A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems
This provides a robust solution for nuclear medicine applications where high-noise conditions are common.
The paper tackles Poisson inverse problems by developing a plug-and-play algorithm that combines Kullback-Leibler data fidelity with neural network regularization, achieving state-of-the-art performance in deconvolution and tomography with clear superiority in high-noise conditions.
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.