pockets, it produces solutions superior to those generated by any single pattern.

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