Two-Dimensional Tomographic Reconstruction From Projections With Unknown Angles and Unknown Spatial Shifts

TL;DR

This paper introduces a novel 2D tomography method that jointly estimates object structure, projection angles, and spatial shifts from unknown and noisy projection data, improving reconstruction accuracy.

Contribution

It extends existing 2D UVT algorithms by incorporating spatial shifts and proposes a three-way alternating minimization approach for joint estimation.

Findings

Achieves superior reconstruction quality over baseline methods that ignore shifts.

Effectively estimates unknown projection angles and shifts in noisy conditions.

Demonstrates applicability on ribosome image data.

Abstract

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.