Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Abstract

Compton scattering describes the scattering of a photon after its collision with an electron. The recent developments of spectral cameras, able to collect photons in terms of energy, open the way to a new imaging concept: 3D Compton scattering imaging (CSI), which seeks to exploit the scattered radiation as a vector of information while a specimen of interest is illuminated by a monochromatic ionizing source. Focusing on modelling the first-order scattering, image reconstruction from CSI data remains a difficult challenge. In particular, physical constraints (detector and architecture of the scanner) lead to various incompleteness scenario within the data and thus streak artifacts when using filtered backprojection type formulas. This paper addresses the problem of recovering an object under study using CSI data subject to incompleteness and assuming only first-order scattering. The proposed method consists of suitably tuning the multiplicative Kaczmarz algorithm and is implemented and tested for two architectures of the scanner. Furthermore, the modality on CSI considered here presents the advantage of not requiring any rotation of the source or object.

Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography

“…The goal of this work was to consider a best case scenario in CST, in terms of data dimensionality. The literature [24,25,18,23,16,17,2] considers exclusively Radon transforms which define the integrals of a function over three-dimensional sets of apple or lemon surfaces. In these works, artifacts are present in the reconstruction due to data limitations, and regularization strategies are used to combat the artifacts.…”

“…The acquisition geometry consists of a single rotating source and detector on a fixed axis. As in [17], the data is three-dimensional, and, in this case, consists of a 2-D rotation and a 1-D energy variable. The lemon transform is shown to violate the Bolker condition, and there are artifacts induced by flowout which appear as a spherical blurring effect in the reconstruction.…”

“…So, in the context of CST, our geometry consists of all source and detector positions which lie outside the unit ball (this is a six-dimensional set). Additionally, we can vary the torus radius (r), which in CST is equivalent to the photon energy [17]. Thus, in total, our data set is seven-dimensional.…”

“…See figure 1 for a 2-D cross-section of a spindle torus, where we have highlighted the lemon and apple parts. The literature considers lemon and apple transforms in 3-D CST [24,25,18,23,16,17,2], where the goal is to reconstruct an electron density map from Compton scattered photons. There is also a growing interest in the literature in Emission CST (ECST) [22,9,14,13,12], where the aim is to reconstruct a gamma ray source from cone integral data.…”

“…In [17], two fixed-source CST configurations, with spherical and cylindrical detector arrays, are considered. In both cases, the data is three dimensional, and consists of a twodimensional detector coordinate and a one-dimensional energy variable.…”