Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography

TL;DR

This paper introduces a novel orthogonal matrix retrieval method with spatial consensus for 3D unknown-view tomography, improving robustness and accuracy in low-SNR conditions by jointly recovering density maps and orientations.

Contribution

It proposes a new joint recovery framework with spatial autocorrelation features and a robust initialization strategy, advancing the state-of-the-art in UVT reconstruction.

Findings

Outperforms previous OMR methods in low-SNR scenarios

Provides closed-form spatial autocorrelation features for better regularization

Demonstrates improved robustness and accuracy in experiments

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) 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.