arXiv subjects

Xiaohao Cai

Publications and source records attributed to Xiaohao Cai.

At least 55 records · Page 3Linked to original sources

arXiv2024

Discrepancy-based Diffusion Models for Lesion Detection in Brain MRI

Diffusion probabilistic models (DPMs) have exhibited significant effectiveness in computer vision tasks, particularly in image generation. However, their notable performance heavily relies on labelled datasets, which limits their application in medical images due to the associated high-cost annotations. Current DPM-related methods for lesion detection in medical imaging, which can be categorized into two distinct approaches, primarily rely on image-level annotations. The first approach, based on anomaly detection, involves learning reference healthy brain representations and identifying anomalies based on the difference in inference results. In contrast, the second approach, resembling a segmentation task, employs only the original brain multi-modalities as prior information for generating pixel-level annotations. In this paper, our proposed model - discrepancy distribution medical diffusion (DDMD) - for lesion detection in brain MRI introduces a novel framework by incorporating distinctive discrepancy features, deviating from the conventional direct reliance on image-level annotations or the original brain modalities. In our method, the inconsistency in image-level annotations is translated into distribution discrepancies among heterogeneous samples while preserving information within homogeneous samples. This property retains pixel-wise uncertainty and facilitates an implicit ensemble of segmentation, ultimately enhancing the overall detection performance. Thorough experiments conducted on the BRATS2020 benchmark dataset containing multimodal MRI scans for brain tumour detection demonstrate the great performance of our approach in comparison to state-of-the-art methods.

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arXiv2024

Non-negative Subspace Feature Representation for Few-shot Learning in Medical Imaging

Unlike typical visual scene recognition domains, in which massive datasets are accessible to deep neural networks, medical image interpretations are often obstructed by the paucity of data. In this paper, we investigate the effectiveness of data-based few-shot learning in medical imaging by exploring different data attribute representations in a low-dimensional space. We introduce different types of non-negative matrix factorization (NMF) in few-shot learning, addressing the data scarcity issue in medical image classification. Extensive empirical studies are conducted in terms of validating the effectiveness of NMF, especially its supervised variants (e.g., discriminative NMF, and supervised and constrained NMF with sparseness), and the comparison with principal component analysis (PCA), i.e., the collaborative representation-based dimensionality reduction technique derived from eigenvectors. With 14 different datasets covering 11 distinct illness categories, thorough experimental results and comparison with related techniques demonstrate that NMF is a competitive alternative to PCA for few-shot learning in medical imaging, and the supervised NMF algorithms are more discriminative in the subspace with greater effectiveness. Furthermore, we show that the part-based representation of NMF, especially its supervised variants, is dramatically impactful in detecting lesion areas in medical imaging with limited samples.

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arXiv2023

Thinking Outside the Box: Orthogonal Approach to Equalizing Protected Attributes

There is growing concern that the potential of black box AI may exacerbate health-related disparities and biases such as gender and ethnicity in clinical decision-making. Biased decisions can arise from data availability and collection processes, as well as from the underlying confounding effects of the protected attributes themselves. This work proposes a machine learning-based orthogonal approach aiming to analyze and suppress the effect of the confounder through discriminant dimensionality reduction and orthogonalization of the protected attributes against the primary attribute information. By doing so, the impact of the protected attributes on disease diagnosis can be realized, undesirable feature correlations can be mitigated, and the model prediction performance can be enhanced.

