You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors

The use of Plug-and-Play (PnP) methods has become a central approach for solving inverse problems, with denoisers serving as regularising priors that guide optimisation towards a clean solution. In this work, we introduce KAN-PnP, an optimisation framework that incorporates Kolmogorov-Arnold Networks (KANs) as denoisers within the Plug-and-Play (PnP) paradigm. KAN-PnP is specifically designed to solve inverse problems with single-instance priors, where only a single noisy observation is available, eliminating the need for large datasets typically required by traditional denoising methods. We show that KANs, based on the Kolmogorov-Arnold representation theorem, serve effectively as priors in such settings, providing a robust approach to denoising. We prove that the KAN denoiser is Lipschitz continuous, ensuring stability and convergence in optimisation algorithms like PnP-ADMM, even in the context of single-shot learning. Additionally, we provide theoretical guarantees for KAN-PnP, demonstrating its convergence under key conditions: the convexity of the data fidelity term, Lipschitz continuity of the denoiser, and boundedness of the regularisation functional. These conditions are crucial for stable and reliable optimisation. Our experimental results show, on super-resolution and joint optimisation, that KAN-PnP outperforms exiting methods, delivering superior performance in single-shot learning with minimal data. The method exhibits strong convergence properties, achieving high accuracy with fewer iterations.

Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey

Implicit Neural Representations (INRs) have emerged as a paradigm in knowledge representation, offering exceptional flexibility and performance across a diverse range of applications. INRs leverage multilayer perceptrons (MLPs) to model data as continuous implicit functions, providing critical advantages such as resolution independence, memory efficiency, and generalisation beyond discretised data structures. Their ability to solve complex inverse problems makes them particularly effective for tasks including audio reconstruction, image representation, 3D object reconstruction, and high-dimensional data synthesis. This survey provides a comprehensive review of state-of-the-art INR methods, introducing a clear taxonomy that categorises them into four key areas: activation functions, position encoding, combined strategies, and network structure optimisation. We rigorously analyse their critical properties, such as full differentiability, smoothness, compactness, and adaptability to varying resolutions while also examining their strengths and limitations in addressing locality biases and capturing fine details. Our experimental comparison offers new insights into the trade-offs between different approaches, showcasing the capabilities and challenges of the latest INR techniques across various tasks. In addition to identifying areas where current methods excel, we highlight key limitations and potential avenues for improvement, such as developing more expressive activation functions, enhancing positional encoding mechanisms, and improving scalability for complex, high-dimensional data. This survey serves as a roadmap for researchers, offering practical guidance for future exploration in the field of INRs. We aim to foster new methodologies by outlining promising research directions for INRs and applications.

Semi-Supervised Video Desnowing Network via Temporal Decoupling Experts and Distribution-Driven Contrastive Regularization

Snow degradations present formidable challenges to the advancement of computer vision tasks by the undesirable corruption in outdoor scenarios. While current deep learning-based desnowing approaches achieve success on synthetic benchmark datasets, they struggle to restore out-of-distribution real-world snowy videos due to the deficiency of paired real-world training data. To address this bottleneck, we devise a new paradigm for video desnowing in a semi-supervised spirit to involve unlabeled real data for the generalizable snow removal. Specifically, we construct a real-world dataset with 85 snowy videos, and then present a Semi-supervised Video Desnowing Network (SemiVDN) equipped by a novel Distribution-driven Contrastive Regularization. The elaborated contrastive regularization mitigates the distribution gap between the synthetic and real data, and consequently maintains the desired snow-invariant background details. Furthermore, based on the atmospheric scattering model, we introduce a Prior-guided Temporal Decoupling Experts module to decompose the physical components that make up a snowy video in a frame-correlated manner. We evaluate our SemiVDN on benchmark datasets and the collected real snowy data. The experimental results demonstrate the superiority of our approach against state-of-the-art image- and video-level desnowing methods.

Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs

Partial differential equations (PDEs) are widely used to model complex physical systems, but solving them efficiently remains a significant challenge. Recently, Transformers have emerged as the preferred architecture for PDEs due to their ability to capture intricate dependencies. However, they struggle with representing continuous dynamics and long-range interactions. To overcome these limitations, we introduce the Mamba Neural Operator (MNO), a novel framework that enhances neural operator-based techniques for solving PDEs. MNO establishes a formal theoretical connection between structured state-space models (SSMs) and neural operators, offering a unified structure that can adapt to diverse architectures, including Transformer-based models. By leveraging the structured design of SSMs, MNO captures long-range dependencies and continuous dynamics more effectively than traditional Transformers. Through extensive analysis, we show that MNO significantly boosts the expressive power and accuracy of neural operators, making it not just a complement but a superior framework for PDE-related tasks, bridging the gap between efficient representation and accurate solution approximation.

