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The COVID-19 pandemic has highlighted the importance of diagnosis and monitoring as early and accurately as possible. However, the reverse-transcription polymerase chain reaction (RT-PCR) test results in two issues: (1) protracted turnaround time from sample collection to testing result and (2) compromised test accuracy, as low as 67%, due to when the test is administered and due to how the samples are collected, handled, and delivered to the lab to conduct the RT-PCR test. Thus, we present ComputeCOVID19+, our computed tomography-based framework to improve the testing speed and accuracy of COVID-19 (plus its variants) via a deep learning-based network for CT image enhancement called DDnet. To demonstrate its speed and accuracy, we evaluate ComputeCOVID19+ across many sources of computed tomography (CT) images and on many heterogeneous platforms, including multi-core CPU, many-core GPU, and even FPGA. Our results show that ComputeCOVID19+ can significantly shorten the turnaround time from days to minutes and improve the testing accuracy to 91%.