Compressive Imaging with Iterative Forward Models
This addresses the challenge of inaccurate linear models in compressive imaging for applications like medical or seismic imaging, but it appears incremental as it builds on existing optimization and sparsity techniques.
The paper tackles the problem of reconstructing 2D or 3D objects from scattered wave-field measurements by proposing a compressive imaging method with a nonlinear measurement model that accounts for multiple scattering, and it validates the method analytically and with numerical simulations.
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon, which makes the method preferable in applications where linear measurement models are inaccurate. We construct the measurement model by expanding the scattered wave-field with an accelerated-gradient method, which is guaranteed to converge and is suitable for large-scale problems. We provide explicit formulas for computing the gradient of our measurement model with respect to the unknown image, which enables image formation with a sparsity- driven numerical optimization algorithm. We validate the method both analytically and with numerical simulations.