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Intelligent mobile image sensing powered by deep learning analyzes images captured by cameras from mobile devices, such as smartphones or smartwatches. It supports numerous mobile applications, such as image classification, face recognition, and camera scene detection. Unfortunately, mobile devices often lack the resources necessary for deep learning, leading to increased inference latency and rapid battery consumption. Moreover, the inference accuracy may decline over time due to potential data drift. To address these issues, we introduce a new cost-efficient framework, called Corun, designed to simultaneously handle multiple inference queries and continual model retraining/fine-tuning of a pre-trained model on a single commodity GPU in an edge server to significantly improve the inference throughput, upholding the inference accuracy. The scheduling method of Corun undertakes offline profiling to find the maximum number of concurrent inferences that can be executed along with a retraining job on a single GPU without incurring an out-of-memory error or significantly increasing the latency. Our evaluation verifies the cost-effectiveness of Corun. The inference throughput provided by Corun scales with the number of concurrent inference queries. However, the latency of inference queries and the length of a retraining epoch increase at substantially lower rates. By concurrently processing multiple inference and retraining tasks on one GPU instead of using a separate GPU for each task, Corun could reduce the number of GPUs and cost required to deploy mobile image sensing applications based on deep learning at the edge.