Data redundancy and reduced-scan reconstruction in reflectivity tomography.

In reflectivity tomography, conventional reconstruction approaches require that measurements be acquired at view angles that span a full angular range of 2pi. It is often, however, advantageous to reduce the angular range over which measurements are acquired, in order, for example, to minimize artifacts due to movements of the imaged object. Moreover, in certain situations, it may not be experimentally possible to collect data over a 2pi angular range. We investigate the problem of reconstructing images from reduced-scan data in reflectivity tomography. By exploiting symmetries in the data function of reflectivity tomography, we demonstrate heuristically that an image function can be uniquely specified by reduced-scan data that correspond to measurements taken over an angular interval (possibly disjoint) that spans at least pi radians. We also identify sufficient conditions that permit for a stable reconstruction of image boundaries from reduced-scan data. Numerical results in computer-simulation studies indicate that images can be reconstructed accurately from reduced-scan data.