SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering

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 an iterative forward model and a total variation (TV) regularizer. The proposed method can account for multiple scattering, which makes it advantageous in applications where single scattering approximations are inaccurate. Specifically, the method relies on a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence of the forward model 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 an iterative 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 diffraction tomography where complex electric field is captured at different illumination angles.