Nonlinear Optimization of Radar Images From a Through-Wall Sensing System via the Lagrange Multiplier Method

Through-wall radar images have limited resolution due to the finite bandwidth and aperture size of man-portable systems. These images may be enhanced by optimizing image sparseness. The inverse imaging function is posed as a constrained nonlinear optimization problem that is solved using the Lagrange multiplier (LM) method. This robust approach has the advantage over related image optimization algorithms in that the LMs are solved within the algorithm rather than being chosen a priori. This yields a system of equations that are solved iteratively rather than by gradient search. Through-wall and free-space measurement examples are presented using a small portable wideband UHF radar system to collect scattered energy from several trihedral (pointlike) targets to demonstrate the enhancement of the radar images.