Optimal scan for time-varying tomography. I. Theoretical analysis and fundamental limitations

The authors consider the tomographic reconstruction of objects with spatially localized temporal variation, such as a thorax cross section with a beating heart. The conventional scan format, in which projections are taken progressively around the object, requires high and sometimes infeasible scan rates to avoid motion artifacts in the reconstructed images. The authors formulate the problem of data acquisition as a time-sequential sampling problem of spatially and temporally bandlimited signals, where only one view can be taken at a time, but the time interval between successive views is independent of their angular separation. These conditions, naturally satisfied in magnetic resonance imaging and in X-ray CT using the Imatron system, can also be satisfied by a conventional system with a continuously and rapidly spinning gantry with source pulsing. Theoretical analysis, which includes tight performance bounds, shows that by using an optimally scrambled angular sampling order, the required scan rate can be lowered as much as four times, while preserving image quality. The analysis also greatly simplifies the design of the optimum scan pattern by reducing it to a constrained geometric packing problem.