An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction

TL;DR

This paper introduces an adversarial learning framework that jointly reconstructs images and estimates unknown projection angles in 2D tomographic imaging, even with noisy data, using a Wasserstein GAN approach.

Contribution

It presents a novel adversarial learning method that recovers both the image and the projection angle distribution without prior angle knowledge, employing Gumbel-Softmax reparameterization.

Findings

Accurately recovers images and projection angles under noise.

Theoretical guarantees for unique recovery up to rotation and reflection.

Effective in scenarios with completely unknown projection angles.

Abstract

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.