Lambda tomography with discontinuous scanning trajectories

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

A scheme for multisource interior tomography

Currently, x-ray computed tomography (CT) requires source scanning so that projections can be collected from various orientations for image reconstruction. Limited by the scanning time, the temporal resolution of CT is often inadequate when rapid dynamics is involved in an object to be reconstructed. To meet this challenge, here the authors propose a scheme of multisource interior tomography for ultrafast imaging that reconstructs a relatively small region of interest (ROI). Specifically, such a ROI is irradiated in parallel with narrow x-ray beams defined by many source-detector pairs for data acquisition. This ROI can be then reconstructed using the interior tomography approach. To demonstrate the merits of this approach, the authors report interior reconstruction from in vivo lung CT data at a much reduced radiation dose, which is roughly proportional to the ROI size. The results suggest a scheme for ultrafast tomography (such as with a limited number of sources and in a scanning mode) to shorten data acquisition time and to suppress motion blurring.

An outlook on x-ray CT research and development

Over the past decade, computed tomography (CT) theory, techniques and applications have undergone a rapid development. Since CT is so practical and useful, undoubtedly CT technology will continue advancing biomedical and non-biomedical applications. In this outlook article, we share our opinions on the research and development in this field, emphasizing 12 topics we expect to be critical in the next decade: analytic reconstruction, iterative reconstruction, local/interior reconstruction, flat-panel based CT, dual-source CT, multi-source CT, novel scanning modes, energy-sensitive CT, nano-CT, artifact reduction, modality fusion, and phase-contrast CT. We also sketch several representative biomedical applications.

A General Scheme for Velocity Tomography

With the rapid development of x-ray source and detector technologies, multi-source scanners become a hot topic in the CT field, which can acquire several projections simultaneously. Aided with the ECG-gating technique, the multi-source scanner can collect sufficient projections to reconstruct one or more specific phases of a beating heart. Hence, we are motivated to develop velocity tomography as a new dynamic imaging mode to recover the velocity field from the projections. First, we derive a velocity field constraint equation subject to the mass conservation. Then, we present a two-step general scheme to estimate the velocity field. The first step directly or indirectly computes partial derivatives. The second step iteratively determines the velocity field subject to the constraint equation and other conditions. Finally, we describe numerical experiments in the fan-beam geometry to demonstrate the correctness and utility of our scheme.