Information-theoretic Bounds of Resampling Forensics: New Evidence for Traces Beyond Cyclostationarity

Although several methods have been proposed for the detection of resampling operations in multimedia signals and the estimation of the resampling factor, the fundamental limits for this forensic task leave open research questions. In this work, we explore the effects that a downsampling operation introduces in the statistics of a 1D signal as a function of the parameters used. We quantify the statistical distance between an original signal and its downsampled version by means of the Kullback-Leibler Divergence (KLD) in case of a wide-sense stationary 1st-order autoregressive signal model. Values of the KLD are derived for different signal parameters, resampling factors and interpolation kernels, thus predicting the achievable hypothesis distinguishability in each case. Our analysis reveals unexpected detectability in case of strong downsampling due to the local correlation structure of the original signal. Moreover, since existing detection methods generally leverage the cyclostationarity of resampled signals, we also address the case where the autocovariance values are estimated directly by means of the sample autocovariance from the signal under investigation. Under the considered assumptions, the Wishart distribution models the sample covariance matrix of a signal segment and the KLD under different hypotheses is derived.

[1]  Fernando Pérez-González,et al.  On the role of differentiation for resampling detection , 2010, 2010 IEEE International Conference on Image Processing.

[2]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3]  Rob J Hyndman,et al.  A unified view of linear AR(1) models , 1999 .

[4]  P. P. Vaidyanathan,et al.  Effects of Multirate Systems on the Statistical Properties of Random Signals , 1993, IEEE Trans. Signal Process..

[5]  David Vazquez-Padin,et al.  An SVD approach to forensic image resampling detection , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[6]  Hany Farid,et al.  Exposing digital forgeries by detecting traces of resampling , 2005, IEEE Transactions on Signal Processing.

[7]  David Vazquez-Padin,et al.  Prefilter design for forensic resampling estimation , 2011, 2011 IEEE International Workshop on Information Forensics and Security.

[8]  Andrew C. Gallagher.  Detection of linear and cubic interpolation in JPEG compressed images , 2005, The 2nd Canadian Conference on Computer and Robot Vision (CRV'05).

[9]  Ingemar J. Cox,et al.  Normalized Energy Density-Based Forensic Detection of Resampled Images , 2012, IEEE Transactions on Multimedia.

[10]  Frank Nielsen,et al.  Clustering Multivariate Normal Distributions , 2009, ETVC.

[11]  K. J. Ray Liu,et al.  Information Theoretical Limit of Media Forensics: The Forensicability , 2016, IEEE Transactions on Information Forensics and Security.

[12]  David Vazquez-Padin,et al.  ML estimation of the resampling factor , 2012, 2012 IEEE International Workshop on Information Forensics and Security (WIFS).

[13]  David Vazquez-Padin,et al.  Two-dimensional statistical test for the presence of almost cyclostationarity on images , 2010, 2010 IEEE International Conference on Image Processing.

[14]  Pedro Comesaña.  Detection and information theoretic measures for quantifying the distinguishability between multimedia operator chains , 2012, 2012 IEEE International Workshop on Information Forensics and Security (WIFS).

[15]  Matthias Kirchner,et al.  Fast and reliable resampling detection by spectral analysis of fixed linear predictor residue , 2008, MM&Sec '08.

[16]  Mauro Barni,et al.  Source Distinguishability Under Distortion-Limited Attack: An Optimal Transport Perspective , 2014, IEEE Transactions on Information Forensics and Security.

[17]  Matthias Kirchner,et al.  Linear row and column predictors for the analysis of resized images , 2010, MM&Sec '10.

[18]  Fernando Pérez-González,et al.  Multimedia Operator Chain Topology and Ordering Estimation Based on Detection and Information Theoretic Tools , 2012, IWDW.

[19]  Renato J. Cintra,et al.  Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[20]  David Vazquez-Padin,et al.  Set-membership identification of resampled signals , 2013, 2013 IEEE International Workshop on Information Forensics and Security (WIFS).

[21]  Babak Mahdian,et al.  Ieee Transactions on Information Forensics and Security 1 Blind Authentication Using Periodic Properties of Interpolation , 2022 .

[22]  Christian Cachin,et al.  An information-theoretic model for steganography , 1998, Inf. Comput..

[23]  M. L. Eaton.  Multivariate statistics : a vector space approach , 1985 .