OPTIMAL SCAN FOR TIME-VARYING TOMOGRAPHY .1. THEORETICAL-ANALYSIS ANDFUNDAMENTAL LIMITATIONS

We consider the tomographic reconstruction of objects with spatially l ocalized temporal variation, such as a thorax cross section with a bea ting heart, The conventional scan format, in which projections are tak en progressively around the object, requires high and sometimes infeas ible scan rates to avoid motion artifacts in the reconstructed images, We formulate the problem of data acquisition as a time-sequential sam pling problem of spatially and temporally bandlimited signals, where o nly one view can be taken at a time, but the time interval between suc cessive views is independent of their angular separation, These condit ions, naturally satisfied in magnetic resonance imaging and in x-ray C T using the Imatron system, can also be satisfied by a conventional sy stem with a continuously and rapidly spinning gantry with source pulsi ng, Theoretical analysis, which includes tight performance bounds, sho ws that by using an optimally scrambled angular sampling order, the re quired scan rate can be lowered as much as four times, while preservin g image quality, The analysis also greatly simplifies the design of th e optimum scan pattern by reducing it to a constrained geometric packi ng problem.