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 (MoM) 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 non-convex 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 non-convexity 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-SNR scenario of 3D UVT.

翻译：未知视角断层成像（Unknown-View Tomography, UVT）从未知随机方向的二维投影中重建三维密度图。自Kam（1980）起的一系列研究工作采用矩方法（Method of Moments, MoM）与旋转不变傅里叶特征，在频域中求解UVT问题，其前提假设为投影方向均匀分布。该研究脉络包括近期基于矩阵分解的正交矩阵恢复（Orthogonal Matrix Retrieval, OMR）方法——这类方法虽具数学优雅性，但要么需要无法获取的密度侧信息，要么鲁棒性不足。为使OMR突破上述限制，我们提出通过要求密度图与正交矩阵相互一致来实现联合恢复。我们利用去噪参考投影与非负性约束对由此产生的非凸优化问题进行正则化，这一过程得益于空间自相关特征的新型闭式表达式。此外，我们设计了易于计算的初始密度图，有效缓解了重建问题的非凸性。实验结果表明，在三维UVT典型的低信噪比场景中，所提出的空间一致性OMR方法相比现有最优OMR方法具有更强的鲁棒性，且性能显著提升。