Analytic Inversion of a Conical Radon Transform Arising in Application of Compton Cameras on the Cylinder

Single photon emission computed tomography (SPECT) is a well-established clinical tool for functional imaging. A limitation of current SPECT systems is the use of mechanical collimation, where only a small fraction of the emitted photons are actually used for image reconstruction. This results in a large noise level and finally in a limited spatial resolution. In order to decrease the noise level and to increase the imaging resolution, Compton cameras have been proposed as an alternative to mechanical collimators. Image reconstruction in SPECT with Compton cameras yields the problem of recovering a marker distribution from integrals over conical surfaces. Due to this and other applications, such conical Radon transforms recently got significant attention. In the current paper we consider the case where the cones of integration have vertices on a circular cylinder and axis pointing to the symmetry axis of the cylinder. Our setup does not use all emitted photons but a much larger fraction than systems based on mechanical collimation. Further, it may be simpler to be fabricated than a Compton camera system collecting full five-dimensional data. As main theoretical results in this paper we derive analytic reconstruction methods for the considered transform. We also investigate the V-line transform with vertices on a circle and symmetry axis orthogonal to the circle, which arises in the special case where the absorber distribution is located in a horizontal plane

Detecting small low emission radiating sources

The article addresses the possibility of robust detection of geometrically small, low emission sources on a significantly stronger background. This problem is important for homeland security. A technique of detecting such sources using Compton type cameras is developed, which is shown on numerical examples to have high sensitivity and specificity and also allows to assign confidence probabilities of the detection. 2D case is considered in detail

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography

In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is used at the detector. Such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the associated Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inversion formula is established for this new Radon transform. This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency conditions in Cormack's sense. Moreover, a fast and efficient numerical implementation via an alternative formulation based on Hilbert transform is carried out. Simulation results illustrate the theoretical feasibility of the new system. From a practical point of view, an uncollimated detector system considerably increases the amount of collected data, which is particularly significant in a scatter imaging system.Comment: 14 pages, 5 figure