Factorized Geometrical Autofocus: On the geometry search

This paper deals with local geometry optimization within the scope of Factorized Geometrical Autofocus (FGA). The FGA algorithm is a Fast Factorized Back-Projection (FFBP) formulation with six free geometry parameters. These are tuned until a sharp image is obtained, i.e. with respect to an object function. To optimize the geometry (from a focus perspective) for a small image area, we propose an efficient routine based on correlation, sensitivity analysis and Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization. The new routine is evaluated using simulated Ultra-WideBand (UWB) data. By applying the FGA algorithm step-by-step, an erroneous geometry is compensated. This gives a focused image. In regard to run time, the new routine is approximately 100 times faster than a brute-force approach, i.e. for this FGA problem. For a general problem, the run time reduction will be far greater. To be more specific: with x parameters and N values to assess for each parameter; it is anticipated that the computational effort will decrease exponentially by a factor close to N-x