arXiv subjects

Carola-Bibiane Schönlieb

Publications and source records attributed to Carola-Bibiane Schönlieb.

At least 55 records · Page 3Linked to original sources

arXiv2026

Neural Fields for Highly Accelerated 2D Cine Phase Contrast MRI

2D cine phase contrast (CPC) MRI provides quantitative information on blood velocity and flow within the human vasculature. However, data acquisition is time-consuming, motivating the reconstruction of the velocity field from undersampled measurements to reduce scan times. In this work, neural fields are proposed as a continuous spatiotemporal parametrization of complex-valued images, jointly modeling magnitude and phase across multiple echoes to enable velocity estimation, and leveraging their inductive bias for the reconstruction of the velocity data. Additionally, to compensate for the oversmoothing tendency observed in neural-field reconstructions under severe undersampling, a simple voxel-based postprocessing step is introduced. The method is validated numerically in Cartesian and radial k-space with both high and low temporal resolution data. This approach achieves accurate reconstructions at high acceleration factors, with low errors even at 32$\times$ and 64$\times$ undersampling for the high temporal resolution data, and 16$\times$ for the low temporal resolution data, and consistently outperforms classical locally low-rank regularized voxel-based methods in both flow estimates and anatomical depiction.

eess.IV↗

arXiv2026

Learning Regularization Functionals for Inverse Problems: A Comparative Study

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.

cs.LG↗

arXiv2025

Training-Free Dual Hyperbolic Adapters for Better Cross-Modal Reasoning

Recent research in Vision-Language Models (VLMs) has significantly advanced our capabilities in cross-modal reasoning. However, existing methods suffer from performance degradation with domain changes or require substantial computational resources for fine-tuning in new domains. To address this issue, we develop a new adaptation method for large vision-language models, called \textit{Training-free Dual Hyperbolic Adapters} (T-DHA). We characterize the vision-language relationship between semantic concepts, which typically has a hierarchical tree structure, in the hyperbolic space instead of the traditional Euclidean space. Hyperbolic spaces exhibit exponential volume growth with radius, unlike the polynomial growth in Euclidean space. We find that this unique property is particularly effective for embedding hierarchical data structures using the Poincaré ball model, achieving significantly improved representation and discrimination power. Coupled with negative learning, it provides more accurate and robust classifications with fewer feature dimensions. Our extensive experimental results on various datasets demonstrate that the T-DHA method significantly outperforms existing state-of-the-art methods in few-shot image recognition and domain generalization tasks.

cs.CV↗

arXiv2025

DNA-Prior: Unsupervised Denoise Anything via Dual-Domain Prior

Medical imaging pipelines critically rely on robust denoising to stabilise downstream tasks such as segmentation and reconstruction. However, many existing denoisers depend on large annotated datasets or supervised learning, which restricts their usability in clinical environments with heterogeneous modalities and limited ground-truth data. To address this limitation, we introduce DNA-Prior, a universal unsupervised denoising framework that reconstructs clean images directly from corrupted observations through a mathematically principled hybrid prior. DNA-Prior integrates (i) an implicit architectural prior, enforced through a deep network parameterisation, with (ii) an explicit spectral-spatial prior composed of a frequency-domain fidelity term and a spatial regularisation functional. This dual-domain formulation yields a well-structured optimisation problem that jointly preserves global frequency characteristics and local anatomical structure, without requiring any external training data or modality-specific tuning. Experiments across multiple modalities show that DNA achieves consistent noise suppression and structural preservation under diverse noise conditions.

cs.CV↗

arXiv2025

Towards Efficient Training of Graph Neural Networks: A Multiscale Approach

Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant computational and memory challenges, limiting their scalability and efficiency. In this paper, we present a novel framework for efficient multiscale training of GNNs. Our approach leverages hierarchical graph representations and subgraphs, enabling the integration of information across multiple scales and resolutions. By utilizing coarser graph abstractions and subgraphs, each with fewer nodes and edges, we significantly reduce computational overhead during training. Building on this framework, we propose a suite of scalable training strategies, including coarse-to-fine learning, subgraph-to-full-graph transfer, and multiscale gradient computation. We also provide some theoretical analysis of our methods and demonstrate their effectiveness across various datasets and learning tasks. Our results show that multiscale training can substantially accelerate GNN training for large scale problems while maintaining, or even improving, predictive performance.

