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.
翻译:以不同角度的预测为根据, 地形重建恢复了一个未知的图像。 解决这一问题的最先进的方法假定了与预测相关的角度。 根据这一知识, 重建过程是直截了当的, 因为它可以被设计成一个曲线问题。 在这里, 我们处理一个更具挑战性的设置 :1 投影角度未知, 2) 它们来自未知的概率分布。 在这个设置中, 我们的目标是使用一种不受监督的对抗性学习方法, 恢复图像和投影角分布。 为此, 我们把问题发展成真实投影线与估计图像和投影分布产生的线之间的配对。 然后, 通过在生成器和制导师之间的微轴游戏中达到平衡来解决这个问题。 我们的新贡献是利用对抗性学习同时恢复未知的投影分布和图像。 为了适应这一点, 我们使用绝对分布样本的 Gumbel- socomax 近似比度来估计生成器的损失, 作为未知图像和投影分布的函数。 我们的方法可以被概括为不同的反向问题。 我们的模拟结果显示我们在图像中成功恢复的方法的分布。