Noise- and Outlier-Resistant Tomographic Reconstruction under Unknown Viewing Parameters
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.