Quadratic Majorization-Minimization in Regularized Radar Imaging

Quadratic majorization-minimization is found in a 1937 paper by Weiszfeld and provides an easily accessible iterative optimization algorithm for non-convex and non-smooth optimization tasks; the iteration is often referred to as “iteratively re-weighted least squares” (IRLS). In this manuscript, IRLS is employed as a unifying tutorial description of many regularized imaging techniques previously proposed for radar imaging. The cost function implicit in an IRLS imaging approach is made explicit, yielding a Bayesian interpretation with specific underlying assumptions regarding clutter, noise, and prior distribution on the unknown range-angle-Doppler maps. In particular, the IRLS framework is used to establish the convergence and sparse imaging properties of the reiterative super-resolution (RISR) [1] and background supplemental loading (BaSL) [2] algorithms.