A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems

• URL: http://arxiv.org/abs/2603.24156v1
• Date: Wed, 25 Mar 2026 10:25:20 GMT
• Title: A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems
• Abstract summary: We present a novel variational plug-and-play algorithm for Poisson inverse problems.<n>Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a pre-trained neural network.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present a novel variational plug-and-play algorithm for Poisson inverse problems. Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a pre-trained neural network. By combining classical likelihood maximization methods with recent advances in gradient-based denoisers, we allow the use of pre-trained Gaussian denoisers without sacrificing convergence guarantees. The algorithm is formulated in the majorization-minimization framework, which guarantees convergence to a stationary point. Numerical experiments confirm state-of-the-art performance in deconvolution and tomography under moderate noise, and demonstrate clear superiority in high-noise conditions, making this method particularly valuable for nuclear medicine applications.

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