  We consider the problem of estimating an unbiased and reference-free ab-inito
model for non-symmetric molecules from images generated by single-particle
cryo-electron microscopy. The proposed algorithm finds the globally optimal
assignment of orientations that simultaneously respects all common lines
between all images. The contribution of each common line to the estimated
orientations is weighted according to a statistical model for common lines'
detection errors. The key property of the proposed algorithm is that it finds
the global optimum for the orientations given the common lines. In particular,
any local optima in the common lines energy landscape do not affect the
proposed algorithm. As a result, it is applicable to thousands of images at
once, very robust to noise, completely reference free, and not biased towards
any initial model. A byproduct of the algorithm is a set of measures that allow
to asses the reliability of the obtained ab-initio model. We demonstrate the
algorithm using class averages from two experimental data sets, resulting in
ab-initio models with resolutions of 20A or better, even from class averages
consisting of as few as three raw images per class.