cs.LG↗

arXiv2025

Deep Spectral Prior

We introduce the Deep Spectral Prior (DSP), a new framework for unsupervised image reconstruction that operates entirely in the complex frequency domain. Unlike the Deep Image Prior (DIP), which optimises pixel-level errors and is highly sensitive to overfitting, DSP performs joint learning of amplitude and phase to capture the full spectral structure of images. We derive a rigorous theoretical characterisation of DSP's optimisation dynamics, proving that it follows frequency-dependent descent trajectories that separate informative low-frequency modes from stochastic high-frequency noise. This spectral mode separation explains DSP's self-regularising behaviour and, for the first time, formally establishes the elimination of DIP's major limitation-its reliance on manual early stopping. Moreover, DSP induces an implicit projection onto a frequency-consistent manifold, ensuring convergence to stable, physically plausible reconstructions without explicit priors or supervision. Extensive experiments on denoising, inpainting, and deblurring demonstrate that DSP consistently surpasses DIP and other unsupervised baselines, achieving superior fidelity, robustness, and theoretical interpretability within a unified, unsupervised data-free framework.

cs.CV↗

arXiv2025

Laplace Learning in Wasserstein Space

The manifold hypothesis posits that high-dimensional data typically resides on low-dimensional sub spaces. In this paper, we assume manifold hypothesis to investigate graph-based semi-supervised learning methods. In particular, we examine Laplace Learning in the Wasserstein space, extending the classical notion of graph-based semi-supervised learning algorithms from finite-dimensional Euclidean spaces to an infinite-dimensional setting. To achieve this, we prove variational convergence of a discrete graph p- Dirichlet energy to its continuum counterpart. In addition, we characterize the Laplace-Beltrami operator on asubmanifold of the Wasserstein space. Finally, we validate the proposed theoretical framework through numerical experiments conducted on benchmark datasets, demonstrating the consistency of our classification performance in high-dimensional settings.

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arXiv2025

HIBMatch: Hypergraph Information Bottleneck for Semi-supervised Alzheimer's Progression

Alzheimer's disease progression prediction is critical for patients with early Mild Cognitive Impairment (MCI) to enable timely intervention and improve their quality of life. While existing progression prediction techniques demonstrate potential with multimodal data, they are highly limited by their reliance on labelled data and fail to account for a key element of future progression prediction: not all features extracted at the current moment may be relevant for predicting progression several years later. To address these limitations in the literature, we design a novel semi-supervised multimodal learning hypergraph architecture, termed HIBMatch, by harnessing hypergraph knowledge based on information bottleneck and consistency regularisation strategies. Firstly, our framework utilises hypergraphs to represent multimodal data, encompassing both imaging and non-imaging modalities. Secondly, to harmonise relevant information from the currently captured data for future MCI conversion prediction, we propose a Hypergraph Information Bottleneck (HIB) that discriminates against irrelevant information, thereby focusing exclusively on harmonising relevant information for future MCI conversion prediction. Thirdly, our method enforces consistency regularisation between the HIB and a discriminative classifier to enhance the robustness and generalisation capabilities of HIBMatch under both topological and feature perturbations. Finally, to fully exploit the unlabeled data, HIBMatch incorporates a cross-modal contrastive loss for data efficiency. Extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that our proposed HIBMatch framework surpasses existing state-of-the-art methods in Alzheimer's disease prognosis.

cs.CV↗

arXiv2025

Real-time CBCT reconstructions using Krylov solvers in repeated scanning procedures

This work introduces a new efficient iterative solver for the reconstruction of real-time cone-beam computed tomography (CBCT), which is based on the Prior Image Constrained Compressed Sensing (PICCS) regularization and leverages the efficiency of Krylov subspace methods. In particular, we focus on the setting where a sequence of under-sampled CT scans are taken on the same object with only local changes (e.g. changes in a tumour size or the introduction of a surgical tool). This is very common, for example, in image-guided surgery, where the amount of measurements is limited to ensure the safety of the patient. In this case, we can also typically assume that a (good) initial reconstruction for the solution exists, coming from a previously over-sampled scan, so we can use this information to aid the subsequent reconstructions. The effectiveness of this method is demonstrated in both a synthetic scan and using real CT data, where it can be observed that the PICCS framework is very effective for the reduction of artifacts, and that the new method is faster than other common alternatives used in the same setting.

