SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1398-1439, September 2023.
Abstract. Unknown view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. A line of work starting with Kam (1980) employs the method of moments with rotation-invariant Fourier features to solve UVT in the frequency domain, assuming that the orientations are uniformly distributed. This line of work includes the recent orthogonal matrix retrieval (OMR) approaches based on matrix factorization, which, while elegant, either require side information about the density that is not available or fail to be sufficiently robust. For OMR to break free from those restrictions, we propose to jointly recover the density map and the orthogonal matrices by requiring that they be mutually consistent. We regularize the resulting nonconvex optimization problem by a denoised reference projection and a nonnegativity constraint. This is enabled by the new closed-form expressions for spatial autocorrelation features. Further, we design an easy-to-compute initial density map which effectively mitigates the nonconvexity of the reconstruction problem. Experimental results show that the proposed OMR with spatial consensus is more robust and performs significantly better than the previous state-of-the-art OMR approach in the typical low signal-to-noise-ratio scenario of 3D UVT.

中文翻译：

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3D 未知视图层析成像的空间一致性正交矩阵检索

SIAM 影像科学杂志，第 16 卷，第 3 期，第 1398-1439 页，2023 年 9 月。
抽象的。未知视图断层扫描 (UVT) 根据未知、随机方向的 2D 投影重建 3D 密度图。Kam (1980) 开始的一系列工作采用具有旋转不变傅里叶特征的矩方法来求解频域中的 UVT，假设方向均匀分布。这一工作包括最近基于矩阵分解的正交矩阵检索（OMR）方法，该方法虽然很优雅，但要么需要有关不可用的密度的辅助信息，要么不够鲁棒。为了让 OMR 摆脱这些限制，我们建议通过要求密度图和正交矩阵相互一致来联合恢复它们。我们通过去噪参考投影和非负约束来正则化所得到的非凸优化问题。这是通过空间自相关特征的新封闭式表达式实现的。此外，我们设计了一个易于计算的初始密度图，它有效地减轻了重建问题的非凸性。实验结果表明，在 3D UVT 的典型低信噪比场景中，所提出的具有空间一致性的 OMR 更加稳健，并且比之前最先进的 OMR 方法表现得更好。