Information theoretical limit of compression forensics

Multimedia forensics concerns on extracting forensic information from suspicious multimedia contents. This information was embedded into the content inadvertently whenever an operation happened. Investigators may estimate the possible operations by obtaining features from the multimedia content and applying detection algorithms based on the statistics. While most existing works focus on improving detection performance and finding what more we can do, understanding the fundamental limit on the forensic information that we can obtain from the extracted features is also important. It enables us to understand the limit of forensicability. In this paper, we explore the fundamental limit of forensicability by introducing an information theoretical framework for multimedia forensics. We use mutual information as the measure of forensic information conveyed by features to investigators. To show the analytical process, we take the case of multiple JPEG compression forensics as an example. We claim that, under typical circumstances, the maximum number of compressions that we can detect by examine DCT coefficients is up to 4, in an expected sense. In addition, we also find the patterns of compression quality factors that contain the most and least forensic information.