Convex set estimation from support line measurements and applications to target reconstruction from laser radar data

In this paper, we extend techniques of convex set reconstruction from support line measurements, assess their performance with respect to various parameters, and apply these radar data. Specifically, the techniques are applied to both range-resolved and Doppler-resolved data, which provide one and two support line measurements respectively. The resulting reconstructions provide size and shape estimates of the targets under observation. While such information can be obtained by other means (e.g. from reconstructed images using tomography), the present methods yield this information more directly. Furthermore, estimates obtained using these methods are more robust to noisy and/or sparse measurement data and are much more robust to data suffering from registration errors. Finally, the present methods are used to improve tomographic images in the presence of registration errors.