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Camera identification has recently attracted considerable attention in the image forensic field of research. Several algorithms have been established based on the hand-crafted features and deep learning, through analysis of the traces achieved by the digital image acquisition process. Although these approaches have led to a breakthrough in the image forensics, some important problems still remain unsolved. For instance, extracting the hand-crafted features with human efforts is a difficult and time-consuming process, while data-driven deep learning methods tend to learn features that represent image contents rather than cameras' characteristics. To fully take advantages of both hand-crafted and data-driven technologies, we propose a domain knowledge-driven method, which consists of one pre-processing module, one feature extractor, and one hierarchical multi-task learning procedure. The pre-processing module can introduce the domain knowledge to the subsequent deep learning network. Moreover, for device-level identification, hierarchical multi-task learning can provide more supervise information from the brand and model. The proposed framework is evaluated on three different tasks, i.e., the brand, model, and device-level identification using original and manipulated images. Our classification results demonstrate that the proposed method is effective and robust. To evaluate the robustness of the proposed method, we create a new database for the cell-phone identification and evaluate the proposed method. It is found that the accuracy of the cell-phone device identification can reach 84.3%, which is much higher than that of the camera identification. Moreover, the t-distributed stochastic neighbor embedding visualization results confirm that the features of different cell-phone devices are visually more separable than cameras.