带图像恢复的扩频水印模型的统计力学评价
Statistical mechanical evaluation of spread spectrum watermarking model with image restoration
摘要：
在原始图像是盲的情况下，期望能够同时估计图像和消息两者的解码方法。提出了一种基于贝叶斯估计的带图像恢复的扩频水印模型。因此，我们需要假设一些先验概率。消息估计的概率由均匀分布给出，图像估计的概率由无限范围模型和二维伊辛模型给出。任何来自未授权用户的攻击都可以用信道模型来表示。我们可以通过最大化后验概率来获得估计的消息和图像。在无限范围模型下，利用复制方法分析了该方法的性能。我们首先从鞍点方程计算出误码率的理论值，然后通过计算机模拟进行验证。为此，我们假设图像是二进制的，并且是从给定的先验概率生成的。我们还假设攻击可以由高斯信道表示。计算机模拟结果与理论值基本一致。在先验概率由二维伊辛模型给出的情况下，其中每个像素与四个邻居静态连接，我们通过计算机模拟来评估解码性能，因为副本理论不能应用。使用二维伊辛模型的结果表明，所提出的方法与图像恢复是有效的无限范围模型解码消息。我们比较的情况下，其中的图像是盲目的，其中之一，它被告知的性能。只要嵌入率和攻击率很小，这些病例之间的差异就很小。这表明，所提出的方法与同时估计是有效的水印解码器。
英文摘要：
In cases in which an original image is blind, a decoding method where both the image and the messages can be estimated simultaneously is desirable. We propose a spread spectrum watermarking model with image restoration based on Bayes estimation. We therefore need to assume some prior probabilities. The probability for estimating the messages is given by the uniform distribution, and the ones for the image are given by the infinite range model and 2D Ising model. Any attacks from unauthorized users can be represented by channel models. We can obtain the estimated messages and image by maximizing the posterior probability. We analyzed the performance of the proposed method by the replica method in the case of the infinite range model. We first calculated the theoretical values of the bit error rate from obtained saddle point equations and then verified them by computer simulations. For this purpose, we assumed that the image is binary and is generated from a given prior probability. We also assume that attacks can be represented by the Gaussian channel. The computer simulation retults agreed with the theoretical values. In the case of prior probability given by the 2D Ising model, in which each pixel is statically connected with four-neighbors, we evaluated the decoding performance by computer simulations, since the replica theory could not be applied. Results using the 2D Ising model showed that the proposed method with image restoration is as effective as the infinite range model for decoding messages. We compared the performances in a case in which the image was blind and one in which it was informed. The difference between these cases was small as long as the embedding and attack rates were small. This demonstrates that the proposed method with simultaneous estimation is effective as a watermarking decoder.
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