math.NA↗

arXiv2025

FedMAP: Personalised Federated Learning for Real Large-Scale Healthcare Systems

Federated learning (FL) promises to enable collaborative machine learning across healthcare sites whilst preserving data privacy. Practical deployment remains limited by statistical heterogeneity arising from differences in patient demographics, treatments, and outcomes, and infrastructure constraints. We introduce FedMAP, a personalised FL (PFL) framework that addresses heterogeneity through local Maximum a Posteriori (MAP) estimation with Input Convex Neural Network priors. These priors represent global knowledge gathered from other sites that guides the model while adapting to local data, and we provide a formal proof of convergence. Unlike many PFL methods that rely on fixed regularisation, FedMAP's prior adaptively learns patterns that capture complex inter-site relationships. We demonstrate improved performance compared to local training, FedAvg, and several PFL methods across three large-scale clinical datasets: 10-year cardiovascular risk prediction (CPRD, 387 general practitioner practices, 258,688 patients), iron deficiency detection (INTERVAL, 4 donor centres, 31,949 blood donors), and mortality prediction (eICU, 150 hospitals, 44,842 patients). FedMAP incorporates a three-tier design that enables participation across healthcare sites with varying infrastructure and technical capabilities, from full federated training to inference-only deployment. Geographical analysis reveals substantial equity improvements, with underperforming regions achieving up to 14.3% performance gains. This framework provides the first practical pathway for large-scale healthcare FL deployment, which ensures clinical sites at all scales can benefit, equity is enhanced, and privacy is retained.

cs.LG↗

arXiv2025

Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromises the computational efficiency that characterized early spatial message-passing architectures, and typically disregards the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNet model allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring. Across several benchmarks, Stable-ChebNet achieves near state-of-the-art performance.

cs.LG↗

arXiv2025

Graph Neural Regularizers for PDE Inverse Problems

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that alternates between FEM-based inversion and learned graph neural regularization. The forward problem is numerically solved using the finite element method (FEM), enabling applicability to a wide range of geometries and PDEs. By leveraging the graph structure inherent to FEM discretizations, we employ physics-inspired graph neural networks as learned regularizers, providing a robust, interpretable, and generalizable alternative to standard approaches. Numerical experiments demonstrate that our framework outperforms classical regularization techniques and achieves accurate reconstructions even in highly ill-posed scenarios.

math.NA↗

arXiv2025

Approximation theory for 1-Lipschitz ResNets

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and study their approximation capabilities. Leveraging the Restricted Stone-Weierstrass Theorem, we first show that these 1-Lipschitz ResNets are dense in the set of scalar 1-Lipschitz functions on any compact domain when width and depth are allowed to grow. We also show that these networks can exactly represent scalar piecewise affine 1-Lipschitz functions. We then prove a stronger statement: by inserting norm-constrained linear maps between the residual blocks, the same density holds when the hidden width is fixed. Because every layer obeys simple norm constraints, the resulting models can be trained with off-the-shelf optimisers. This paper provides the first universal approximation guarantees for 1-Lipschitz ResNets, laying a rigorous foundation for their practical use.

cs.LG↗

arXiv2025

PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils

Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost. We present FINO, a finite-difference-inspired neural architecture that enforces strict locality while retaining multiscale representational power. FINO replaces fixed finite-difference stencil coefficients with learnable convolutional kernels and evolves states via an explicit, learnable time-stepping scheme. A central Local Operator Block leverage a differential stencil layer, a gating mask, and a linear fuse step to construct adaptive derivative-like local features that propagate forward in time. Embedded in an encoder-decoder with a bottleneck, FINO captures fine-grained local structures while preserving interpretability. We establish (i) a composition error bound linking one-step approximation error to stable long-horizon rollouts under a Lipschitz condition, and (ii) a universal approximation theorem for discrete time-stepped PDE dynamics. (iii) Across six benchmarks and a climate modelling task, FINO achieves up to 44\% lower error and up to around 2\times speedups over state-of-the-art operator-learning baselines, demonstrating that strict locality with learnable time-stepping yields an accurate and scalable foundation for neural PDE solvers.

