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Lossy compression brings artifacts into the compressed image and degrades the visual quality. In recent years, many compression artifacts removal methods based on convolutional neural network (CNN) have been developed with great success. However, these methods usually train a model based on one specific value or a small range of quality factors. Obviously, if the test image's quality factor does not match to the assumed value range, then degraded performance will be resulted. With this motivation and further consideration of practical usage, a highly robust compression artifacts removal network is proposed in this paper. Our proposed network is a single model approach that can be trained for handling a wide range of quality factors while consistently delivering superior or comparable image artifacts removal performance. To demonstrate, we focus on the JPEG compression with quality factors, ranging from 1 to 60. Note that a turnkey success of our proposed network lies in the novel utilization of the quantization tables as part of the training data. Furthermore, it has two branches in parallel---i.e., the restoration branch and the global branch. The former effectively removes the local artifacts, such as ringing artifacts removal. On the other hand, the latter extracts the global features of the entire image that provides highly instrumental image quality improvement, especially effective on dealing with the global artifacts, such as blocking, color shifting. Extensive experimental results performed on color and grayscale images have clearly demonstrated the effectiveness and efficacy of our proposed single-model approach on the removal of compression artifacts from the decoded image.