  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.
