Can interior tomography outperform lambda tomography?

Abstract

Whereas classic computed tomography (CT) theory targets the exact reconstruction of a whole cross-section or entire volume from complete projections, a real-world application often focuses on a region of interest (ROI). It has been a long-standing challenge to reconstruct an internal ROI only from truncated projections collected with a radiative beam through the ROI because this “interior problem” does not have a unique solution (1). When a traditional CT algorithm such as “filtered backprojection” is applied for an interior reconstruction from truncated projections, features outside the ROI may create artifacts overlapping inside features, rendering the images inaccurate or useless. On the other hand, over past decades, lambda tomography has been developed as a branch of applied mathematics that recovers gradient-like features within an ROI from truncated projections. With lambda tomography, the outcomes are not always the most appealing because of their nonquantitative nature. Recently, Quinto et al. (2) demonstrated the utility and limitation of electron lambda tomography and pointed out that “unless prior knowledge is being used…structures in the specimen cannot be exactly recovered even if we have access to noise-free continuum data….”