Compressive Sensing Forensics

Identifying a signal´s origin and how it was acquired is an important forensic problem. While forensic techniques currently exist to determine a signal´s acquisition history, these techniques do not account for the possibility that a signal could be compressively sensed. This is an important problem since compressive sensing techniques have seen increased popularity in recent years. In this paper, we propose a set of forensic techniques to identify signals acquired by compressive sensing. We do this by first identifying the fingerprints left in a signal by compressive sensing. We then propose two compressive sensing detection techniques that can operate on a broad class of signals. Since compressive sensing fingerprints can be confused with fingerprints left by traditional image compression techniques, we propose a forensic technique specifically designed to identify compressive sensing in digital images. In addition, we propose a technique to forensically estimate the number of compressive measurements used to acquire a signal. Through a series of experiments, we demonstrate that each of our proposed techniques can perform reliably under realistic conditions. Simulation results show that both our zero ratio detector and distribution-based detector yield perfect detections for all reasonable conditions that compressive sensing is used in applications, and the specific two-step detector for images can at least achieve probability of detection of 90% for probability of false alarm <;10%. In addition, our estimator for the number of compressive measurements can well reflect the real number.