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We propose a new compressive imaging method for reconstructing 2D or 3Dobjects from their scattered wave-field measurements. Our method relies on anovel, nonlinear measurement model that can account for the multiple scatteringphenomenon, which makes the method preferable in applications where linearmeasurement models are inaccurate. We construct the measurement model byexpanding the scattered wave-field with an accelerated-gradient method, whichis guaranteed to converge and is suitable for large-scale problems. We provideexplicit formulas for computing the gradient of our measurement model withrespect to the unknown image, which enables image formation with a sparsity-driven numerical optimization algorithm. We validate the method bothanalytically and with numerical simulations.

Compressive Imaging with Iterative Forward Models