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Detecting double JPEG compression with the same quantization matrix is a challenging task in image forensics. To address this problem, in this paper, a novel method is proposed by leveraging the component convergence during repeated JPEG compressions. Firstly, an in-depth analysis of the pipeline in successive JPEG compressions is conducted, and it reveals that the rounding/truncation errors as well as JPEG coefficients tend to converge after multiple recompressions. Based on this fact, the backward quantization error (BQE) is defined, and we find that the ratio of non-zero BQE for single compression is larger than that for double compression. Moreover, to exploit the convergence property of JPEG coefficients, a multi-threshold strategy is designed for capturing the statistics of the number of different JPEG coefficients between two sequential compressions. Finally, the statistical features of the dual components are concatenated into a 15-D vector to detect double JPEG compression. Experimental results demonstrate the efficiency of the proposed method, which outperforms some state-of-the-art schemes. [ABSTRACT FROM AUTHOR]