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Timely discovery of COVID-19 could aid in formulating a suitable treatment plan for disease mitigation and containment decisions. The widely used COVID-19 test necessitates a regular method and has a low sensitivity value. Computed tomography and chest X-ray are also other methods utilized by numerous studies for detecting COVID-19. In this article, we propose a CNN called depthwise separable convolution network with wavelet multiresolution analysis module (WMR-DepthwiseNet) that is robust to automatically learn details from both spatialwise and channelwise for COVID-19 identification with a limited radiograph dataset, which is critical due to the rapid growth of COVID-19. This model utilizes an effective strategy to prevent loss of spatial details, which is a prevalent issue in traditional convolutional neural network, and second, the depthwise separable connectivity framework ensures reusability of feature maps by directly connecting previous layer to all subsequent layers for extracting feature representations from few datasets. We evaluate the proposed model by utilizing a public domain dataset of COVID-19 confirmed case and other pneumonia illness. The proposed method achieves 98.63% accuracy, 98.46% sensitivity, 97.99% specificity, and 98.69% precision on chest X-ray dataset, whereas using the computed tomography dataset, the model achieves 96.83% accuracy, 97.78% sensitivity, 96.22% specificity, and 97.02% precision. According to the results of our experiments, our model achieves up-to-date accuracy with only a few training cases available, which is useful for COVID-19 screening. This latest paradigm is expected to contribute significantly in the battle against COVID-19 and other life-threatening diseases. [ABSTRACT FROM AUTHOR]