SPECT with a multi-bang assumption on attenuation
SPECT with a multi-bang assumption on attenuation
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DOI：
10.1088/1361-6420/abab59
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发表时间：
2020-07
期刊：
影响因子：
2.1
通讯作者：
S. Holman;Philip Richardson
中科院分区：
文献类型：
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作者：
S. Holman;Philip Richardson
我们考虑了在单光子发射计算机断层扫描（SPECT）中出现的衰减a和源密度f的联合重建的识别问题。假设a只取100个值，f∈Cc1（R2），我们能够消除衰减Radon变换R a f中出现的奇异性，该变换模拟SPECT数据。利用这个特征，我们证明了在某些情况下，a和f都可以由R a f确定。我们还提出了一个数值算法，联合计算a和f从R a f的基础上弱凸正则化时，只采取的值从一个已知的有限列表，并表明该算法在一些合成的例子。
We consider the identification problem which arises in single photon emission computed tomography (SPECT) of joint reconstruction of both attenuation a and source density f. Assuming that a takes only finitely many values and f∈Cc1(R2) we are able to characterise singularities appearing in the attenuated Radon transform R a f, which models SPECT data. Using this characterisation we prove that both a and f can be determined in some circumstances from R a f. We also propose a numerical algorithm to jointly compute a and f from R a f 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.