Information Theoretical Limit of Media Forensics: The Forensicability
While more and more forensic techniques have been proposed to detect the processing history of multimedia content, one starts to wonder if there exists a fundamental limit on the capability of forensics. In other words, besides keeping on searching what investigators can do, it is also important to find out the limit of their capability and what they cannot do. In this paper, we explore the fundamental limit of operation forensics by proposing an information theoretical framework. In particular, we consider a general forensic system of estimating operations' hypotheses based on extracted features from the multimedia content. In this system, forensicability is defined as the maximum forensic information that features contain about operations. Then, due to its conceptual similarity with mutual information in an information theory, forensicability is measured as the mutual information between features and operations' hypotheses. Such a measurement gives the error probability lower bound of all practical estimators, which use these features to detect the operations' hypotheses. Furthermore, it can determine the maximum number of hypotheses that we can theoretically detect. To demonstrate the effectiveness of our proposed information theoretical framework, we apply this framework on a forensic example of detecting the number of JPEG compressions based on normalized discrete cosine transform (DCT) coefficient histograms. We conclude that, when subband (2, 3) is used in detection and the size of the testing database is <;20000, the maximum number of JPEG compressions that we can expectedly perfectly detect using normalized DCT coefficient histogram features is four. Furthermore, we obtain the optimal strategies for investigators and forgers based on the fundamental measurement of forensicability.