Fast Optimization of Through-Wall Radar Images Via the Method of Lagrange Multipliers

Through-wall radar images taken from man-portable systems have limited resolution due to the finite bandwidth and aperture size. However, these images can be enhanced by exploiting scene sparseness (leading to sharper images) or homogeneity (leading to more natural, i.e., visually intuitive, images). To realize these enhancements, we employ a constrained non-linear optimization algorithm based on the Lagrange multiplier method. This approach has an advantage over related image optimization algorithms in that the Lagrange multipliers are solved within the algorithm rather than being selected a priori. This yields a system of equations that is solved iteratively rather than by gradient search. Data from a portable wideband UHF radar is used to test algorithm performance for several through-wall (cinder block) and free-space scenarios.