重采样取证的信息理论界限:超越循环平稳性的新证据

Cecilia Pasquini, Rainer Böhme
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引用次数: 6

摘要

虽然已经提出了几种方法来检测多媒体信号中的重采样操作和估计重采样因子,但这一法医任务的基本限制留下了开放的研究问题。在这项工作中,我们探讨了降采样操作作为所使用参数的函数在一维信号统计中引入的影响。在广义平稳一阶自回归信号模型中,我们利用Kullback-Leibler散度(KLD)量化了原始信号与其下采样版本之间的统计距离。针对不同的信号参数、重采样因子和插值核,导出了KLD的值,从而预测了每种情况下可实现的假设可分辨性。我们的分析揭示了由于原始信号的局部相关结构,在强下采样情况下的意外可检测性。此外,由于现有的检测方法通常利用重采样信号的循环平稳性,我们还解决了通过调查信号的样本自协方差直接估计自协方差值的情况。在所考虑的假设条件下,推导了信号段样本协方差矩阵的Wishart分布模型和不同假设条件下的KLD。
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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.
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