Fourier rebinning applied to 3-D reconstruction in Compton imaging

Objectives In Compton imaging, as the direction of the scattered photon is determined by the two detected positions in the scatterer and the absorber, the incident direction of the emitted photon is computed within a conical surface of ambiguity. To overcome the problem of massive data set computations for conical projection and backprojection, we develop a method of Fourier rebinning (FORE), which can approximately estimate equivalent parallel projections from conical projections. With parallel projection data, a variety of existing reconstruction methods developed for conventional emission tomography can be directly used for Compton camera reconstruction.

Methods To convert conical projections into parallel projections, we performed the following three steps. First, a cone surface is sampled with a number of lines. The sampled lines are then rebinned into a set of parallel projection data in the transaxial plane maintaining oblique angles with respect to the axis of rotation. Finally, the Fourier rebinning relation is applied to estimate equivalent parallel projections in the transaxial planes from the oblique projections. To validate our rebinning method, we tested with the conventional algorithms, such as the filtered backprojection (FBP) method and the algebraic reconstruction technique (ART).

Results We compared two different reconstructions; reconstruction from Fourier rebinned parallel projection data and reconstruction from rebinned parallel projection data by ignoring oblique projections. Our experimental results show that, while the method ignoring the oblique projections yields truncations in reconstruction, the method using Fourier rebinning restores images without truncation, thereby improving the reconstruction accuracy.

Conclusions The Fourier rebinning method provides a good approximation in rebinning the conical projection data into the parallel projection data. Since the Fourier rebinning algorithm is very fast, it can be useful for rapidly reconstructing Compton scattered data using fast conventional reconstruction methods