l1 - based Optimization Methods in Array Imaging and Synthetic Aperture Radar (SAR)

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 can be 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 consider the case where data from "multiple measurements" are available and discuss the resolution improvements brought by it. We present numerical simulations of the discussed results.

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