Geometric Invariants for Sparse Unknown View Tomography
Geometric Invariants for Sparse Unknown View Tomography
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DOI：
10.1109/icassp.2019.8682401
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
Mona Zehni;Shuai Huang;Ivan Dokmanić;Zhizhen Zhao
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文献类型：
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作者：
Mona Zehni;Shuai Huang;Ivan Dokmanić;Zhizhen Zhao
研究了具有随机未知视角的点源模型的二维层析成像问题。我们不是恢复投影角度，而是通过一组从投影数据估计的旋转不变特征来重建模型。对于点源模型，我们证明了这些特征揭示了模型的几何信息，如径向和成对距离。这建立了未知视图层析成像和未分配距离几何问题（uDGP）之间的联系。我们提出了新的方法来提取距离和近似的成对距离分布的基础上的点。然后利用恢复的分布通过约束非凸优化来估计点的位置。仿真结果表明，我们的点源重构管道对噪声具有鲁棒性，并且优于正则化期望最大化（EM）基线。
In this paper, we study a 2D tomography problem for point source models with random unknown view angles. Rather than recovering the projection angles, we reconstruct the model through a set of rotation-invariant features that are estimated from the projection data. For a point source model, we show that these features reveal geometric information about the model such as the radial and pairwise distances. This establishes a connection between unknown view tomography and unassigned distance geometry problem (uDGP). We propose new methods to extract the distances and approximate the pairwise distance distribution of the underlying points. We then use the recovered distribution to estimate the locations of the points through constrained non-convex optimization. Our simulation results show that our point source reconstruction pipeline is robust to noise and outperforms the regularized expectation maximization (EM) baseline.