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COVID-19 pandemic continues to spread rapidly over the world and causes a tremendous crisis in global human health and the economy. Its early detection and diagnosis are crucial for controlling the further spread. Many deep learning-based methods have been proposed to assist clinicians in automatic COVID-19 diagnosis based on computed tomography imaging. However, challenges still remain, including low data diversity in existing datasets, and unsatisfied detection resulting from insufficient accuracy and sensitivity of deep learning models. To enhance the data diversity, we design augmentation techniques of incremental levels and apply them to the largest open-access benchmark dataset, COVIDx CT-2A. Meanwhile, similarity regularization (SR) derived from contrastive learning is proposed in this study to enable CNNs to learn more parameter-efficient representations, thus improving the accuracy and sensitivity of CNNs. The results on seven commonly used CNNs demonstrate that CNN performance can be improved stably through applying the designed augmentation and SR techniques. In particular, DenseNet121 with SR achieves an average test accuracy of 99.44% in three trials for three-category classification, including normal, non-COVID-19 pneumonia, and COVID-19 pneumonia. And the achieved precision, sensitivity, and specificity for the COVID-19 pneumonia category are 98.40%, 99.59%, and 99.50%, respectively. These statistics suggest that our method has surpassed the existing state-of-the-art methods on the COVIDx CT-2A dataset.