论文标题
与空间共识的正交基质检索3D未知视图断层扫描
Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography
论文作者
论文摘要
未知视图层析成像（UVT）从其未知的随机方向以其2D投影重建了3D密度图。从Kam（Kam（1980））开始的一条工作采用了具有旋转不变的傅立叶特征的矩（MOM）方法，以在频域中求解UVT，假设方向均匀分布。这项工作系列包括基于矩阵分解的最新正交矩阵检索（OMR）方法，虽然优雅地需要有关无法可用的密度的侧面信息，或者无法充分强大。为了使OMR摆脱这些限制，我们建议通过要求它们相互一致来共同恢复密度图和正交矩阵。我们通过deno的参考投影和非阴性约束来使所得的非凸优化问题正常。这是通过空间自相关功能的新闭合表达式启用的。此外，我们设计了一个易于计算的初始密度图，可有效地降低重建问题的非跨性别性。实验结果表明，在典型的3D UVT的典型低SNR情况下，提出的具有空间共识的OMR比以前最新的OMR方法更强大，并且表现明显好。
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.
