The past few years have seen a surge of activity around integration of deep learning networks and optimization algorithms for solving inverse problems. Recent work on plug-and-play priors (PnP), regularization by denoising (RED), and deep unfolding has shown the state-of-the-art performance of such integration in a variety of applications. However, the current paradigm for designing such algorithms is inherently Euclidean, due to the usage of the quadratic norm within the projection and proximal operators. We propose to broaden this perspective by considering a non-Euclidean setting based on the more general Bregman distance. Our new Bregman Proximal Gradient Method variant of PnP (PnP-BPGM) and Bregman Steepest Descent variant of RED (RED-BSD) replace the traditional updates in PnP and RED from the quadratic norms to more general Bregman distance. We present a theoretical convergence result for PnP-BPGM and demonstrate the effectiveness of our algorithms on Poisson linear inverse problems.
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This content will become publicly available on December 10, 2024
Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems
Plug-and-Play (PnP) methods are efficient iterative algorithms for solving ill-posed image inverse problems. PnP methods are obtained by using deep Gaussian denoisers instead of the proximal operator or the gradient-descent step within proximal algorithms. Current PnP schemes rely on data-fidelity terms that have either Lipschitz gradients or closed-form proximal operators, which is not applicable to Poisson inverse problems. Based on the observation that the Gaussian noise is not the adequate noise model in this setting, we propose to generalize PnP using the Bregman Proximal Gradient (BPG) method. BPG replaces the Euclidean distance with a Bregman divergence that can better capture the smoothness properties of the problem. We introduce the Bregman Score Denoiser specifically parametrized and trained for the new Bregman geometry and prove that it corresponds to the proximal operator of a nonconvex potential. We propose two PnP algorithms based on the Bregman Score Denoiser for solving Poisson inverse problems. Extending the convergence results of BPG in the nonconvex settings, we show that the proposed methods converge, targeting stationary points of an explicit global functional. Experimental evaluations conducted on various Poisson inverse problems validate the convergence results and showcase effective restoration performance.
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- Award ID(s):
- 2043134
- NSF-PAR ID:
- 10504933
- Publisher / Repository:
- Conference on Neural Information Processing Systems (NeurIPS)
- Date Published:
- Format(s):
- Medium: X
- Location:
- New Orleans, LA, USA
- Sponsoring Org:
- National Science Foundation
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