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Due to the popularity of JPEG as an image compression standard, the ability to detect tampering in JPEG images has become increasingly important. Tampering of compressed images often involves recompression and tends to erase traces of tampering found in uncompressed images. In this paper, we present a new technique to discover traces caused by recompression. We assume all source images are in JPEG format and propose to formulate the periodic characteristics of JPEG images both in spatial and transform domains. Using theoretical analysis, we design a robust detection approach which is able to detect either block-aligned or misaligned recompression. Experimental results demonstrate the validity and effectiveness of the proposed approach, and also show it outperforms existing methods.