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. In order 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：未知视图断层仪( UVT) 从 2D 的预测中以未知的随机方向重建三维密度图。 与 Kam( 1980) 开始的一行工作使用时间方法( MoM), 使用旋转异性方格, 在频率域内解决紫外线问题, 假设方向分布一致。 该行工作包括基于矩阵因子化的最近正方位矩阵检索( OMR) 方法, 虽然该方法优雅, 但需要侧面信息, 无法提供密度信息, 或者不够强健。 为了让 OMR 摆脱这些限制, 我们提议联合恢复密度图和正方形矩阵, 要求它们相互一致。 我们通过解开参考投影和不增强约束, 将由此产生的非convex优化问题正规化。 这是由基于矩阵因子化的新的封闭式空间自动关系特性表达式( OMR) ( OMR- D) ( UMR- D) ( UMR- D) (O- D) (O- D) (MR- D) (O- D) (O- D) (S) (S) (S) (OMR) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S-) ) ) ) (的典型的 ) (S) (S- ) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) (S) ) ) ) ) (的 ) ) ) ) ) ) (以 的 ) (以 的 的 ) 的 的 3) 的 ) ) ) 的 的 和 的 的 ) 和 的 的 ) 的 的 和(S) 和(S) 的 ) 的 的 的 和 的 比较性变型
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