论文标题
发射断层扫描具有多个衰减的多个假设
Emission tomography with a multi-bang assumption on attenuation
论文作者
论文摘要
我们考虑衰减$ a $和源密度$ f $ in排放断层扫描的联合重建问题的问题。这有时称为单个光子发射计算机断层扫描（SPECT）识别问题，或称为SPECT中的衰减校正。假设$ a $仅占c_c^1（\ mathbb {r}^2）$中的$ f \ $ f \ $ f \，我们能够表征出现在衰减的radon transform $ r_a f $中的奇异性，它们模拟了发射断层扫描数据。使用此表征，我们证明在某些情况下可以确定$ a $ a和$ f $。我们还提出了一种数值算法，以基于$ r_af $的$ r_af $共同计算$ r_af $的$ a $ a和$ f $，而$ a $仅从已知的有限列表中获取值，并表明该算法在某些合成示例上的性能良好。
We consider the problem of joint reconstruction of both attenuation $a$ and source density $f$ in emission tomography in two dimensions. This is sometimes called the Single Photon Emission Computed Tomography (SPECT) identification problem, or referred to as attenuation correction in SPECT. Assuming that $a$ takes only finitely many values and $f \in C_c^1(\mathbb{R}^2)$ we are able to characterise singularities appearing in the Attenuated Radon Transform $R_a f$, which models emission tomography data. Using this characterisation we prove that both $a$ and $f$ can be determined in some circumstances. We also propose a numerical algorithm to jointly compute $a$ and $f$ from $R_af$ based on a weakly convex regularizer when $a$ only takes values from a known finite list, and show that this algorithm performs well on some synthetic examples.
