IEEE Trans Image Process. 2014 Jan;23(1):332-41. doi: 10.1109/TIP.2013.2288143.
During the acquisition process with the Compton gamma-camera, integrals of the intensity distribution of the source on conical surfaces are measured. They represent the Compton projections of the intensity. The inversion of the Compton transform reposes on a particular Fourier-Slice theorem. This paper proposes a filtered backprojection algorithm for image reconstruction from planar Compton camera data. We show how different projections are related together and how they may be combined in the tomographical reconstruction step. Considering a simulated Compton imaging system, we conclude that the proposed method yields accurate reconstructed images for simple sources. An elongation of the source in the direction orthogonal to the camera may be observed and is to be related to the truncation of the projections induced by the finite extent of the device. This phenomenon was previously observed with other reconstruction methods, e.g., iterative maximum likelihood expectation maximization. The redundancy of the Compton transform is thus an important feature for the reduction of noise in Compton images, since the ideal assumptions of infinite width and observation time are never met in practice. We show that a selection operated on the set of data allows to partially get around projection truncation, at the expense of an enhancement of the noise in the images.
在使用康普顿伽马相机进行采集的过程中，会测量源的强度分布在圆锥面上的积分。它们代表强度的康普顿投影。康普顿变换的反演依赖于一个特定的傅里叶切片定理。本文提出了一种基于滤波反投影算法的平面康普顿相机数据图像重建方法。我们展示了不同的投影是如何相互关联的，以及它们如何在层析重建步骤中结合在一起。考虑到一个模拟的康普顿成像系统，我们得出结论，对于简单的源，所提出的方法可以得到准确的重建图像。在与相机正交的方向上，源可能会出现伸长现象，这与设备有限的投影截断有关。这种现象以前在其他重建方法中也有观察到，例如迭代最大似然期望最大化。因此，康普顿变换的冗余性是减少康普顿图像噪声的一个重要特征，因为在实践中，理想的无限宽度和观测时间的假设从未得到满足。我们表明，对数据集的选择可以部分绕过投影截断，代价是图像噪声的增加。
