Reliable Learning with PDE-Based CNNs and DenseNets for Detecting COVID-19, Pneumonia, and Tuberculosis from Chest X-Ray Images

Anca Nicoleta Marginean, Delia Doris Muntean, George Adrian Muntean, Adelina Priscu, Adrian Groza, Radu Razvan Slavescu, Calin Lucian Timbus, Gabriel Zeno Munteanu, Cezar Octavian Morosanu, Maria Margareta Cosnarovici and Camelia-M. Pintea
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Anca Nicoleta Marginean: Computer Science Department, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Delia Doris Muntean: County Clinical Emergency Hospital of Cluj-Napoca, 400006 Cluj-Napoca, Romania
George Adrian Muntean: County Clinical Emergency Hospital of Cluj-Napoca, 400006 Cluj-Napoca, Romania
Adelina Priscu: Department of Internal Medicine, Indiana University Health Ball Memorial Hospital, Muncie, IN 47303, USA
Adrian Groza: Computer Science Department, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Radu Razvan Slavescu: Computer Science Department, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Calin Lucian Timbus: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Gabriel Zeno Munteanu: County Clinical Emergency Hospital of Cluj-Napoca, 400006 Cluj-Napoca, Romania
Cezar Octavian Morosanu: University Hospital Bristol, Bristol BS2 8HW, UK
Maria Margareta Cosnarovici: The Oncology Institute Prof. Dr. Ion Chiricuta, 400015 Cluj-Napoca, Romania
Camelia-M. Pintea: Department of Mathematics and Informatics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2021, vol. 9, issue 4, 1-20

Abstract: It has recently been shown that the interpretation by partial differential equations (PDEs) of a class of convolutional neural networks (CNNs) supports definition of architectures such as parabolic and hyperbolic networks. These networks have provable properties regarding the stability against the perturbations of the input features. Aiming for robustness, we tackle the problem of detecting changes in chest X-ray images that may be suggestive of COVID-19 with parabolic and hyperbolic CNNs and with domain-specific transfer learning. To this end, we compile public data on patients diagnosed with COVID-19, pneumonia, and tuberculosis, along with normal chest X-ray images. The negative impact of the small number of COVID-19 images is reduced by applying transfer learning in several ways. For the parabolic and hyperbolic networks, we pretrain the networks on normal and pneumonia images and further use the obtained weights as the initializers for the networks to discriminate between COVID-19, pneumonia, tuberculosis, and normal aspects. For DenseNets, we apply transfer learning twice. First, the ImageNet pretrained weights are used to train on the CheXpert dataset, which includes 14 common radiological observations (e.g., lung opacity, cardiomegaly, fracture, support devices). Then, the weights are used to initialize the network which detects COVID-19 and the three other classes. The resulting networks are compared in terms of how well they adapt to the small number of COVID-19 images. According to our quantitative and qualitative analysis, the resulting networks are more reliable compared to those obtained by direct training on the targeted dataset.

Keywords: partial differential equations (PDEs); COVID-19; convolutional neural network (CNN); imbalanced dataset (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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