Learning Task-Specific Sampling Strategy for Sparse-View CT Reconstruction

Sparse-View Computed Tomography (SVCT) offers low-dose and fast imaging but suffers from severe artifacts. Optimizing the sampling strategy is an essential approach to improving the imaging quality of SVCT. However, current methods typically optimize a universal sampling strategy for all types of scans, overlooking the fact that the optimal strategy may vary depending on the specific scanning task, whether it involves particular body scans (e.g., chest CT scans) or downstream clinical applications (e.g., disease diagnosis). The optimal strategy for one scanning task may not perform as well when applied to other tasks. To address this problem, we propose a deep learning framework that learns task-specific sampling strategies with a multi-task approach to train a unified reconstruction network while tailoring optimal sampling strategies for each individual task. Thus, a task-specific sampling strategy can be applied for each type of scans to improve the quality of SVCT imaging and further assist in performance of downstream clinical usage. Extensive experiments across different scanning types provide validation for the effectiveness of task-specific sampling strategies in enhancing imaging quality. Experiments involving downstream tasks verify the clinical value of learned sampling strategies, as evidenced by notable improvements in downstream task performance. Furthermore, the utilization of a multi-task framework with a shared reconstruction network facilitates deployment on current imaging devices with switchable task-specific modules, and allows for easily integrate new tasks without retraining the entire model.

LGRNet: Local-Global Reciprocal Network for Uterine Fibroid Segmentation in Ultrasound Videos

Regular screening and early discovery of uterine fibroid are crucial for preventing potential malignant transformations and ensuring timely, life-saving interventions. To this end, we collect and annotate the first ultrasound video dataset with 100 videos for uterine fibroid segmentation (UFUV). We also present Local-Global Reciprocal Network (LGRNet) to efficiently and effectively propagate the long-term temporal context which is crucial to help distinguish between uninformative noisy surrounding tissues and target lesion regions. Specifically, the Cyclic Neighborhood Propagation (CNP) is introduced to propagate the inter-frame local temporal context in a cyclic manner. Moreover, to aggregate global temporal context, we first condense each frame into a set of frame bottleneck queries and devise Hilbert Selective Scan (HilbertSS) to both efficiently path connect each frame and preserve the locality bias. A distribute layer is then utilized to disseminate back the global context for reciprocal refinement. Extensive experiments on UFUV and three public Video Polyp Segmentation (VPS) datasets demonstrate consistent improvements compared to state-of-the-art segmentation methods, indicating the effectiveness and versatility of LGRNet. Code, checkpoints, and dataset are available at https://github.com/bio-mlhui/LGRNet

Optimised ProPainter for Video Diminished Reality Inpainting

In this paper, part of the DREAMING Challenge - Diminished Reality for Emerging Applications in Medicine through Inpainting, we introduce a refined video inpainting technique optimised from the ProPainter method to meet the specialised demands of medical imaging, specifically in the context of oral and maxillofacial surgery. Our enhanced algorithm employs the zero-shot ProPainter, featuring optimized parameters and pre-processing, to adeptly manage the complex task of inpainting surgical video sequences, without requiring any training process. It aims to produce temporally coherent and detail-rich reconstructions of occluded regions, facilitating clearer views of operative fields. The efficacy of our approach is evaluated using comprehensive metrics, positioning it as a significant advancement in the application of diminished reality for medical purposes.

Biophysics Informed Pathological Regularisation for Brain Tumour Segmentation

Recent advancements in deep learning have significantly improved brain tumour segmentation techniques; however, the results still lack confidence and robustness as they solely consider image data without biophysical priors or pathological information. Integrating biophysics-informed regularisation is one effective way to change this situation, as it provides an prior regularisation for automated end-to-end learning. In this paper, we propose a novel approach that designs brain tumour growth Partial Differential Equation (PDE) models as a regularisation with deep learning, operational with any network model. Our method introduces tumour growth PDE models directly into the segmentation process, improving accuracy and robustness, especially in data-scarce scenarios. This system estimates tumour cell density using a periodic activation function. By effectively integrating this estimation with biophysical models, we achieve a better capture of tumour characteristics. This approach not only aligns the segmentation closer to actual biological behaviour but also strengthens the model's performance under limited data conditions. We demonstrate the effectiveness of our framework through extensive experiments on the BraTS 2023 dataset, showcasing significant improvements in both precision and reliability of tumour segmentation.

Single-Shot Plug-and-Play Methods for Inverse Problems

The utilisation of Plug-and-Play (PnP) priors in inverse problems has become increasingly prominent in recent years. This preference is based on the mathematical equivalence between the general proximal operator and the regularised denoiser, facilitating the adaptation of various off-the-shelf denoiser priors to a wide range of inverse problems. However, existing PnP models predominantly rely on pre-trained denoisers using large datasets. In this work, we introduce Single-Shot PnP methods (SS-PnP), shifting the focus to solving inverse problems with minimal data. First, we integrate Single-Shot proximal denoisers into iterative methods, enabling training with single instances. Second, we propose implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients. We demonstrate, through extensive numerical and visual experiments, that our method leads to better approximations.

TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations

Implicit neural representations (INRs) have garnered significant interest recently for their ability to model complex, high-dimensional data without explicit parameterisation. In this work, we introduce TRIDENT, a novel function for implicit neural representations characterised by a trilogy of nonlinearities. Firstly, it is designed to represent high-order features through order compactness. Secondly, TRIDENT efficiently captures frequency information, a feature called frequency compactness. Thirdly, it has the capability to represent signals or images such that most of its energy is concentrated in a limited spatial region, denoting spatial compactness. We demonstrated through extensive experiments on various inverse problems that our proposed function outperforms existing implicit neural representation functions.