Two-Dimensional Tomography from Noisy Projection Tilt Series Taken at Unknown View Angles with Non-Uniform Distributi

Abstract

We consider a problem that recovers a 2-D object and the underlying view angle distribution from its noisy projection tilt series taken at unknown view angles. Traditional approaches rely on the estimation of the view angles of the projections, which do not scale well with the sample size and are sensitive to noise. We introduce a new approach using the moment features to simultaneously recover the underlying object and the distribution of view angles. This problem is formulated as constrained nonlinear least squares in terms of the truncated Fourier-Bessel expansion coefficients of the object and is solved by a new alternating direction method of multipliers (ADMM)-based algorithm. Our numerical experiments show that the new approach outperforms the expectation maximization (EM)-based maximum marginalized likelihood estimation in efficiency and accuracy. Furthermore, the hybrid method that uses EM to refine ADMM solution achieves the best performance.

An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction

“…Now p corresponds to a discrete or categorical distribution over θ, which implies the sampled projection angles from p can only belong to N θ discrete categories. Therefore, we rewrite the loss function (14) as:…”

“…A closer look at (16) reveals that δ(θ t − θ b ), θ b ∼ p is a sample from the discrete distribution p. This enables us to incorporate the notion of Gumbel-Softmax distribution and approximate (14) as:…”

“…In another class of methods, to circumvent the estimation/refinement of the projection angles, a set of rotation invariant features are estimated from the noisy projections. These features are later on used to reconstruct the unknown image [11]- [14]. Note that these methods require only one pass through the projection dataset and are therefore computationally more efficient.…”