Enhanced Denoising and Convergent Regularisation Using Tweedie Scaling
This addresses a critical limitation in deep learning-based inverse problem solvers for image processing, though it appears incremental as it builds on existing Plug-and-Play frameworks.
The paper tackles the lack of a control parameter for regularization strength in Plug-and-Play methods for image reconstruction, introducing a novel scaling method that enhances interpretability and optimization, and proves stability and convergence.
The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying image. The iterative framework of Plug-and-Play methods, specifically designed for tackling such inverse problems, achieves state-of-the-art performance by replacing the regularisation with a generic denoiser, which may be parametrised by a neural network architecture. However, these deep learning approaches suffer from a critical limitation: the absence of a control parameter to modulate the regularisation strength, which complicates the design of a convergent regularisation. To address this issue, this work introduces a novel scaling method that explicitly integrates and adjusts the strength of regularisation. The scaling parameter enhances interpretability by reflecting the quality of the denoiser's learning process, and also systematically improves its optimisation. Furthermore, the proposed approach ensures that the resulting family of regularisations is provably stable and convergent.