Modeling and Reconstruction Strategy for Compton Scattering Tomography with Scintillation Crystals

Abstract

The recent development of energy-resolved scintillation crystals opens the way to build novel imaging concepts based on the variable energy. Among them, Compton scattering tomography (CST) is one of the most ambitious concepts. Akin to Computerized Tomography (CT), it consists in probing the attenuation map of an object of interest using external ionizing sources but strives to exploit the scattered radiation as an imaging agent. For medical applications, the scattered radiation represents 70 to 80% when the energy of the source is larger than 100 keV and results from the Compton effect. This phenomenon stands for the collision of a photon with an electron and rules the change of course and loss of energy undergone by the photon. In this article, we propose a modeling for the scattered radiation assuming polychromatic sources such as 60Co and scintillation crystals such as LBC:Ce. Further, we design a general strategy for reconstructing the electron density of the target specimen. Our results are illustrated for toy objects.

Imaging based on Compton scattering: model-uncertainty and data-driven reconstruction methods

“…At one half of this sphere n s = 10 sources are evenly positioned. For each source we evenly sample 80% of the detector space at n d locations for the detectors, which is illustrated in Further research and simulations shall take into account the polychromacy of the source as in [26] but our proposed method can be adapted to this physical aspect. We also discard the backscattering, i.e.…”

“…Given a monochromatic γ-ray source s of energy E 0 and an energy-resolved detector d, the illumination of a specimen represented by its attenuation map µ leads by the Compton effect to a polychromatic response measured at d. This would also hold for a polychromatic source as studied in [25,26] but for the sake of simplicity we consider in this work only monochromatic sources. Assuming only Compton scattering and photoelectric absorption events, we can decompose the spectrum Spec(E, d, s) measured at a detector d with energy E as follows Spec(E, d, s) = i∈N g i (E, d, s).…”

“…Using g 0 in the reconstruction process is sensible. For instance, it is possible to reconstruct under sparsity constraints a first approximation of the attenuation map which can help to refine the forward model, in particular the weight functions, see [26,25]. However, we discarded this part of the spectrum as we wanted to stress the model uncertainty using a weaker a priori of the attenuation map.…”

“…η P j < η j , but this remains to be proved. This strategy was successfully applied: in 3D using FBP-type algorithm for the extraction of the contours in [36] and in 2D using iterative total-variation (TV) regularization in [26,25]. However errors and artifacts due to an inaccurate model can appear and need to be addressed using data-driven algorithm.…”

“…where c p,k := τ (ρ η p,k + δ p,k ) is a model correction term inspired from the RESESOP method studied in the previous section. The connection to RESESOP-Kaczmarz is revealed by the following observation: If we assume that one of the summands in ‡ https://github.com/jleuschn/dival/tree/master/dival/reconstructors/networks (26) is zero, then it is not difficult to see that ϕ θ (z) belongs to the boundary of the restricted stripe B ρ (0) ∩ H(u η,δ,j p,k , α η,δ,j p,k , ξ η,δ,j p,k ), where u η,δ,j p,k := (A η,j p,k ) * (A η,j p,k ϕ θ (z) − g δ p,k ), α p,k := A η,j p,k ϕ θ (z) − g δ p,k , g δ p,k , ξ η,δ,j p,k := c p,k A η,j p,k ϕ θ (z) − g δ p,k are analogously defined as in Algorithm 3.3. Hence, if θ opt is a minimizer of 2 , then ϕ θopt (z) is expected to be close to the boundary of all those stripes.…”