  An efficient nonlinear contrast source inversion scheme for electromagnetic
imaging of sparse two-dimensional investigation domains is proposed. To avoid
generating a sequence of linear sparse optimization problems, the non-linearity
is directly tackled using the nonlinear Landweber (NLW) iterations. A
self-adaptive projected accelerated steepest descent (A-PASD) algorithm is
incorporated to enhance the efficiency of the NLW iterations. The algorithm
enforces the sparsity constraint by projecting the result of each steepest
descent iteration into the L1-norm ball and selects the largest-possible
iteration step without sacrificing from convergence. Numerical results, which
demonstrate the proposed schemes accuracy, efficiency, and applicability, are
presented.