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arXiv2023

IIHT: Medical Report Generation with Image-to-Indicator Hierarchical Transformer

Automated medical report generation has become increasingly important in medical analysis. It can produce computer-aided diagnosis descriptions and thus significantly alleviate the doctors' work. Inspired by the huge success of neural machine translation and image captioning, various deep learning methods have been proposed for medical report generation. However, due to the inherent properties of medical data, including data imbalance and the length and correlation between report sequences, the generated reports by existing methods may exhibit linguistic fluency but lack adequate clinical accuracy. In this work, we propose an image-to-indicator hierarchical transformer (IIHT) framework for medical report generation. It consists of three modules, i.e., a classifier module, an indicator expansion module and a generator module. The classifier module first extracts image features from the input medical images and produces disease-related indicators with their corresponding states. The disease-related indicators are subsequently utilised as input for the indicator expansion module, incorporating the "data-text-data" strategy. The transformer-based generator then leverages these extracted features along with image features as auxiliary information to generate final reports. Furthermore, the proposed IIHT method is feasible for radiologists to modify disease indicators in real-world scenarios and integrate the operations into the indicator expansion module for fluent and accurate medical report generation. Extensive experiments and comparisons with state-of-the-art methods under various evaluation metrics demonstrate the great performance of the proposed method.

cs.CV↗

arXiv2023

A Randomized Block Krylov Method for Tensor Train Approximation

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some randomized algorithms have been proposed; however, they are not suitable for noisy data. The randomized block Krylov method is capable of dealing with heavy-tailed noisy data in the low-rank approximation of matrices. In this paper, we present a randomized algorithm for low-rank tensor train approximation of large-scale tensors based on randomized block Krylov subspace iteration and provide theoretical guarantees. Numerical experiments on synthetic and real-world tensor data demonstrate the effectiveness of the proposed algorithm.

math.NA↗

arXiv2023

Proximal nested sampling with data-driven priors for physical scientists

Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the imaging sciences. The purpose of this article is two-fold. First, we review proximal nested sampling in a pedagogical manner in an attempt to elucidate the framework for physical scientists. Second, we show how proximal nested sampling can be extended in an empirical Bayes setting to support data-driven priors, such as deep neural networks learned from training data.

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arXiv2023

A Bilevel Formalism for the Peer-Reviewing Problem

Due to the large number of submissions that more and more conferences experience, finding an automatized way to well distribute the submitted papers among reviewers has become necessary. We model the peer-reviewing matching problem as a {\it bilevel programming (BP)} formulation. Our model consists of a lower-level problem describing the reviewers' perspective and an upper-level problem describing the editors'. Every reviewer is interested in minimizing their overall effort, while the editors are interested in finding an allocation that maximizes the quality of the reviews and follows the reviewers' preferences the most. To the best of our knowledge, the proposed model is the first one that formulates the peer-reviewing matching problem by considering two objective functions, one to describe the reviewers' viewpoint and the other to describe the editors' viewpoint. We demonstrate that both the upper-level and lower-level problems are feasible and that our BP model admits a solution under mild assumptions. After studying the properties of the solutions, we propose a heuristic to solve our model and compare its performance with the relevant state-of-the-art methods. Extensive numerical results show that our approach can find fairer solutions with competitive quality and less effort from the reviewers.

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arXiv2023

Few-shot Learning for Inference in Medical Imaging with Subspace Feature Representations

Unlike the field of visual scene recognition where tremendous advances have taken place due to the availability of very large datasets to train deep neural networks, inference from medical images is often hampered by the fact that only small amounts of data may be available. When working with very small dataset problems, of the order of a few hundred items of data, the power of deep learning may still be exploited by using a model pre-trained on natural images as a feature extractor and carrying out classic pattern recognition techniques in this feature space, the so-called few-shot learning problem. In regimes where the dimension of this feature space is comparable to or even larger than the number of items of data, dimensionality reduction is a necessity and is often achieved by principal component analysis, i.e., singular value decomposition (SVD). In this paper, noting the inappropriateness of using SVD for this setting, we usher in and explore two alternatives based on discriminant analysis and non-negative matrix factorization (NMF). Using 14 different datasets spanning $11$ distinct disease types, we demonstrate that discriminant subspaces at low dimensions achieve significant improvements over SVD-based subspaces and the original feature space. We also show that NMF at modest dimensions is a competitive alternative to SVD in this setting.

