Detectability of the Order of Operations: An Information Theoretic Approach

As it is more and more convenient to manipulate multimedia content, the authenticity of multimedia content becomes questionable. While there are many forensic techniques developed to identify the use of a single manipulation operation, a few has considered the cases where multiple operations may be involved. In these cases, investigators not only need to identify the use of each operation, but also need to detect the order of these operations. However, due to the interplay among operations, the order of operations may not always be detectable. This leads to a fundamental question of when we can and cannot detect the order of operations. In this paper, we formulate the problem of detecting the order of operations as a multiple hypotheses testing problem. Then, we propose an information theoretical framework to model the relationship between the detected hypothesis and the true hypothesis. Under this framework, we propose a mutual information-based criterion to obtain the best detector and use it to determine whether we can or cannot detect the order of operations based on certain set of features. A case study of detecting the order of resizing and blurring has been examined to demonstrate the effectiveness of the proposed framework and criteria. In addition, two known forensic problems are considered in the simulations to show that the results obtained from the proposed framework and criteria match those of the existing works.