Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence even for strongly scattering objects. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). The proposed method is validated on both simulated and experimentally measured data.
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