Security Analysis on Spatial  $\pm$1 Steganography for JPEG Decompressed Images
Although many existing steganalysis works have shown that the spatial ±1 steganography on JPEG pre-compressed images is relatively easier to be detected compared with that on the never-compressed images, most experimental results seem not very convincing since these methods usually assume that the quantization table of the JPEG stegos previously used is known before detection and/or the length of embedded message is fixed. Furthermore, there are just few effective quantitative algorithms for further estimating the spatial modifications. In this letter, we firstly propose an effective method to detect the quantization table from the contaminated digital images which are originally stored as JPEG format based on our recently developed work about JPEG compression error analysis , and then we present a quantitative method to reliably estimate the length of spatial modifications in those gray-scale JPEG stegos by using data fitting technology. The extensive experimental results show that our estimators are very effective, and the order of magnitude of prediction error can remain around measured by the mean absolute difference.