SPECT中使用康普顿相机的衰减V线变换反演
Inversion of the attenuated V-line transform for SPECT with Compton cameras
AI总结：
本文研究了SPECT中使用康普顿相机时衰减V线变换的反演问题，提出基于圆谐分析的解析解法，并通过数值实验验证了算法的有效性。
摘要：
康普顿相机是一种有潜力替代昂格相机的成像装置，可能显著提高SPECT的灵敏度。通过反演V线变换可以实现二维康普顿相机图像重建，该变换整合了发射分布沿V线（两个半线的并集）的积分，这些V线的顶点位于周围探测器阵列上。最近已有学者研究了无衰减情况下的V线变换反演。然而，标准SPECT已知忽略衰减会显著降低重建图像的质量。本文针对此问题，研究了考虑SPECT中康普顿相机中光子衰减的衰减V线变换。我们基于圆谐分析推导了解析反演方法，并证明了衰减V线变换的重建唯一性。我们进一步开发了基于解析研究的离散图像重建算法，并通过数值结果展示了算法的有效性。
英文摘要：
The Compton camera is a promising alternative to the Anger camera for imaging gamma radiation, with the potential to significantly increase the sensitivity of SPECT. Two-dimensional Compton camera image reconstruction can be implemented by inversion of the V-line transform, which integrates the emission distribution over V-lines (unions of two half-lines), that have vertices on a surrounding detector array. Inversion of the V-line transform without attenuation has recently been addressed by several authors. However, it is well known from standard SPECT that ignoring attenuation can significantly degrade the quality of the reconstructed image. In this paper we address this issue and study the attenuated V-line transform accounting for attenuation of photons in SPECT with Compton cameras. We derive an analytic inversion approach based on circular harmonics expansion, and show uniqueness of reconstruction for the attenuated V-line transform. We further develop a discrete image reconstruction algorithm based on our analytic studies, and present numerical results that demonstrate the effectiveness of our algorithm.
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