Inverse Multiple Scattering with Phaseless Measurements

We study the problem of reconstructing an object from phaseless measurements in the context of inverse multiple scattering. Our formulation explicitly decouples the variables that represent the unknown object image and the unknown phase, respectively, in the forward model. This enables us to simultaneously optimize over both unknowns with appropriate regularization for each. The resulting optimization problem is nonconvex due to the nonlinear propagation model for multiple scattering and the nonconvex regularization of the phase variables. Nevertheless, we demonstrate experimentally that we can solve the optimization problem using a variation of the fast iterative shrinkage-thresholding algorithm (FISTA)-a convex algorithm, popular for its speed and simplicity-that converges well in our experiments. Numerical results with both simulated and experimentally measured data show that the proposed method outperforms the state-of-the-art phaseless inverse scattering method.