Machine learning methods offer great promise for fast and accurate detection and prognostication of coronavirus disease 2019 (COVID-19) from standard-of-care chest radiographs (CXR) and chest computed tomography (CT) images. Many articles have been published in 2020 describing new machine learning-based models for both of these tasks, but it is unclear which are of potential clinical utility. In this systematic review, we consider all published papers and preprints, for the period from 1 January 2020 to 3 October 2020, which describe new machine learning models for the diagnosis or prognosis of COVID-19 from CXR or CT images. All manuscripts uploaded to bioRxiv, medRxiv and arXiv along with all entries in EMBASE and MEDLINE in this timeframe are considered. Our search identified 2,212 studies, of which 415 were included after initial screening and, after quality screening, 62 studies were included in this systematic review. Our review finds that none of the models identified are of potential clinical use due to methodological flaws and/or underlying biases. This is a major weakness, given the urgency with which validated COVID-19 models are needed. To address this, we give many recommendations which, if followed, will solve these issues and lead to higher-quality model development and well-documented manuscripts.

The Cahn-Hilliard equation is a nonlinear fourth order diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the Cahn-Hilliard equation is a new approach in image processing. In this paper we discuss the stationary state of the proposed model and introduce a generalization for grayvalue images of bounded variation. This is realized by using subgradients of the total variation functional within the flow, which leads to structure inpainting with smooth curvature of level sets.

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Automatic segmentation methods are an important advancement in medical image analysis. Machine learning techniques, and deep neural networks in particular, are the state-of-the-art for most medical image segmentation tasks. Issues with class imbalance pose a significant challenge in medical datasets, with lesions often occupying a considerably smaller volume relative to the background. Loss functions used in the training of deep learning algorithms differ in their robustness to class imbalance, with direct consequences for model convergence. The most commonly used loss functions for segmentation are based on either the cross entropy loss, Dice loss or a combination of the two. We propose the Unified Focal loss, a new hierarchical framework that generalises Dice and cross entropy-based losses for handling class imbalance. We evaluate our proposed loss function on five publicly available, class imbalanced medical imaging datasets: CVC-ClinicDB, Digital Retinal Images for Vessel Extraction (DRIVE), Breast Ultrasound 2017 (BUS2017), Brain Tumour Segmentation 2020 (BraTS20) and Kidney Tumour Segmentation 2019 (KiTS19). We compare our loss function performance against six Dice or cross entropy-based loss functions, across 2D binary, 3D binary and 3D multiclass segmentation tasks, demonstrating that our proposed loss function is robust to class imbalance and consistently outperforms the other loss functions. Source code is available at: https://github.com/mlyg/unified-focal-loss .

We consider recent work of [17] and [9], where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. The differential equation setting lends itself to learning additional parameters such as the time discretisation. We explore this extension alongside natural constraints (e.g. time steps lie in a simplex). We compare these deep learning algorithms numerically in terms of induced flow and generalisation ability.arXiv:1904.05657v3 [math.OC]