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Since JPEG has been a popularly used image compression standard, forgery detection in JPEG images now plays an important role. Forgeries on compressed images often involve recompression and tend to erase those forgery traces existed in uncompressed images. We could, however, try to discover new traces caused by recompression and use these traces to detect the recompression forgeries. Quantization is the critical step in lossy compression which maps the DCT coefficients in an irreversible way under the quantization constraint set (QCS) theorem. In this paper, we first derive that a doubly compressed image no longer follows the QCS theorem and then propose a novel quantization noise model to characterize single and doubly compressed images. In order to detect double compression forgery, we further propose to approximate the uncompressed ground truth image using image restoration techniques. We conduct a series of experiments to demonstrate the validity of the proposed quantization noise model and also the effectiveness of the forgery detection method with the proposed image restoration techniques.