Dr. Ilker Kocyigit, University of Michigan
In this talk, we discuss l1 based optimization methods and their applications to some inverse problems such as the ones arising from array imaging and SAR. These inverse problems are formulated as a sparsity promoting l1 optimization problem. We discuss the conditions where the solution of these optimization problems are close to the exact solution and therefore useful. We present estimates that quantify the resolution of the images reconstructed by these methods. We then discuss the multiple data case and the resolution improvements brought by it. We present numerical simulations of the discussed results.