Graph clustering discovers groups or communities within networks. Increasingly, models use autoencoders to achieve effective clustering combined with Graph Neural Networks (GNN) for structure incorporation. However, GNNs based on convolution or attention variants lack dynamic fusion, suffer from over-smoothing, noise, node heterophily, are computationally expensive and typically require the complete graph being present. Instead, we propose SCGC, capable of dynamic soft structure fusion via augmentation-less edge-contrastive loss. Further, we propose SCGC*, with a more expressive novel distance metric, Influence, and our Influence Augmented Contrastive (IAC) loss, requiring only half the model parameters. Our models, SCGC and SCGC*, dynamically fuse discriminative node representations, jointly refine soft cluster assignments, completely eliminate convolutions and attention of traditional GNNs, use only simple linear units, and yet efficiently incorporate structure. They are impervious to layer depth; robust to over-smoothing, incorrect edges and heterophily; scalable by batching; augmentation-less; relaxes the homophily assumption and trivially parallelizable. We improve significantly over the state-of-the-art on a wide range of benchmarks, including images, sensor data, text, and citation networks, with superb efficiency. Specifically, 20% on ARI and 18% on NMI for DBLP; overall 55% reduction in training time and overall, 81% reduction on inference time. code: https://github.com/gayanku/SCGC .

In medical image analysis, automated segmentation of multi-component anatomical entities, with the possible presence of variable anomalies or pathologies, is a challenging task. In this work, we develop a multi-step approach using U-Net-based models to initially detect anomalies (bone marrow lesions, bone cysts) in the distal femur, proximal tibia and patella from 3D magnetic resonance (MR) images in individuals with varying grades of knee osteoarthritis. Subsequently, the extracted data are used for downstream tasks involving semantic segmentation of individual bone and cartilage volumes as well as bone anomalies. For anomaly detection, U-Net-based models were developed to reconstruct bone volume profiles of the femur and tibia in images via inpainting so anomalous bone regions could be replaced with close to normal appearances. The reconstruction error was used to detect bone anomalies. An anomaly-aware segmentation network, which was compared to anomaly-naïve segmentation networks, was used to provide a final automated segmentation of the individual femoral, tibial and patellar bone and cartilage volumes from the knee MR images which contain a spectrum of bone anomalies. The anomaly-aware segmentation approach provided up to 58% reduction in Hausdorff distances for bone segmentations compared to the results from anomaly-naïve segmentation networks. In addition, the anomaly-aware networks were able to detect bone anomalies in the MR images with greater sensitivity and specificity (area under the receiver operating characteristic curve [AUC] up to 0.896) compared to anomaly-naïve segmentation networks (AUC up to 0.874).

Traumatic brain injury (TBI) remains a growing significant public health problem and prognosis of outcome is difficult due to the multitude of factors that underlie the heterogeneity of TBI. Prognosis aims to forecast the likely development of the disease and significantly affects patient's recovery and healthcare. Traditionally, TBI prognosis relies on the physician's insights and their empirical knowledge which makes it infeasible for large-scale implementation. Existing methods utilize a single modality (i.e., either clinical data or Computed Tomography scan images) for TBI prognosis, leaving crucial information from multi-modal data largely underexplored. To address this concern, we explore a Multi-modal Structure-aware Field-wise learning (MSF) method that is capable of mining complex correlations between multi-modal data and TBI outcomes for prognosis on a real-world dataset. Specifically, we develop a High-Level Structure-Aware (HSA) module to capture the structure information of the multilayered clinical data. Experimental results on the publicly available TRACK-TBI dataset demonstrate the viability and effectiveness of our proposed method, by achieving the top-3 accuracy of 96.07% and 98.13% for 3-month and 6-month predictions after injury, respectively.