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arXiv2023

GO-LDA: Generalised Optimal Linear Discriminant Analysis

Linear discriminant analysis (LDA) has been a useful tool in pattern recognition and data analysis research and practice. While linearity of class boundaries cannot always be expected, nonlinear projections through pre-trained deep neural networks have served to map complex data onto feature spaces in which linear discrimination has served well. The solution to binary LDA is obtained by eigenvalue analysis of within-class and between-class scatter matrices. It is well known that the multiclass LDA is solved by an extension to the binary LDA, a generalised eigenvalue problem, from which the largest subspace that can be extracted is of dimension one lower than the number of classes in the given problem. In this paper, we show that, apart from the first of the discriminant directions, the generalised eigenanalysis solution to multiclass LDA does neither yield orthogonal discriminant directions nor maximise discrimination of projected data along them. Surprisingly, to the best of our knowledge, this has not been noted in decades of literature on LDA. To overcome this drawback, we present a derivation with a strict theoretical support for sequentially obtaining discriminant directions that are orthogonal to previously computed ones and maximise in each step the Fisher criterion. We show distributions of projections along these axes and demonstrate that discrimination of data projected onto these discriminant directions has optimal separation, which is much higher than those from the generalised eigenvectors of the multiclass LDA. Using a wide range of benchmark tasks, we present a comprehensive empirical demonstration that on a number of pattern recognition and classification problems, the optimal discriminant subspaces obtained by the proposed method, referred to as GO-LDA (Generalised Optimal LDA), can offer superior accuracy.

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arXiv2023

Practical Sketching Algorithms for Low-Rank Tucker Approximation of Large Tensors

Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data compression and dimensionality reduction technique applied to the low-rank approximation of large matrices. This paper presents two practical randomized algorithms for low-rank Tucker approximation of large tensors based on sketching and power scheme, with a rigorous error-bound analysis. Numerical experiments on synthetic and real-world tensor data demonstrate the competitive performance of the proposed algorithms.

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arXiv2022

Proximal nested sampling for high-dimensional Bayesian model selection

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.

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arXiv2021

Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on simulations, before applying the developed formalism to two observational datasets of the Abel-520 cluster. Initial reconstructions of the Abel-520 catalogs reported the detection of an anomalous 'dark core' -- an over dense region with no optical counterpart -- which was taken to be evidence for self-interacting dark-matter. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of such dark cores at 99% confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

astro-ph.CO↗

arXiv2021

Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic - the peak count as a function of signal to noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well defined confidence levels.

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arXiv2021

Sparse Bayesian mass-mapping with uncertainties: local credible intervals

Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA - a state of the art proximal Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\geq 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid.

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arXiv2020

3D Orientation Field Transform

The two-dimensional (2D) orientation field transform has been proved to be effective at enhancing 2D contours and curves in images by means of top-down processing. It, however, has no counterpart in three-dimensional (3D) images due to the extremely complicated orientation in 3D compared to 2D. Practically and theoretically, the demand and interest in 3D can only be increasing. In this work, we modularise the concept and generalise it to 3D curves. Different modular combinations are found to enhance curves to different extents and with different sensitivity to the packing of the 3D curves. In principle, the proposed 3D orientation field transform can naturally tackle any dimensions. As a special case, it is also ideal for 2D images, owning simpler methodology compared to the previous 2D orientation field transform. The proposed method is demonstrated with several transmission electron microscopy tomograms ranging from 2D curve enhancement to, the more important and interesting, 3D ones.

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arXiv2020

Offline and online reconstruction for radio interferometric imaging

Radio astronomy is transitioning to a big-data era due to the emerging generation of radio interferometric (RI) telescopes, such as the Square Kilometre Array (SKA), which will acquire massive volumes of data. In this article we review methods proposed recently to resolve the ill-posed inverse problem of imaging the raw visibilities acquired by RI telescopes in the big-data scenario. We focus on the recently proposed online reconstruction method [4] and the considerable savings in data storage requirements and computational cost that it yields.

astro-ph.IM↗

arXiv2019

Distributed and parallel sparse convex optimization for radio interferometry with PURIFY

Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article.

astro-ph.IM↗

arXiv2019

Wavelet-Based Segmentation on the Sphere

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on real-world spherical images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.

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