Reconstructing without Angles in Unknown-View Tomography
Presenter
July 15, 2026
Abstract
Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown random orientations. A foundational line of work starting with Kam (1980) employs the method of moments (MoM) to solve UVT in the frequency domain, assuming uniformly distributed orientations to bypass the brittle angle estimation required by traditional MAP techniques. However, Kam's autocorrelation method yields an underdetermined system with missing orthogonal matrices. In the first part of this talk, we extend previous orthogonal matrix retrieval (OMR) methods to jointly recover the density map and the orthogonal matrices. Empowered by closed-form expressions for spatial autocorrelation features, this approach easily incorporates physical spatial constraints, such as nonnegativity. Numerical results demonstrate that our spatial-consensus approach is highly robust, significantly outperforming the previous state-of-the-art in typical low-SNR 3D UVT scenarios.
In the second part of the talk, we move beyond the assumption of uniform distributions, tackling 2D UVT problems where the probability distribution of projection angles is completely unknown. We propose a novel adversarial learning framework that recovers both the image and the projection angle distribution via distribution matching. Formulated as a min-max game using a Wasserstein Generative Adversarial Network (WGAN), we approximate the loss using the Gumbel-Softmax reparameterization to allow gradient backpropagation through the discrete angle distribution.