Deep neural networks have demonstrated promising performance on image recognition tasks. However, they may heavily rely on confounding factors, using irrelevant artifacts or bias within the dataset as the cue to improve performance. When a model performs decision-making based on these spurious correlations, it can become untrustable and lead to catastrophic outcomes when deployed in the realworld scene. In this paper, we explore and try to solve this problem in the context of skin cancer diagnosis. We introduce a human-in-the-loop framework in the model training process such that users can observe and correct the model's decision logic when confounding behaviors happen. Specifically, our method can automatically discover confounding factors by analyzing the co-occurrence behavior of the samples. It is capable of learning confounding concepts using easily obtained concept exemplars. By mapping the black-box model's feature representation onto an explainable concept space, human users can interpret the concept and intervene via first order-logic instruction. We systematically evaluate our method on our newly crafted, well-controlled skin lesion dataset and several public skin lesion datasets. Experiments show that our method can effectively detect and remove confounding factors from datasets without any prior knowledge about the category distribution and does not require fully annotated concept labels. We also show that our method enables the model to focus on clinical-related concepts, improving the model's performance and trustworthiness during model inference.

Contrastive learning has recently achieved remarkable success in many domains including graphs. However contrastive loss, especially for graphs, requires a large number of negative samples which is unscalable and computationally prohibitive with a quadratic time complexity. Sub-sampling is not optimal. Incorrect negative sampling leads to sampling bias. In this work, we propose a meta-node based approximation technique that is (a) simple, (b) canproxy all negative combinations (c) in quadratic cluster size time complexity, (d) at graph level, not node level, and (e) exploit graph sparsity. By replacing node-pairs with additive cluster-pairs, we compute the negatives in cluster-time at graph level. The resulting Proxy approximated meta-node Contrastive (PamC) loss, based on simple optimized GPU operations, captures the full set of negatives, yet is efficient with a linear time complexity. By avoiding sampling, we effectively eliminate sample bias. We meet the criterion for larger number of samples, thus achieving block-contrastiveness, which is proven to outperform pair-wise losses. We use learnt soft cluster assignments for the meta-node construction, and avoid possible heterophily and noise added during edge creation. Theoretically, we show that real world graphs easily satisfy conditions necessary for our approximation. Empirically, we show promising accuracy gains over state-of-the-art graph clustering on 6 benchmarks. Importantly, we gain substantially in efficiency; over 2x reduction in training time and over 5x in GPU memory reduction. Additionally, our embeddings, combined with a single learnt linear transformation, is sufficient for node classification; we achieve state-of-the-art on Citeseer classification benchmark. code:https://github.com/gayanku/PAMC

In this letter, we demonstrate how characteristics of a permutation of the Hadamard transform (HT), known as the binary discrete Hartley transform (BDHT), can be leveraged to develop a Hadamard slice theorem (HST). In doing so, we establish an orthogonal binary two dimensional (2D) transform consisting of square wave basis functions. Typically, the 2D-HT is separated into a series of one dimensional (1D) transforms of the columns and rows of an image. This process yields binary, checkerboard pattern basis functions similar in appearance to the 2D separable discrete Hartley transform (SDHT). Instead, basis functions of our proposed non-separable 2D Hartley-Hadamard transform (HHT) are analogous to sinusoids of the non-separable 2D-discrete Hartley transform (DHT). This new transform closely mimics the 2D-DHT, while preserving the benefits and characteristics of the HT (such as being multiplication free). To our knowledge, this is the first non-separable 2D-HT, with the accompanying HST being the first to relate projections of the discrete Radon transform (DRT) to the 2D-HT of an image.

Convolutional neural networks (CNN) have demonstrated outstanding Compressed Sensing (CS) performance compared to traditional, hand-crafted methods. However, they are broadly limited in terms of generalisability, inductive bias and difficulty to model long distance relationships. Transformer neural networks (TNN) overcome such issues by implementing an attention mechanism designed to capture dependencies between inputs. However, high-resolution tasks typically require vision Transformers (ViT) to decompose an image into patch-based tokens, limiting inputs to inherently local contexts. We propose a novel image decomposition that naturally embeds images into low-resolution inputs. These Kaleidoscope tokens (KD) provide a mechanism for global attention, at the same computational cost as a patch-based approach. To showcase this development, we replace CNN components in a well-known CS-MRI neural network with TNN blocks and demonstrate the improvements afforded by KD. We also propose an ensemble of image tokens, which enhance overall image quality and reduces model size. Supplementary material is available: https://github.com/uqmarlonbran/TCS.git.

Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with finite, iterative reconstruction schemes to form an image from limited samples. Using a sampling pattern constructed entirely from periodic lines in DFT space, chaotic sensing was found to outperform traditional compressed sensing for magnetic resonance imaging; however, only one such sampling pattern was presented and the reason for its fractal nature was not proven. Through the introduction of a novel image transform known as the kaleidoscope transform, which formalises and extends upon the concept of downsampling and concatenating an image with itself, this paper: (1) demonstrates a fundamental relationship between multiplication in modular arithmetic and downsampling; (2) provides a rigorous mathematical explanation for the fractal nature of the sampling pattern in the DFT; and (3) leverages this understanding to develop a collection of novel fractal sampling patterns for the 2D DFT with customisable properties. The ability to design tailor-made fractal sampling patterns expands the utility of the DFT in chaotic imaging and may form the basis for a bespoke chaotic sensing methodology, in which the fractal sampling matches the imaging task for improved reconstruction.

We propose a sparse imaging methodology called Chaotic Sensing (ChaoS) that enables the use of limited yet deterministic linear measurements through fractal sampling. A novel fractal in the discrete Fourier transform is introduced that always results in the artefacts being turbulent in nature. These chaotic artefacts have characteristics that are image independent, facilitating their removal through dampening (via image denoising) and obtaining the maximum likelihood solution. In contrast with existing methods, such as compressed sensing, the fractal sampling is based on digital periodic lines that form the basis of discrete projected views of the image without requiring additional transform domains. This allows the creation of finite iterative reconstruction schemes in recovering an image from its fractal sampling that is also new to discrete tomography. As a result, ChaoS supports linear measurement and optimisation strategies, while remaining capable of recovering a theoretically exact representation of the image. We apply the method to simulated and experimental limited magnetic resonance (MR) imaging data, where restrictions imposed by MR physics typically favour linear measurements for reducing acquisition time.

This study presents an integer‐only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with low‐computational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round‐off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number‐theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real‐valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low‐computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.

The discrete Fourier slice theorem is an important tool for signal processing, especially in the context of the exact reconstruction of an image from its projected views. This paper presents a digital reconstruction algorithm to recover a two dimensional (2-D) image from sets of discrete one dimensional (1-D) projected views. The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise. A mapping of discrete projections is constructed to allow aperiodic projections to be converted to projections that assume periodic image boundary conditions. Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation. The discrete projection angles are selected so that the set of remapped 1-D slices exactly tile the 2-D DFT space. This permits direct and mathematically exact reconstruction of the image via the inverse DFT. The reconstructions are artefact free, except for projection inconsistencies that arise from any additive and remapped noise. We also present methods to generate compact sets of rational projection angles that exactly tile the 2-D DFT space. The improvement in noise suppression that comes with the reconstruction of larger sized images needs to be balanced against the corresponding increase in computation time.

We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servières et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N2). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.

Accurate localization of the prostate and its surrounding tissue is essential in the treatment of prostate cancer. This paper presents a novel approach to fully automatically segment the prostate, including its seminal vesicles, within a few minutes of a magnetic resonance (MR) scan acquired without an endorectal coil. Such MR images are important in external beam radiation therapy, where using an endorectal coil is highly undesirable. The segmentation is obtained using a deformable model that is trained on-the-fly so that it is specific to the patient's scan. This case specific deformable model consists of a patient specific initialized triangulated surface and image feature model that are trained during its initialization. The image feature model is used to deform the initialized surface by template matching image features (via normalized cross-correlation) to the features of the scan. The resulting deformations are regularized over the surface via well established simple surface smoothing algorithms, which is then made anatomically valid via an optimized shape model. Mean and median Dice's similarity coefficients (DSCs) of 0.85 and 0.87 were achieved when segmenting 3T MR clinical scans of 50 patients. The median DSC result was equal to the inter-rater DSC and had a mean absolute surface error of 1.85 mm. The approach is showed to perform well near the apex and seminal vesicles of the prostate.

This paper presents a technique to remove image artefacts, formed under the cyclic additive group Zp, during the inverse Radon reconstruction from prime-dimensioned discrete projections. The cyclic artefacts are circulant matrices that arise from gaps in the known projection data. These artefacts are superimposed periodically on the reconstructed image. The summed value of unknown artefacts at an arbitrary image pixel location is determined using other, overlapping artefact combinations that are located at image positions where their component values are known. Latin squares are used to optimise the selection of these known elements. The result requires an irregular sampling to obtain the known correction values, but, once found, provides a multitude of exact solutions, as the sampling pattern for artefact corrections is translation invariant.