I. INTRODUCTION A Compton camera is a device with electronic collimation

allowing detection of single gamma rays of a very wide energy range (0.2 - 15 MeV). Therefore, it is obvious to use a Compton camera for applications in astronomy [1], homeland security [2] and medical imaging [3] if wide energy range photons have to be measured.

A particular application of a Compton camera in medical imaging can be the monitoring of ion radiation therapy. Up to now the only method for such monitoring is positron emission tomography (PET) [4]. The main disadvantage of the PET technique is the distortion of the measured β+-activity by metabolism and blood flow [5]. Imaging of prompt gamma rays produced during the irradiation can be used in order to overcome this problem. In contrast to up to 20 min half-life of radiotherapy relevant positron emitters, the time scale of prompt gamma ray emission is in fs - ps range. Therefore, there will be no problem with distortion of the activity by metabolism and blood flow in case of prompt gamma imaging. Because of the wide energy spectra of prompt gamma rays produced during ion therapy, a Compton camera is the only possibility for imaging in this case. Its feasibility has been proven by means of simplified simulations (Fig. 1) [6].

Compton cameras can also be used in homeland security in order to detect and identify radioactive material at distances. In scope of the iFind project a large Compton camera with 1 × 1 m2 detectors has been proposed [2].

This paper presents a common approach for system matrix calculation and reconstruction for the Compton camera independently of its application.

II. A GENERIC APPROACH TO RECONSTRUCTION OF COMPTON CAMERA DATA

The aim of the image reconstruction is to find an image b’ with maximum similarity to the unknown study object b. This study object is mapped to a hardware response (measurement) h by the system matrix (SM) A:

A: bØ h (1) The definition of the SM is a crucial point in image

reconstruction. An application independent and extensible method for SM calculation for Compton camera is proposed in this paper.

Corresponding author – S. Schöne (e-mail: sebastian.schoene@fzd.de). 1 with the Department of Radiation Physics, Research Center Dresden-

Rossendorf, Dresden, Germany 2 now with Philips Research Laboratories, Eindhoven, Netherlands 3 with the Center for Radiation Research in Oncology – OncoRay,

Technische Universität Dresden, Germany 4 with ICx Technologies GmbH, Solingen, Germany

A. Model elements Corresponding to the operating principles of a two plane

Compton camera [2] the event space H has the attributes P and E1, R and E2, describing event location and energy deposition to the scatter and absorber detector, respectively. Every valid measurement of the camera is located in this space. The output of a physical camera always has uncertainties [7]. Therefore, the event space attributes can be represented as probability distributions or simplified to scalars. Additionally, there is the implicit attribute q, the scattering angle from the Compton formula, which is defined by E1 and E2.

The image space B defines properties of the activity distribution of the origin and reconstructed object. The image space attributes Q and E0 are the location and energy of the photon emissions, respectively.

Fig. 1. Reconstructed images of annihilation points distribution acquired with the PET scanner (left) and Compton camera (right). A distribution of positron emitters was simulated from real treatment plan of carbon ion irradiation at GSI, Darmstadt, Germany. All important features as maximum particle range, emptiness of cavities and high activity in bone structures can be observed in image reconstructed from data measured by a Compton camera.

As mentioned above, the system matrix A maps a study object to a measurement. The SM elements aij are the probabilities that an emission in a discrete region of the image space j (of Qj, E0,j) will result in the event space region i (of E1,i, E2,i, Ri, Pi, qi). The mapping is done by

∑=j jiji bah , (2)

where b and h are a study object and a camera measurement within a task, respectively.

B. System matrix layering A matrix element aij can be factorized down into sub-

probabilities aij = aij(X0)·aij(X1)·… for independent random variables X0, X1,… [8]. The appropriate selection of this splitting reduces the complexity of the algorithm, simplifies the implementation, and dramatically reduces the computational costs by skipping most of the calculations due to aij = 0 if aij(Xk) = 0 at least for one k.

Two classes of sub-probabilities can be distinguished: 1) Plausibility probabilities

The plausibility tests work on the redundancies coming out of the SM definition, e.g. based on the Compton kinematics.

Sebastian Schöne1, Student Member, IEEE, Georgy Shakirin2, Member, IEEE, Thomas Kormoll3, Student Member, IEEE, Claus-Michael Herbach4, Guntram Pausch4, Member, IEEE, and Wolfgang Enghardt3

A Common Approach to Image Reconstruction for Different Applications of Compton Cameras

2292978-1-4244-9105-6/10/$26.00 ©2010 IEEE

These tests are the major source for reduction of the computational costs. If the event attributes are probability distribution, these plausibility probabilities are real-valued; in case of scalars they are binary-valued.

