  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 generator's 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.
