  In this paper, we present an algorithm for effectively reconstructing an
object from a set of its tomographic projections without any knowledge of the
viewing directions or any prior structural information, in the presence of
pathological amounts of noise, unknown shifts in the projections, and outliers.
We introduce a novel statistically motivated pipeline of first processing the
projections, then obtaining an initial estimate for the orientations and the
shifts, and eventually performing a refinement procedure to obtain the final
reconstruction. Even in the presence of high noise variance (up to $50\%$ of
the average value of the (noiseless) projections) and presence of outliers, we
are able to reconstruct the object successfully. We also provide interesting
empirical comparisons of our method with popular sparsity-based optimization
procedures that have been used earlier for image reconstruction tasks.
