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We consider a problem that recovers a 2-D object and the underlying viewangle distribution from its noisy projection tilt series taken at unknown viewangles. Traditional approaches rely on the estimation of the view angles of theprojections, which do not scale well with the sample size and are sensitive tonoise. We introduce a new approach using the moment features to simultaneouslyrecover the underlying object and the distribution of view angles. This problemis formulated as constrained nonlinear least squares in terms of the truncatedFourier-Bessel expansion coefficients of the object and is solved by a newalternating direction method of multipliers (ADMM)-based algorithm. Ournumerical experiments show that the new approach outperforms the expectationmaximization (EM)-based maximum marginalized likelihood estimation inefficiency and accuracy. Furthermore, the hybrid method that uses EM to refineADMM solution achieves the best performance.

Two-Dimensional Tomography From Noisy Projection Tilt Series Taken At Unknown View Angles With Non-Uniform Distribution