A Deterministic Approach to Detect Median Filtering in 1D Data

In this paper, we propose a forensic technique that is able to detect the application of a median filter to 1D data. The method relies on deterministic mathematical properties of the median filter, which lead to the identification of specific relationships among the sample values that cannot be found in the filtered sequences. Hence, their presence in the analyzed 1D sequence allows excluding the application of the median filter. Owing to its deterministic nature, the method ensures 0% false negatives, and although false positives (sequences not filtered classified as filtered) are theoretically possible, experimental results show that the false alarm rate is null for sufficiently long sequences. Furthermore, the proposed technique has the capability to locate with good precision a median filtered part of 1-D data and provides a good estimate of the window size used.