An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction
This addresses a challenging scenario in medical imaging or materials science where precise angle information is unavailable, offering a novel solution with potential practical impact, though it appears incremental as it builds on existing adversarial techniques.
The paper tackles the problem of 2D tomographic reconstruction when projection angles are unknown or approximate, proposing an adversarial learning approach to recover both the image and angle distribution by matching measurement distributions. The method achieves accurate recovery of the image and projection angles under noise, as verified by theoretical analysis and numerical experiments.
The goal of 2D tomographic reconstruction is to recover an image given its projections from various views. It is often presumed that projection angles associated with the projections are known in advance. Under certain situations, however, these angles are known only approximately or are completely unknown. It becomes more challenging to reconstruct the image from a collection of random projections. We propose an adversarial learning based approach to recover the image and the projection angle distribution by matching the empirical distribution of the measurements with the generated data. Fitting the distributions is achieved through solving a min-max game between a generator and a critic based on Wasserstein generative adversarial network structure. To accommodate the update of the projection angle distribution through gradient back propagation, we approximate the loss using the Gumbel-Softmax reparameterization of samples from discrete distributions. Our theoretical analysis verifies the unique recovery of the image and the projection distribution up to a rotation and reflection upon convergence. Our extensive numerical experiments showcase the potential of our method to accurately recover the image and the projection angle distribution under noise contamination.