2) Transition probabilities Different physical effects influence the probability of photon

detection. A logic photon state machine is introduced in order to reflect this. The simple state machine shows possible photon interactions, reduced to those related to a successfully measured event (Fig. 2).

Within this state machine a state is determined by a set of positions of the photon, a set of directions, and energy. Each transition describes an abstract photon interaction. The probability of a transition towards the final state is a sub-probability in terms of the SM and can be calculated separately. The final state corresponds to a successful measurement.

Fig. 2. State diagram for the logic photon state machine. It illustrates the states with a set of locations, a set of directions, and energy of the photon. A transition which meets the mentioned condition (box brackets) leads towards an event (final state) and is associated with a sub-probability (blue).

III. CURRENT IMPLEMENTATION AND FIRST RESULTS Currently there are two plausibility tests implemented. They

check for E1,i + E2,i ≙ E0,j and for the spatial localization of Qj onto a conical surface defined by the apex Pi, the axis RiPi, and aperture of 2·qi (aka cone projection). Both implementations are done with respect to the stochastic nature of the event attributes.

Figure 2 illustrates the implemented state machine. The transition probability can be calculated for four of the charted transitions: Tdirscat, Tscat1, Tscat2, Tabs. For all of them algorithms were developed and implemented.

The mechanism described above was applied to different hardware setups and SM were constructed for applications in the field of homeland security (Fig. 3) and medical imaging (Fig. 4). Based on events got from Geant4 simulated cameras reconstructions via the standard ML-EM algorithm were done.

IV. CONCLUSIONS A unified method for representation and calculation of the

system matrix for Compton cameras has been proposed. The method defines first a photon interaction scheme in form of a

logic photon state machine and then calculates the system matrix elements based on the transition probabilities for each state. Additionally uncertainties of the measurement can be taken into account in form of probability density distributions or, in case of simplifications, as scalars. The method provides a structured approach for the system matrix calculation which simplifies the software development process and the optimization of the computational performance. Additionally, the system matrix calculation is completely independent of the reconstruction algorithm itself. Therefore, the same code can be used for the reconstruction of the measured data collected with the different hardware and for different applications (i.e. medical imaging or homeland security).

Fig. 3. Reconstructed photon emission distribution after 1 (left), 3 (center) and 5 (right) iterations of the ML-EM algorithm. The spatial image space attribute is defined in geographic angular domain. The emission scene is determined by monoenergetic (662 keV) sources at distances around 100 m: 50% of total activity at location (30°, -20°), 33% at (0°, 0°), and 17% at (0°, 20°). The simulated Compton camera consists of scatter and absorber detectors at a distance of 30 cm. The square of each detector is 1 × 1 m² divided into 40 × 40 segments made of CaF2 (scatter) and NaI (absorber).

Fig. 4. Reconstructed photon emission distribution after 1, 3 and 5 iterations of the ML-EM algorithm. Object: a line source of 2.2 MeV at x=[-150,60], y=z=0. The scatter (CdZnTe) and absorber (BGO) planes were located at x=y=[-20,20], z=250 and x=y=[-40, 40], z=300, respectively. Both were divided into 40 × 40 segments.

V. ACKNOWLEDGEMENTS This work was partially funded by DTRA under contract #HDTRA1-09-C-0012 and ICx Radiation.

VI. REFERENCES [1] E. I. Novikova et al., Simulation of a Si-based Advanced Compton

Telescope, 2005 IEEE NSS Conf. Record N19-5, 985-989. [2] C.-M. Herbach et al., Concept Study of a Two-Plane Compton Camera

Designed for Location and Nuclide Identification of Remote Radiation Sources, 2009 IEEE NSS Conf. Record N13-224, 909-911.

[3] N. Kawachi et al., Basic Characteristics of a Newly Developed Si/CdTe Compton Camera for Medical Imaging, 2008 IEEE NSS Conf. Record NMR-6, 1540-1543.

[4] W. Enghardt et al., Charged hadron tumour therapy monitoring by means of PET, Nucl. Instr. Meth. A 525, 284-8, 2004.

[5] F. Fiedler et al., In-beam PET measurements of biological half-lives of 12C irradiation induced β+-activity, Acta Oncol. 47, 1077-86, 2008.

[6] Baumann et al. (ed.), OncoRay Annual Report 2009, OncoRay Dresden. [7] T. Kormoll et al., A Compton imager for in-vivo dosimetry of proton

beams – A design study, Nucl. Instr. Meth. Phys. Res. A, 2010. [8] Laurette et al., A three-dimensional ray-driven attenuation, scatter and

geometric response correction technique for SPECT in inhomogenous media, Phys. Med. Biol. 45, 3459-3480, 2000.

2293