Determination of exact reconstruction regions in composite-circling cone-beam tomography

Image reconstruction of a short portion of a long object using longitudinally truncated cone-beam data is important for major medical computed tomography (CT) applications, especially cardiac CT. Cardiac CT is an essential imaging tool for the diagnosis and therapeutic assessment of heart defects, cardiovascular diseases, and lung diseases, but it is still limited by suboptimal image quality. Recently, saddle-curve and composite-circling scanning modes have been proposed to solve this problem using exact reconstruction formulas. However, saddle-curve scanning involves both circular and linear motions, while composite-circling scanning conveniently involves just circular motions. Because saddle-curve scanning is difficult to implement mechanically, composite-circling scanning provides another, hopefully easier, approach: An x-ray focal spot in an x-ray tube is rotated on a plane facing the heart, while the x-ray tube and possibly the detector are simultaneously rotated on the gantry plane. This article determines regions for chord-based exact reconstruction in the composite-circling scanning mode and compares them to those in the saddle-curve scanning mode. For different scanning parameter combinations, this article finds the largest sphere centered at the origin that can be embedded inside the exact reconstruction region. This article also shows that the embedded spheres become larger when the x-ray focal spot rotates at variable speeds, allowing the scanning curve to cover a larger object. In summary, this article derives guidelines for prototyping a new cardiac CT scanner to meet the goals of reducing radiation dose and increasing spatial and temporal resolution.