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 (MoM) to solve UVT in the frequency domain, assuming that the orientations are uniformly distributed. Such approaches bypass the estimation of individual viewing orientations that traditional MAP estimation requires. Kam's autocorrelation method leads to an underdetermined system, with missing orthogonal matrices. In this talk, we extend the previous orthogonal matrix retrieval (OMR) methods to jointly recover the density map and the orthogonal matrices such that spatial constraints, such as nonnegativity, can be easily incorporated. This is enabled by the closed-form expressions for spatial autocorrelation features. Numerical results show that the new approach 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.