Progress in Tomography with Unknown Shifts and View Angles

Parallel beam computed tomography (CT) is a foundational imaging modality in medical diagnostics and industrial inspection. It reconstructs an object from a series of projections taken at different angles. In many practical scenarios, however, the viewing angles and spatial shifts associated with the projections are not precisely known, such as in cryo-electron microscopy, microfluidic imaging, or low-dose CT acquisition. We address the problem of reconstructing a two-dimensional object from Radon projections acquired at unknown view angles and affected by unknown spatial shifts. To resolve this geometric ambiguity, we propose an analytic framework that first centers each projection using its first moment, then compares second- and third-order projection moments to identify the correct angle. The proposed method is non-iterative, requires only a few known projections of the base function, and supports full parallelization. Numerical experiments on synthetic and structured test images demonstrate sub-degree angular recovery accuracy and enable good-quality reconstruction via standard inversion techniques. These results underscore the method’s effectiveness and robustness under geometric uncertainty.