Plug-and-Play FISTA for Solving Nonlinear Imaging Inverse Problems

In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. In this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm (FISTA) variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMMbased one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data. IEEE Signal Processing Letters This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2018 201 Broadway, Cambridge, Massachusetts 02139 PLUG-AND-PLAY PRIORS APPROACH FOR NONLINEAR INVERSE PROBLEMS 1 Plug-and-Play FISTA for Solving Nonlinear Imaging Inverse Problems Ulugbek S. Kamilov, Member, IEEE, Hassan Mansour, Senior Member, IEEE, and Brendt Wohlberg, Senior Member, IEEE Abstract—In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. In this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm (FISTA) variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMMbased one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data.In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. In this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm (FISTA) variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMMbased one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data.