Fast and Direct Angle Inference Using Masked Projection Modelling in 2D Tomography with Unknown Views

Tomography with unknown views has been extensively studied due to its wide applications in various fields. The challenge of this problem stems from the difficulty of dealing with unknown projecting angles, which makes conventional ab initio algorithms like expectation-maximization very time-consuming. Moreover, these methods often prioritize the quality of reconstruction over the determination of unknown angles. Therefore, a method that can quickly approximate the angles of unknown view projections within a certain error margin would significantly streamline and enhance both the speed and quality of reconstruction. In response to this challenge, we propose a learning-based approach for direct angle inference. Training a network to take noisy projections from arbitrary shapes as input and predict their angles is exceptionally challenging. To address this, we introduce Masked Projection Modelling (MPM) as a surrogate task, combined with Probabilistic Angle Estimation (PAE) strategy, making direct angle inference feasible. We show that our system can estimate the angles of $\sim 10^{4}$ noisy projections, each generated from arbitrary shapes, in less than a second with reasonable errors, thereby greatly simplifying and accelerating the reconstruction process.