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Since JPEG image format has been a popularly used image compression standard, tampering detection in JPEG images now plays an important role. The artifacts introduced by lossy JPEG compression can be seen as an inherent signature for compressed images. In this paper, we propose a new approach to analyse the blocking periodicity by, 1) developing a linearly dependency model of pixel differences, 2) constructing a probability map of each pixelpsilas belonging to this model, and 3) finally extracting a peak window from the Fourier spectrum of the probability map. We will show that, for single and double compressed images, their peakspsila energy distribution behave very differently. We exploit this property and derive statistic features from peak windows to classify whether an image has been tampered by cropping and recompression. Experimental results demonstrate the validity of the proposed approach.