تقرير
Emission tomography with a multi-bang assumption on attenuation
| العنوان: | Emission tomography with a multi-bang assumption on attenuation |
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| المؤلفون: | Holman, Sean, Richardson, Philip |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 45Q05 |
| الوصف: | 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. Comment: 23 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2001.04190 |
| رقم الأكسشن: | edsarx.2001.04190 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |