Carola-Bibiane Schönlieb

Yijun Yang, Huazhu Fu, Angelica I. Aviles-Rivero et al.

Diffusion Probabilistic Models have recently shown remarkable performance in generative image modeling, attracting significant attention in the computer vision community. However, while a substantial amount of diffusion-based research has focused on generative tasks, few studies have applied diffusion models to general medical image classification. In this paper, we propose the first diffusion-based model (named DiffMIC) to address general medical image classification by eliminating unexpected noise and perturbations in medical images and robustly capturing semantic representation. To achieve this goal, we devise a dual conditional guidance strategy that conditions each diffusion step with multiple granularities to improve step-wise regional attention. Furthermore, we propose learning the mutual information in each granularity by enforcing Maximum-Mean Discrepancy regularization during the diffusion forward process. We evaluate the effectiveness of our DiffMIC on three medical classification tasks with different image modalities, including placental maturity grading on ultrasound images, skin lesion classification using dermatoscopic images, and diabetic retinopathy grading using fundus images. Our experimental results demonstrate that DiffMIC outperforms state-of-the-art methods by a significant margin, indicating the universality and effectiveness of the proposed model. Our code will be publicly available at https://github.com/scott-yjyang/DiffMIC.

Jiahao Huang, Angelica Aviles-Rivero, Carola-Bibiane Schönlieb et al.

Deep learning has shown the capability to substantially accelerate MRI reconstruction while acquiring fewer measurements. Recently, diffusion models have gained burgeoning interests as a novel group of deep learning-based generative methods. These methods seek to sample data points that belong to a target distribution from a Gaussian distribution, which has been successfully extended to MRI reconstruction. In this work, we proposed a Cold Diffusion-based MRI reconstruction method called CDiffMR. Different from conventional diffusion models, the degradation operation of our CDiffMR is based on \textit{k}-space undersampling instead of adding Gaussian noise, and the restoration network is trained to harness a de-aliaseing function. We also design starting point and data consistency conditioning strategies to guide and accelerate the reverse process. More intriguingly, the pre-trained CDiffMR model can be reused for reconstruction tasks with different undersampling rates. We demonstrated, through extensive numerical and visual experiments, that the proposed CDiffMR can achieve comparable or even superior reconstruction results than state-of-the-art models. Compared to the diffusion model-based counterpart, CDiffMR reaches readily competing results using only $1.6 \sim 3.4\%$ for inference time. The code is publicly available at https://github.com/ayanglab/CDiffMR.

Lihao Liu, Jean Prost, Lei Zhu et al.

Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliu-cambridge.github.io/scotch_and_soda/

Krishna Sri Ipsit Mantri, Xinzhi Wang, Carola-Bibiane Schönlieb et al.

In this paper, we propose a novel activation function tailored specifically for graph data in Graph Neural Networks (GNNs). Motivated by the need for graph-adaptive and flexible activation functions, we introduce DiGRAF, leveraging Continuous Piecewise-Affine Based (CPAB) transformations, which we augment with an additional GNN to learn a graph-adaptive diffeomorphic activation function in an end-to-end manner. In addition to its graph-adaptivity and flexibility, DiGRAF also possesses properties that are widely recognized as desirable for activation functions, such as differentiability, boundness within the domain, and computational efficiency. We conduct an extensive set of experiments across diverse datasets and tasks, demonstrating a consistent and superior performance of DiGRAF compared to traditional and graph-specific activation functions, highlighting its effectiveness as an activation function for GNNs. Our code is available at https://github.com/ipsitmantri/DiGRAF.

Konstantinos Papafitsoros, Carola-Bibiane Schönlieb

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.

Simon Deltadahl, Julian Gilbey, Christine Van Laer et al.

Accurate classification of haematological cells is critical for diagnosing blood disorders, but presents significant challenges for machine automation owing to the complexity of cell morphology, heterogeneities of biological, pathological, and imaging characteristics, and the imbalance of cell type frequencies. We introduce CytoDiffusion, a diffusion-based classifier that effectively models blood cell morphology, combining accurate classification with robust anomaly detection, resistance to distributional shifts, interpretability, data efficiency, and superhuman uncertainty quantification. Our approach outperforms state-of-the-art discriminative models in anomaly detection (AUC 0.990 vs. 0.918), resistance to domain shifts (85.85% vs. 74.38% balanced accuracy), and performance in low-data regimes (95.88% vs. 94.95% balanced accuracy). Notably, our model generates synthetic blood cell images that are nearly indistinguishable from real images, as demonstrated by an authenticity test in which expert haematologists achieved only 52.3% accuracy (95% CI: [50.5%, 54.2%]) in distinguishing real from generated images. Furthermore, we enhance model explainability through the generation of directly interpretable counterfactual heatmaps. Our comprehensive evaluation framework, encompassing these multiple performance dimensions, establishes a new benchmark for medical image analysis in haematology, ultimately enabling improved diagnostic accuracy in clinical settings. Our code is available at https://github.com/CambridgeCIA/CytoDiffusion.

Yiran Wei, Xi Chen, Lei Zhu et al.

The isocitrate dehydrogenase (IDH) gene mutation is an essential biomarker for the diagnosis and prognosis of glioma. It is promising to better predict glioma genotype by integrating focal tumor image and geometric features with brain network features derived from MRI. Convolutions neural networks show reasonable performance in predicting IDH mutation, which, however, cannot learn from non-Euclidean data, e.g., geometric and network data. In this study, we propose a multi-modal learning framework using three separate encoders to extract features of focal tumor image, tumor geometrics and global brain networks. To mitigate the limited availability of diffusion MRI, we develop a self-supervised approach to generate brain networks from anatomical multi-sequence MRI. Moreover, to extract tumor-related features from the brain network, we design a hierarchical attention module for the brain network encoder. Further, we design a bi-level multi-modal contrastive loss to align the multi-modal features and tackle the domain gap at the focal tumor and global brain. Finally, we propose a weighted population graph to integrate the multi-modal features for genotype prediction. Experimental results on the testing set show that the proposed model outperforms the baseline deep learning models. The ablation experiments validate the performance of different components of the framework. The visualized interpretation corresponds to clinical knowledge with further validation. In conclusion, the proposed learning framework provides a novel approach for predicting the genotype of glioma.

Tolou Shadbahr, Michael Roberts, Jan Stanczuk et al.

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data.

Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz et al.

Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other. In this work, we compare the methodologies in a systematic computational study. Indeed, we employ both methods to numerically solve various linear and nonlinear partial differential equations: Poisson in 1D, 2D, and 3D, Allen-Cahn in 1D, semilinear Schrödinger in 1D and 2D. We then compare computational costs and approximation accuracies. In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study. In some experiments, they were faster at evaluating the solved PDE.

Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Schönlieb et al.

Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion models which have similar structure to this of multi-scale normalizing flows. We experimentally find that in the same or less training time, the multi-scale diffusion model achieves better FID score than the standard uniform diffusion model. More importantly, it generates samples $4.4$ times faster in $128\times 128$ resolution. The speed-up is expected to be higher in higher resolutions where more scales are used. Moreover, we show that non-uniform diffusion leads to a novel estimator for the conditional score function which achieves on par performance with the state-of-the-art conditional denoising estimator. Our theoretical and experimental findings are accompanied by an open source library MSDiff which can facilitate further research of non-uniform diffusion models.

Subhadip Mukherjee, Andreas Hauptmann, Ozan Öktem et al.

In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for precise characterization of correctness and reliability of data-driven methods in critical use-cases, for instance in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding their stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature. In this article, we will specify relevant notions of convergence for data-driven image reconstruction, which will form the basis of a survey of learned methods with mathematically rigorous reconstruction guarantees. An example that is highlighted is the role of ICNN, offering the possibility to combine the power of deep learning with classical convex regularization theory for devising methods that are provably convergent. This survey article is aimed at both methodological researchers seeking to advance the frontiers of our understanding of data-driven image reconstruction methods as well as practitioners, by providing an accessible description of useful convergence concepts and by placing some of the existing empirical practices on a solid mathematical foundation.

Simon Graham, Quoc Dang Vu, Mostafa Jahanifar et al.

Nuclear detection, segmentation and morphometric profiling are essential in helping us further understand the relationship between histology and patient outcome. To drive innovation in this area, we setup a community-wide challenge using the largest available dataset of its kind to assess nuclear segmentation and cellular composition. Our challenge, named CoNIC, stimulated the development of reproducible algorithms for cellular recognition with real-time result inspection on public leaderboards. We conducted an extensive post-challenge analysis based on the top-performing models using 1,658 whole-slide images of colon tissue. With around 700 million detected nuclei per model, associated features were used for dysplasia grading and survival analysis, where we demonstrated that the challenge's improvement over the previous state-of-the-art led to significant boosts in downstream performance. Our findings also suggest that eosinophils and neutrophils play an important role in the tumour microevironment. We release challenge models and WSI-level results to foster the development of further methods for biomarker discovery.

Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb et al.

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).

Dongdong Chen, Mike Davies, Matthias J. Ehrhardt et al.

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to transformations such as translation, rotation or scaling. Symmetry can also be incorporated into deep neural networks in the form of equivariance, allowing for more data-efficient learning. While there has been important advances in the design of end-to-end equivariant networks for image classification in recent years, computational imaging introduces unique challenges for equivariant network solutions since we typically only observe the image through some noisy ill-conditioned forward operator that itself may not be equivariant. We review the emerging field of equivariant imaging and show how it can provide improved generalization and new imaging opportunities. Along the way we show the interplay between the acquisition physics and group actions and links to iterative reconstruction, blind compressed sensing and self-supervised learning.

Yiran Wei, Stephen J. Price, Carola-Bibiane Schönlieb et al.

Alzheimer's disease (AD) is the most common age-related dementia. Mild cognitive impairment (MCI) is the early stage of cognitive decline before AD. It is crucial to predict the MCI-to-AD conversion for precise management, which remains challenging due to the diversity of patients. Previous evidence shows that the brain network generated from diffusion MRI promises to classify dementia using deep learning. However, the limited availability of diffusion MRI challenges the model training. In this study, we develop a self-supervised contrastive learning approach to generate structural brain networks from routine anatomical MRI under the guidance of diffusion MRI. The generated brain networks are applied to train a learning framework for predicting the MCI-to-AD conversion. Instead of directly modelling the AD brain networks, we train a graph encoder and a variational autoencoder to model the healthy ageing trajectories from brain networks of healthy controls. To predict the MCI-to-AD conversion, we further design a recurrent neural networks based approach to model the longitudinal deviation of patients' brain networks from the healthy ageing trajectory. Numerical results show that the proposed methods outperform the benchmarks in the prediction task. We also visualize the model interpretation to explain the prediction and identify abnormal changes of white matter tracts.

Hong Ye Tan, Subhadip Mukherjee, Junqi Tang et al.

Plug-and-Play (PnP) methods are a class of efficient iterative methods that aim to combine data fidelity terms and deep denoisers using classical optimization algorithms, such as ISTA or ADMM, with applications in inverse problems and imaging. Provable PnP methods are a subclass of PnP methods with convergence guarantees, such as fixed point convergence or convergence to critical points of some energy function. Many existing provable PnP methods impose heavy restrictions on the denoiser or fidelity function, such as non-expansiveness or strict convexity, respectively. In this work, we propose a novel algorithmic approach incorporating quasi-Newton steps into a provable PnP framework based on proximal denoisers, resulting in greatly accelerated convergence while retaining light assumptions on the denoiser. By characterizing the denoiser as the proximal operator of a weakly convex function, we show that the fixed points of the proposed quasi-Newton PnP algorithm are critical points of a weakly convex function. Numerical experiments on image deblurring and super-resolution demonstrate 2--8x faster convergence as compared to other provable PnP methods with similar reconstruction quality.

Lipei Zhang, Yiran Wei, Ying Fu et al.

Whole slide images (WSI) provide valuable phenotypic information for histological assessment and malignancy grading of tumors. The WSI-based grading promises to provide rapid diagnostic support and facilitate digital health. Currently, the most commonly used WSIs are derived from formalin-fixed paraffin-embedded (FFPE) and Frozen section. The majority of automatic tumor grading models are developed based on FFPE sections, which could be affected by the artifacts introduced by tissue processing. The frozen section exists problems such as low quality that might influence training within single modality as well. To overcome this problem in a single modal training and achieve better multi-modal and discriminative representation disentanglement in brain tumor, we propose a mutual contrastive low-rank learning (MCL) scheme to integrate FFPE and frozen sections for glioma grading. We first design a mutual learning scheme to jointly optimize the model training based on FFPE and frozen sections. In this proposed scheme, we design a normalized modality contrastive loss (NMC-loss), which could promote to disentangle multi-modality complementary representation of FFPE and frozen sections from the same patient. To reduce intra-class variance, and increase inter-class margin at intra- and inter-patient levels, we conduct a low-rank (LR) loss. Our experiments show that the proposed scheme achieves better performance than the model trained based on each single modality or mixed modalities and even improves the feature extraction in classical attention-based multiple instances learning methods (MIL). The combination of NMC-loss and low-rank loss outperforms other typical contrastive loss functions.

Angelica I. Aviles-Rivero, Christina Runkel, Nicolas Papadakis et al.

The automatic early diagnosis of prodromal stages of Alzheimer's disease is of great relevance for patient treatment to improve quality of life. We address this problem as a multi-modal classification task. Multi-modal data provides richer and complementary information. However, existing techniques only consider either lower order relations between the data and single/multi-modal imaging data. In this work, we introduce a novel semi-supervised hypergraph learning framework for Alzheimer's disease diagnosis. Our framework allows for higher-order relations among multi-modal imaging and non-imaging data whilst requiring a tiny labelled set. Firstly, we introduce a dual embedding strategy for constructing a robust hypergraph that preserves the data semantics. We achieve this by enforcing perturbation invariance at the image and graph levels using a contrastive based mechanism. Secondly, we present a dynamically adjusted hypergraph diffusion model, via a semi-explicit flow, to improve the predictive uncertainty. We demonstrate, through our experiments, that our framework is able to outperform current techniques for Alzheimer's disease diagnosis.

Simone Saitta, Marcello Carioni, Subhadip Mukherjee et al.

4D flow MRI is a non-invasive imaging method that can measure blood flow velocities over time. However, the velocity fields detected by this technique have limitations due to low resolution and measurement noise. Coordinate-based neural networks have been researched to improve accuracy, with SIRENs being suitable for super-resolution tasks. Our study investigates SIRENs for time-varying 3-directional velocity fields measured in the aorta by 4D flow MRI, achieving denoising and super-resolution. We trained our method on voxel coordinates and benchmarked our approach using synthetic measurements and a real 4D flow MRI scan. Our optimized SIREN architecture outperformed state-of-the-art techniques, producing denoised and super-resolved velocity fields from clinical data. Our approach is quick to execute and straightforward to implement for novel cases, achieving 4D super-resolution.

Fan Zhang, Daniel Kreuter, Yichen Chen et al.

For healthcare datasets, it is often not possible to combine data samples from multiple sites due to ethical, privacy or logistical concerns. Federated learning allows for the utilisation of powerful machine learning algorithms without requiring the pooling of data. Healthcare data has many simultaneous challenges which require new methodologies to address, such as highly-siloed data, class imbalance, missing data, distribution shifts and non-standardised variables. Federated learning adds significant methodological complexity to conventional centralised machine learning, requiring distributed optimisation, communication between nodes, aggregation of models and redistribution of models. In this systematic review, we consider all papers on Scopus that were published between January 2015 and February 2023 and which describe new federated learning methodologies for addressing challenges with healthcare data. We performed a detailed review of the 89 papers which fulfilled these criteria. Significant systemic issues were identified throughout the literature which compromise the methodologies in many of the papers reviewed. We give detailed recommendations to help improve the quality of the methodology development for federated learning in healthcare.

Marie Foged Schmidt, Martin Benning, Carola-Bibiane Schönlieb

We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation functionals, can decompose data represented by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range of the forward operator). We prove that the inverse scale space flow is guaranteed to return a singular vector if the data satisfies a novel dual singular vector condition. We conclude the paper with numerical results that validate the theoretical results and that demonstrate the importance of the additional conditions required to guarantee the decomposition result.

Andreas Hauptmann, Subhadip Mukherjee, Carola-Bibiane Schönlieb et al.

Plug-and-play (PnP) denoising is a popular iterative framework for solving imaging inverse problems using off-the-shelf image denoisers. Their empirical success has motivated a line of research that seeks to understand the convergence of PnP iterates under various assumptions on the denoiser. While a significant amount of research has gone into establishing the convergence of the PnP iteration for different regularity conditions on the denoisers, not much is known about the asymptotic properties of the converged solution as the noise level in the measurement tends to zero, i.e., whether PnP methods are provably convergent regularization schemes under reasonable assumptions on the denoiser. This paper serves two purposes: first, we provide an overview of the classical regularization theory in inverse problems and survey a few notable recent data-driven methods that are provably convergent regularization schemes. We then continue to discuss PnP algorithms and their established convergence guarantees. Subsequently, we consider PnP algorithms with linear denoisers and propose a novel spectral filtering technique to control the strength of regularization arising from the denoiser. Further, by relating the implicit regularization of the denoiser to an explicit regularization functional, we rigorously show that PnP with linear denoisers leads to a convergent regularization scheme. More specifically, we prove that in the limit as the noise vanishes, the PnP reconstruction converges to the minimizer of a regularization potential subject to the solution satisfying the noiseless operator equation. The theoretical analysis is corroborated by numerical experiments for the classical inverse problem of tomographic image reconstruction.

Simone Parisotto, Ninetta Leone, Carola-Bibiane Schönlieb et al.

In this paper we propose an artificial intelligence imaging solution to support archaeologists in the classification task of Roman commonware potsherds. Usually, each potsherd is represented by its sectional profile as a two dimensional black-white image and printed in archaeological books related to specific archaeological excavations. The partiality and handcrafted variance of the fragments make their matching a challenging problem: we propose to pair similar profiles via the unsupervised hierarchical clustering of non-linear features learned in the latent space of a deep convolutional Variational Autoencoder (VAE) network. Our contribution also include the creation of a ROman COmmonware POTtery (ROCOPOT) database, with more than 4000 potsherds profiles extracted from 25 Roman pottery corpora, and a MATLAB GUI software for the easy inspection of shape similarities. Results are commented both from a mathematical and archaeological perspective so as to unlock new research directions in both communities.

Martin Burger, Bertram Düring, Lisa Maria Kreusser et al.

We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called Kücken-Champod model describing the formation of fingerprint patterns. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a long-range attraction structure. In contrast to isotropic interaction models the anisotropic forces in our class of models cannot be derived from a potential. The underlying tensor field introduces an anisotropy leading to complex patterns which do not occur in isotropic models. This anisotropy is characterized by one parameter in the model. We study the variation of this parameter, describing the transition between the isotropic and the anisotropic model, analytically and numerically. We analyze the equilibria of the corresponding mean-field partial differential equation and investigate pattern formation numerically in two dimensions by studying the dependence of the parameters in the model on the resulting patterns.

Yijun Yang, Shujun Wang, Lihao Liu et al.

Breast cancer is a major cause of cancer death among women, emphasising the importance of early detection for improved treatment outcomes and quality of life. Mammography, the primary diagnostic imaging test, poses challenges due to the high variability and patterns in mammograms. Double reading of mammograms is recommended in many screening programs to improve diagnostic accuracy but increases radiologists' workload. Researchers explore Machine Learning models to support expert decision-making. Stand-alone models have shown comparable or superior performance to radiologists, but some studies note decreased sensitivity with multiple datasets, indicating the need for high generalisation and robustness models. This work devises MammoDG, a novel deep-learning framework for generalisable and reliable analysis of cross-domain multi-center mammography data. MammoDG leverages multi-view mammograms and a novel contrastive mechanism to enhance generalisation capabilities. Extensive validation demonstrates MammoDG's superiority, highlighting the critical importance of domain generalisation for trustworthy mammography analysis in imaging protocol variations.

Jan Oscar Cross-Zamirski, Praveen Anand, Guy Williams et al.

Image-to-image reconstruction problems with free or inexpensive metadata in the form of class labels appear often in biological and medical image domains. Existing text-guided or style-transfer image-to-image approaches do not translate to datasets where additional information is provided as discrete classes. We introduce and implement a model which combines image-to-image and class-guided denoising diffusion probabilistic models. We train our model on a real-world dataset of microscopy images used for drug discovery, with and without incorporating metadata labels. By exploring the properties of image-to-image diffusion with relevant labels, we show that class-guided image-to-image diffusion can improve the meaningful content of the reconstructed images and outperform the unguided model in useful downstream tasks.

Chun-Wun Cheng, Christina Runkel, Lihao Liu et al.

Image segmentation is a fundamental task in image analysis and clinical practice. The current state-of-the-art techniques are based on U-shape type encoder-decoder networks with skip connections, called U-Net. Despite the powerful performance reported by existing U-Net type networks, they suffer from several major limitations. Issues include the hard coding of the receptive field size, compromising the performance and computational cost, as well as the fact that they do not account for inherent noise in the data. They have problems associated with discrete layers, and do not offer any theoretical underpinning. In this work we introduce continuous U-Net, a novel family of networks for image segmentation. Firstly, continuous U-Net is a continuous deep neural network that introduces new dynamic blocks modelled by second order ordinary differential equations. Secondly, we provide theoretical guarantees for our network demonstrating faster convergence, higher robustness and less sensitivity to noise. Thirdly, we derive qualitative measures to tailor-made segmentation tasks. We demonstrate, through extensive numerical and visual results, that our model outperforms existing U-Net blocks for several medical image segmentation benchmarking datasets.

Elena Celledoni, Davide Murari, Brynjulf Owren et al.

Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is some underlying geometric structure inherent to the data or to the function to approximate, it is often desirable to take this into account in the design of the neural network. In this work, we start with a non-autonomous ODE and build neural networks using a suitable, structure-preserving, numerical time-discretisation. The structure of the neural network is then inferred from the properties of the ODE vector field. Besides injecting more structure into the network architectures, this modelling procedure allows a better theoretical understanding of their behaviour. We present two universal approximation results and demonstrate how to impose some particular properties on the neural networks. A particular focus is on 1-Lipschitz architectures including layers that are not 1-Lipschitz. These networks are expressive and robust against adversarial attacks, as shown for the CIFAR-10 and CIFAR-100 datasets.

Bertram Düring, Carsten Gottschlich, Stephan Huckemann et al.

Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy. In this anisotropic interaction model the interaction forces not only depend on the distance vector between the cells and the model parameters, but additionally on an underlying tensor field, representing a stress field. This dependence on the tensor field leads to complex, anisotropic patterns. We study the resulting stationary patterns both analytically and numerically. In particular, we show that fingerprint patterns can be modeled as stationary solutions by choosing the underlying tensor field appropriately.

Krishna Sri Ipsit Mantri, Carola-Bibiane Schönlieb, Zorah Lähner et al.

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it is competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs. Our code is published at https://github.com/ipsitmantri/GLOT.

Yiqiu Dong, Carola-Bibiane Schönlieb

In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for spatially varying parameter has been proposed. Their parameter selection rule, however, only applies if measured imaging data are defined in image domain, e.g. for image denoising and image deblurring problems. By introducing an auxiliary variable in their model we show here that this idea can indeed by extended to general inverse imaging problems such as tomographic reconstruction where measurements are not in image domain. We demonstrate the validity of the proposed approach and its effectiveness for computed tomography reconstruction, delivering reconstruction results that are significantly improved compared the state-of-the-art.

Massimo Fornasier, Andreas Langer, Carola-Bibiane Schönlieb

We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee et al.

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularization arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

Sören Dittmer, Michael Roberts, Julian Gilbey et al.

In this perspective, we argue that despite the democratization of powerful tools for data science and machine learning over the last decade, developing the code for a trustworthy and effective data science system (DSS) is getting harder. Perverse incentives and a lack of widespread software engineering (SE) skills are among many root causes we identify that naturally give rise to the current systemic crisis in reproducibility of DSSs. We analyze why SE and building large complex systems is, in general, hard. Based on these insights, we identify how SE addresses those difficulties and how we can apply and generalize SE methods to construct DSSs that are fit for purpose. We advocate two key development philosophies, namely that one should incrementally grow -- not biphasically plan and build -- DSSs, and one should always employ two types of feedback loops during development: one which tests the code's correctness and another that evaluates the code's efficacy.

Zhenda Shen, Yanqi Cheng, Raymond H. Chan et al.

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.

Chaoyu Liu, Zhonghua Qiao, Chao Li et al.

Traditional image processing methods employing partial differential equations (PDEs) offer a multitude of meaningful regularizers, along with valuable theoretical foundations for a wide range of image-related tasks. This makes their integration into neural networks a promising avenue. In this paper, we introduce a novel regularization approach inspired by the reverse process of PDE-based evolution models. Specifically, we propose inverse evolution layers (IELs), which serve as bad property amplifiers to penalize neural networks of which outputs have undesired characteristics. Using IELs, one can achieve specific regularization objectives and endow neural networks' outputs with corresponding properties of the PDE models. Our experiments, focusing on semantic segmentation tasks using heat-diffusion IELs, demonstrate their effectiveness in mitigating noisy label effects. Additionally, we develop curve-motion IELs to enforce convex shape regularization in neural network-based segmentation models for preventing the generation of concave outputs. Theoretical analysis confirms the efficacy of IELs as an effective regularization mechanism, particularly in handling training with label issues.

Jan Oscar Cross-Zamirski, Guy Williams, Elizabeth Mouchet et al.

We propose WS-DINO as a novel framework to use weak label information in learning phenotypic representations from high-content fluorescent images of cells. Our model is based on a knowledge distillation approach with a vision transformer backbone (DINO), and we use this as a benchmark model for our study. Using WS-DINO, we fine-tuned with weak label information available in high-content microscopy screens (treatment and compound) and achieve state-of-the-art performance in not-same-compound mechanism of action prediction on the BBBC021 dataset (98%), and not-same-compound-and-batch performance (96%) using the compound as the weak label. Our method bypasses single cell cropping as a pre-processing step, and using self-attention maps we show that the model learns structurally meaningful phenotypic profiles.

Yanqi Cheng, Lipei Zhang, Zhenda Shen et al.

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.

Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt et al.

Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the weights are appropriately constrained. This is to be contrasted with the ordinary ResNet architecture which, even if the spectral norms of the weights are constrained, has a Lipschitz constant that, in the worst case, grows exponentially with the depth of the network. Further analysis of the proposed architecture shows that the spectral norms of the weights can be further constrained to ensure that the network is an averaged operator, making it a natural candidate for a learned denoiser in Plug-and-Play algorithms. Using a novel adaptive way of enforcing the spectral norm constraints, we show that, even with these constraints, it is possible to train performant networks. The proposed architecture is applied to the problem of adversarially robust image classification, to image denoising, and finally to the inverse problem of deblurring.

James Rowbottom, Georg Maierhofer, Teo Deveney et al.

We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice of mesh points. Mesh relocation (r-adaptivity) seeks to optimise the mesh geometry to obtain the best solution accuracy at given computational budget. Classical r-adaptivity relies on the solution of a separate nonlinear "meshing" PDE to determine mesh point locations. This incurs significant cost at remeshing, and relies on estimates that relate interpolation- and FEM-error. Recent machine learning approaches have focused on the construction of fast surrogates for such classical methods. Instead, our new approach trains a graph neural network (GNN) to determine mesh point locations by directly minimising the FE solution error from the PDE system Firedrake to achieve higher solution accuracy. Our GNN architecture closely aligns the mesh solution space to that of classical meshing methodologies, thus replacing classical estimates for optimality with a learnable strategy. This allows for rapid and robust training and results in an extremely efficient and effective GNN approach to online r-adaptivity. Our method outperforms both classical, and prior ML, approaches to r-adaptive meshing. In particular, it achieves lower FE solution error, whilst retaining the significant speed-up over classical methods observed in prior ML work.

Tamara G. Grossmann, Sören Dittmer, Yury Korolev et al.

The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis. Solving the TV flow is challenging; one reason is the the non-uniqueness of the subgradients. The standard numerical approach for TV flow requires solving multiple non-smooth optimisation problems. Even with state-of-the-art convex optimisation techniques, this is often prohibitively expensive and strongly motivates the use of alternative, faster approaches. Inspired by and extending the framework of physics-informed neural networks (PINNs), we propose the TVflowNET, an unsupervised neural network approach, to approximate the solution of the TV flow given an initial image and a time instance. The TVflowNET requires no ground truth data but rather makes use of the PDE for optimisation of the network parameters. We circumvent the challenges related to the non-uniqueness of the subgradients by additionally learning the related diffusivity term. Our approach significantly speeds up the computation time and we show that the TVflowNET approximates the TV flow solution with high fidelity for different image sizes and image types. Additionally, we give a full comparison of different network architecture designs as well as training regimes to underscore the effectiveness of our approach.

Moshe Eliasof, Krishna Sri Ipsit Mantri, Beatrice Bevilacqua et al.

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.

Moshe Eliasof, Md Shahriar Rahim Siddiqui, Carola-Bibiane Schönlieb et al.

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph directly; instead, noisy and indirect measurements of these properties are available. These scenarios are coined as Graph Inverse Problems (GRIP). In this work, we introduce a framework leveraging GNNs to solve GRIPs. The framework is based on a combination of likelihood and prior terms, which are used to find a solution that fits the data while adhering to learned prior information. Specifically, we propose to combine recent deep learning techniques that were developed for inverse problems, together with GNN architectures, to formulate and solve GRIP. We study our approach on a number of representative problems that demonstrate the effectiveness of the framework.

Jakob Träuble, Lucy Hiscox, Curtis Johnson et al.

In the field of neuroimaging, accurate brain age prediction is pivotal for uncovering the complexities of brain aging and pinpointing early indicators of neurodegenerative conditions. Recent advancements in self-supervised learning, particularly in contrastive learning, have demonstrated greater robustness when dealing with complex datasets. However, current approaches often fall short in generalizing across non-uniformly distributed data, prevalent in medical imaging scenarios. To bridge this gap, we introduce a novel contrastive loss that adapts dynamically during the training process, focusing on the localized neighborhoods of samples. Moreover, we expand beyond traditional structural features by incorporating brain stiffness - a mechanical property previously underexplored yet promising due to its sensitivity to age-related changes. This work presents the first application of self-supervised learning to brain mechanical properties, using compiled stiffness maps from various clinical studies to predict brain age. Our approach, featuring dynamic localized loss, consistently outperforms existing state-of-the-art methods, demonstrating superior performance and paving the way for new directions in brain aging research.

Yi Zhang, Chun-Wun Cheng, Ke Yu et al.

In this paper, we consider the problem of prototype-based vision-language reasoning problem. We observe that existing methods encounter three major challenges: 1) escalating resource demands and prolonging training times, 2) contending with excessive learnable parameters, and 3) fine-tuning based only on a single modality. These challenges will hinder their capability to adapt Vision-Language Models (VLMs) to downstream tasks. Motivated by this critical observation, we propose a novel method called NODE-Adapter, which utilizes Neural Ordinary Differential Equations for better vision-language reasoning. To fully leverage both visual and textual modalities and estimate class prototypes more effectively and accurately, we divide our method into two stages: cross-modal prototype construction and cross-modal prototype optimization using neural ordinary differential equations. Specifically, we exploit VLM to encode hand-crafted prompts into textual features and few-shot support images into visual features. Then, we estimate the textual prototype and visual prototype by averaging the textual features and visual features, respectively, and adaptively combine the textual prototype and visual prototype to construct the cross-modal prototype. To alleviate the prototype bias, we then model the prototype optimization process as an initial value problem with Neural ODEs to estimate the continuous gradient flow. Our extensive experimental results, which cover few-shot classification, domain generalization, and visual reasoning on human-object interaction, demonstrate that the proposed method significantly outperforms existing state-of-the-art approaches.

Jeremy Budd, Yves van Gennip, Jonas Latz et al.

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation methods, such as the Chan--Vese algorithm. In this paper, we present a method for joint reconstruction-segmentation using graph-based segmentation methods, which have been seeing increasing recent interest. Complications arise due to the large size of the matrices involved, and we show how these complications can be managed. We then analyse the convergence properties of our scheme. Finally, we apply this scheme to distorted versions of ``two cows'' images familiar from previous graph-based segmentation literature, first to a highly noised version and second to a blurred version, achieving highly accurate segmentations in both cases. We compare these results to those obtained by sequential reconstruction-segmentation approaches, finding that our method competes with, or even outperforms, those approaches in terms of reconstruction and segmentation accuracy.

Jan Stanczuk, Georgios Batzolis, Teo Deveney et al.

In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted version of the target distribution for varying levels of corruption. We prove that, if the data concentrates around a manifold embedded in the high-dimensional ambient space, then as the level of corruption decreases, the score function points towards the manifold, as this direction becomes the direction of maximal likelihood increase. Therefore, for small levels of corruption, the diffusion model provides us with access to an approximation of the normal bundle of the data manifold. This allows us to estimate the dimension of the tangent space, thus, the intrinsic dimension of the data manifold. To the best of our knowledge, our method is the first estimator of the data manifold dimension based on diffusion models and it outperforms well established statistical estimators in controlled experiments on both Euclidean and image data.

Maximilian B. Kiss, Ander Biguri, Carola-Bibiane Schönlieb et al.

Like in many other research fields, recent developments in computational imaging have focused on developing machine learning (ML) approaches to tackle its main challenges. To improve the performance of computational imaging algorithms, machine learning methods are used for image processing tasks such as noise reduction. Generally, these ML methods heavily rely on the availability of high-quality data on which they are trained. This work explores the application of ML methods, specifically convolutional neural networks (CNNs), in the context of noise reduction for computed tomography (CT) imaging. We utilize a large 2D computed tomography dataset for machine learning to carry out for the first time a comprehensive study on the differences between the observed performances of algorithms trained on simulated noisy data and on real-world experimental noisy data. The study compares the performance of two common CNN architectures, U-Net and MSD-Net, that are trained and evaluated on both simulated and experimental noisy data. The results show that while sinogram denoising performed better with simulated noisy data if evaluated in the sinogram domain, the performance did not carry over to the reconstruction domain where training on experimental noisy data shows a higher performance in denoising experimental noisy data. Training the algorithms in an end-to-end fashion from sinogram to reconstruction significantly improved model performance, emphasizing the importance of matching raw measurement data to high-quality CT reconstructions. The study furthermore suggests the need for more sophisticated noise simulation approaches to bridge the gap between simulated and real-world data in CT image denoising applications and gives insights into the challenges and opportunities in leveraging simulated data for machine learning in computational imaging.

Moshe Eliasof, Davide Murari, Ferdia Sherry et al.

Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This paper introduces an innovative approach to fortify GNNs against adversarial perturbations through the lens of coupled dynamical systems. Our method introduces graph neural layers based on differential equations with contractive properties, which, as we show, improve the robustness of GNNs. A distinctive feature of the proposed approach is the simultaneous learned evolution of both the node features and the adjacency matrix, yielding an intrinsic enhancement of model robustness to perturbations in the input features and the connectivity of the graph. We mathematically derive the underpinnings of our novel architecture and provide theoretical insights to reason about its expected behavior. We demonstrate the efficacy of our method through numerous real-world benchmarks, reading on par or improved performance compared to existing methods.

Lihao Liu, Zhening Huang, Pietro Liò et al.

Medical image registration and segmentation are critical tasks for several clinical procedures. Manual realisation of those tasks is time-consuming and the quality is highly dependent on the level of expertise of the physician. To mitigate that laborious task, automatic tools have been developed where the majority of solutions are supervised techniques. However, in medical domain, the strong assumption of having a well-representative ground truth is far from being realistic. To overcome this challenge, unsupervised techniques have been investigated. However, they are still limited in performance and they fail to produce plausible results. In this work, we propose a novel unified unsupervised framework for image registration and segmentation that we called PC-SwinMorph. The core of our framework is two patch-based strategies, where we demonstrate that patch representation is key for performance gain. We first introduce a patch-based contrastive strategy that enforces locality conditions and richer feature representation. Secondly, we utilise a 3D window/shifted-window multi-head self-attention module as a patch stitching strategy to eliminate artifacts from the patch splitting. We demonstrate, through a set of numerical and visual results, that our technique outperforms current state-of-the-art unsupervised techniques.