cs.LG↗

arXiv2025

GeoSplat: A Deep Dive into Geometry-Constrained Gaussian Splatting

A few recent works explored incorporating geometric priors to regularize the optimization of Gaussian splatting, further improving its performance. However, those early studies mainly focused on the use of low-order geometric priors (e.g., normal vector), and they might also be unreliably estimated by noise-sensitive methods, like local principal component analysis. To address their limitations, we first present GeoSplat, a general geometry-constrained optimization framework that exploits both first-order and second-order geometric quantities to improve the entire training pipeline of Gaussian splatting, including Gaussian initialization, gradient update, and densification. As an example, we initialize the scales of 3D Gaussian primitives in terms of principal curvatures, leading to a better coverage of the object surface than random initialization. Secondly, based on certain geometric structures (e.g., local manifold), we introduce efficient and noise-robust estimation methods that provide dynamic geometric priors for our framework. We conduct extensive experiments on multiple datasets for novel view synthesis, showing that our framework, GeoSplat, significantly improves the performance of Gaussian splatting and outperforms previous baselines.

cs.CV↗

arXiv2025

LamiGauss: Pitching Radiative Gaussian for Sparse-View X-ray Laminography Reconstruction

X-ray Computed Laminography (CL) is essential for non-destructive inspection of plate-like structures in applications such as microchips and composite battery materials, where traditional computed tomography (CT) struggles due to geometric constraints. However, reconstructing high-quality volumes from laminographic projections remains challenging, particularly under highly sparse-view acquisition conditions. In this paper, we propose a reconstruction algorithm, namely LamiGauss, that combines Gaussian Splatting radiative rasterization with a dedicated detector-to-world transformation model incorporating the laminographic tilt angle. LamiGauss leverages an initialization strategy that explicitly filters out common laminographic artifacts from the preliminary reconstruction, preventing redundant Gaussians from being allocated to false structures and thereby concentrating model capacity on representing the genuine object. Our approach effectively optimizes directly from sparse projections, enabling accurate and efficient reconstruction with limited data. Extensive experiments on both synthetic and real datasets demonstrate the effectiveness and superiority of the proposed method over existing techniques. LamiGauss uses only 3$\%$ of full views to achieve superior performance over the iterative method optimized on a full dataset.

cs.CV↗

arXiv2025

Potential Contrast: Properties, Equivalences, and Generalization to Multiple Classes

Potential contrast is typically used as an image quality measure and quantifies the maximal possible contrast between samples from two classes of pixels in an image after an arbitrary grayscale transformation. It has been applied in cultural heritage to evaluate multispectral images using a small number of labeled pixels. In this work, we introduce a normalized version of potential contrast that removes dependence on image format and also prove equalities that enable generalization to more than two classes and to continuous settings. Finally, we exemplify the utility of multi-class normalized potential contrast through an application to a medieval music manuscript with visible bleedthrough from the back of the page. We share our implementations, based on both original algorithms and our new equalities, including generalization to multiple classes, at https://github.com/wallacepeaslee/Multiple-Class-Normalized-Potential-Contrast.

eess.IV↗

arXiv2025

TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows

We introduce TANGO -- a dynamical systems inspired framework for graph representation learning that governs node feature evolution through a learned energy landscape and its associated descent dynamics. At the core of our approach is a learnable Lyapunov function over node embeddings, whose gradient defines an energy-reducing direction that guarantees convergence and stability. To enhance flexibility while preserving the benefits of energy-based dynamics, we incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value. This decomposition into orthogonal flows of energy gradient descent and tangential evolution yields a flexible form of graph dynamics, and enables effective signal propagation even in flat or ill-conditioned energy regions, that often appear in graph learning. Our method mitigates oversquashing and is compatible with different graph neural network backbones. Empirically, TANGO achieves strong performance across a diverse set of node and graph classification and regression benchmarks, demonstrating the effectiveness of jointly learned energy functions and tangential flows for graph neural networks.

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