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The Coronavirus (COVID-19) outbreak in December 2019 has become an ongoing threat to humans worldwide, creating a health crisis that infected millions of lives, as well as devastating the global economy. Deep learning (DL) techniques have proved helpful in analysis and delineation of infectious regions in radiological images in a timely manner. This paper makes an in-depth survey of DL techniques and draws a taxonomy based on diagnostic strategies and learning approaches. DL techniques are systematically categorized into classification, segmentation, and multi-stage approaches for COVID-19 diagnosis at image and region level analysis. Each category includes pre-trained and custom-made Convolutional Neural Network architectures for detecting COVID-19 infection in radiographic imaging modalities; X-Ray, and Computer Tomography (CT). Furthermore, a discussion is made on challenges in developing diagnostic techniques such as cross-platform interoperability and examining imaging modality. Similarly, a review of the various methodologies and performance measures used in these techniques is also presented. This survey provides an insight into the promising areas of research in DL for analyzing radiographic images, and further accelerates the research in designing customized DL based diagnostic tools for effectively dealing with new variants of COVID-19 and emerging challenges.