This study presents a technique for 2D tomography under unknown viewing angles when the distribution of the viewing angles is also unknown. Unknown view tomography (UVT) is a problem encountered in cryo-electron microscopy and in the geometric calibration of CT systems. There exists a moderate-sized literature on the 2D UVT problem, but most existing 2D UVT algorithms assume knowledge of the angle distribution which is not available usually. Our proposed methodology formulates the problem as an optimization task based on cross-validation error, to estimate the angle distribution jointly with the underlying 2D structure in an alternating fashion. We explore the algorithm's capabilities for the case of two probability distribution models: a semi-parametric mixture of von Mises densities and a probability mass function model. We evaluate our algorithm's performance under noisy projections using a PCA-based denoising technique and Graph Laplacian Tomography (GLT) driven by order statistics of the estimated distribution, to ensure near-perfect ordering, and compare our algorithm to intuitive baselines.

翻译：本研究提出了一种在未知视角分布条件下进行二维断层成像的技术。未知视角断层成像（UVT）是冷冻电子显微镜和计算机断层扫描系统几何校准中遇到的问题。现有关于二维UVT问题的文献数量适中，但大多数现有二维UVT算法都假设已知视角分布，而这一信息通常难以获取。我们提出的方法将问题构建为基于交叉验证误差的优化任务，通过交替迭代的方式联合估计视角分布与底层二维结构。我们探讨了算法在两种概率分布模型下的性能：半参数化冯·米塞斯密度混合模型和概率质量函数模型。在含噪投影条件下，我们采用基于主成分分析的去噪技术，并结合基于估计分布顺序统计量的图拉普拉斯断层成像（GLT）方法以确保近乎完美的排序，从而评估算法性能，并与直观基线方法进行比较。