A sequence of candidate paths is created, with each path consisting of a chain connecting the fixed source point with a random point on the screen while passing through a small number of randomly positioned scattering centers within the phantom. The probability associated with each path is computed using standard scattering and attenuation models. While relevant to the CT scan community, the specific set of absorption and scattering rules used in the article is not its essential feature. Of far greater relevance is the fact that, once a path connecting the source with a point on the screen has been identified, its probability can be evaluated based on a suitable set of absorption and scattering rules. The probability 𝑝accept(𝑥𝑖−1 → 𝑦) that path 𝑦 is an acceptable mutation of the previous path 𝑥𝑖−1 is computed using the Metropolis-Hastings algorithm, after which path 𝑦 is either accepted (𝑥𝑖 = 𝑦) with probability 𝑝accept or rejected (𝑥𝑖 = 𝑥𝑖−1) with probability 1−𝑝accept. In this way, a sequence of statistically meaningful paths is thus created connecting the source to the screen.
The authors benchmark their algorithm against a traditional Monte Carlo ray-trace algorithm running on the same platform. They obtain good agreement between the two approaches while reporting a speed-up of between 20 and 40 times using their approach, depending on the nature of the phantom being imaged.
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