Compressive Imaging with Iterative Forward Models

TL;DR

This paper introduces a nonlinear compressive imaging technique that models multiple scattering phenomena, enabling accurate reconstruction of 2D and 3D objects from scattered wave measurements using an accelerated-gradient approach.

Contribution

It presents a novel nonlinear measurement model for compressive imaging that accounts for multiple scattering and employs an accelerated-gradient method for large-scale reconstruction.

Findings

The method accurately reconstructs objects in simulated environments.

The measurement model converges reliably with explicit gradient formulas.

Numerical validation confirms improved performance over linear models.

Abstract

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.