Accelerated Image Reconstruction for Nonlinear Diffractive Imaging
This work addresses nonlinear imaging challenges in applications like microscopy or tomography, but it appears incremental as it builds on existing optimization techniques.
The paper tackles the problem of reconstructing objects from scattered light measurements by proposing CISOR, a method for nonlinear diffractive imaging based on nonconvex optimization with TV regularization, which achieves reliable convergence and is compared favorably with state-of-the-art methods on simulated and experimental 2D/3D data.
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship, there is an increased interest in considering nonlinear formulations that can account for multiple light scattering. In this paper, we propose an image reconstruction method, called CISOR, for nonlinear diffractive imaging, based on a nonconvex optimization formulation with total variation (TV) regularization. The nonconvex solver used in CISOR is our new variant of fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and memory-efficient implementation of the new FISTA variant and prove that it reliably converges for our nonconvex optimization problem. In addition, we systematically compare our method with other state-of-the-art methods on simulated as well as experimentally measured data in both 2D and 3D settings.