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.

Generalized Class Discovery (GCD) aims to dynamically assign labels to unlabelled data partially based on knowledge learned from labelled data, where the unlabelled data may come from known or novel classes. The prevailing approach generally involves clustering across all data and learning conceptions by prototypical contrastive learning. However, existing methods largely hinge on the performance of clustering algorithms and are thus subject to their inherent limitations. Firstly, the estimated cluster number is often smaller than the ground truth, making the existing methods suffer from the lack of prototypes for comprehensive conception learning. To address this issue, we propose an adaptive probing mechanism that introduces learnable potential prototypes to expand cluster prototypes (centers). As there is no ground truth for the potential prototype, we develop a self-supervised prototype learning framework to optimize the potential prototype in an end-to-end fashion. Secondly, clustering is computationally intensive, and the conventional strategy of clustering both labelled and unlabelled instances exacerbates this issue. To counteract this inefficiency, we opt to cluster only the unlabelled instances and subsequently expand the cluster prototypes with our introduced potential prototypes to fast explore novel classes. Despite the simplicity of our proposed method, extensive empirical analysis on a wide range of datasets confirms that our method consistently delivers state-of-the-art results. Specifically, our method surpasses the nearest competitor by a significant margin of 9.7% within the Stanford Cars dataset and 12x clustering efficiency within the Herbarium 19 dataset. We will make the code and checkpoints publicly available at https://github.com/xjtuYW/PNP.git.

Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Moreover, we develop parameter selection strategies. Finally, we quantitatively and qualitatively evaluate the proposed algorithmic scheme on the 3D Open MPI data set with different levels of preprocessing.