Towards A Theory of Jpeg Block Convergence

The convergence statistics of JPEG blocks has been shown to be a useful tool to forensically analyze high quality compressed images. Since current approaches are based on empirical observations, we propose a theoretical analysis explaining the case of grayscale images and maximum quality JPEG compression (i.e., quality factor equal to 100). The approximate distribution of the stable block ratio at different compression stages is derived, showing that it ultimately depends on the variance of the quantization noise in the DCT domain. We apply such results to discriminate never compressed images and images compressed once with maximum quality, by resorting to results on JPEG error statistics. Tests on image patches with different size and content validate the theoretical results, which allow for obtaining high accuracy through a calibration-free maximum likelihood classification rule.