Tomographic reconstruction recovers an unknown image given its projections from different angles. State-of-the-art methods addressing this problem assume the angles associated with the projections are known a-priori. Given this knowledge, the reconstruction process is straightforward as it can be formulated as a convex problem. Here, we tackle a more challenging setting: 1) the projection angles are unknown, 2) they are drawn from an unknown probability distribution. In this set-up our goal is to recover the image and the projection angle distribution using an unsupervised adversarial learning approach. For this purpose, we formulate the problem as a distribution matching between the real projection lines and the generated ones from the estimated image and projection distribution. This is then solved by reaching the equilibrium in a min-max game between a generator and a discriminator. Our novel contribution is to recover the unknown projection distribution and the image simultaneously using adversarial learning. To accommodate this, we use Gumbel-softmax approximation of samples from categorical distribution to approximate the generators loss as a function of the unknown image and the projection distribution. Our approach can be generalized to different inverse problems. Our simulation results reveal the ability of our method in successfully recovering the image and the projection distribution in various settings.
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