Two-Dimensional Tomographic Reconstruction from Projections with Unknown Angles and Unknown Spatial Shifts

In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or partially. In this paper, we present a technique for two-dimensional (2D) tomography in which both viewing angles and spatial shifts associated with the projections are unknown. There exists literature on 2D unknown view tomography (UVT), but most existing 2D UVT algorithms assume that the projections are centered; that is, there are no spatial shifts in the projections. To tackle these geometric ambiguities, we first modify an existing graph Laplacian-based algorithm for 2D UVT to incorporate spatial shifts, and then use it as the initialization for the proposed three-way alternating minimization algorithm that jointly estimates the 2D structure, its projection angles, and the corresponding shifts. We evaluate our method on noisy projections of ribosome images and demonstrate that it achieves superior reconstruction compared to the baseline that neglects shifts.