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In this paper, we study a 2D tomography problem for point source models with random unknown view angles. Rather than recovering the projection angles, we reconstruct the model through a set of rotation-invariant features that are estimated from the projection data. For a point source model, we show that these features reveal geometric information about the model such as the radial and pairwise distances. This establishes a connection between unknown view tomography and unassigned distance geometry problem (uDGP).

This paper presents an empirical Bayesian method to estimate regularisation parameters in imaging inverse problems. The method calibrates regularisation parameters directly from the observed data by maximum marginal likelihood estimation, and is useful for inverse problems that are convex. A main novelty is that maximum likelihood estimation is performed efficiently by using a stochastic proximal gradient algorithm that is driven by two proximal Markov chain Monte Carlo samplers, intimately combining modern optimisation and sampling techniques.