  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.
