An iterative inverse-scattering approach to distributed sensing

The Kaczmarz method is widely used in computed tomography applications to iteratively solve large inverse problems for which a direct solution is computationally prohibitive. In this paper, the Kaczmarz method is generalized to handle sparse frequency data collected from sparse, spatially distributed, multistatic sensors. In addition, the developed algorithm provides a mathematical solution to the underlying diffraction tomography problem described by the scalar wave equation under the Born approximation. The formulation avoids computing the pseudo-inverse of a large forward operator while still converging to the true minimum norm solution to the scattering problem, and the resulting reconstructed images are superior to the matched filter results often employed in SAR/ISAR applications. A fast version of the algorithm that exploits circular symmetries in the sensor geometry is also described.