Scattered Radiation Emission Imaging: Principles and Applications

Abstract

Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields.

SVD inversion for the bi-dimensional Conical Radon Transform

“…They rely on individual analytical relations between f (x, y) and its projections g(ξ, ω). Detailed implementations for FBP in the TV case can be found elsewhere [1,7,8]. …”

“…This transformation has an analytic inverse [2] which rests on the action of a cosine-Fourier transform. We have also established the inversion by FBP in [7,8]. In what follows, we will eventually refer to g(ξ, ω) as the projections.…”

“…Some aspects of the bi-dimensional Conical Radon Transform (TV) have been already studied and both, analytical [1,7,8] and algebraic [9] inversion have been obtained. In particular, it was shown that the TV can be inverted by a filtered back-projection technique (FBP) completely adapted to the geometry of the problem.…”

Attenuation correction in emission tomography using the emission data—A review

“…This extends earlier suggestions of using individual photon energies in PET (Refs. 238 and 239) and, more specifically, applies the idea of Compton scatter (emission) imaging 240,241 to SPECT and PET. In the remainder of this section, unless noted otherwise, we use the term scatter for scattered photons (or coincidences involving the same) in the energy range below the photopeak, acquired in one or more separate scatter acceptance windows.…”

Architecture and characterization of the P4DI CMOS hybrid pixel sensor

“…This energy resolution may prove useful not only for the spectroscopic identification of the emitting source, but also for Compton scattering exploitation. Compton scatter imaging could provide many desirable features [3]: source activity orders of magnitude below conventional systems by avoiding collimators, direct and quantitative measurement of the electronic density of the studied object, sensitivity to low-density materials, it permits placement of both the radiation source and the detector on the same side of the object etc.…”