This article presents a refined notion of incompatible JPEG images for a quality factor of 100. It can detect the presence of steganographic schemes embedding in DCT coefficients. We show that, within the JPEG pipeline, the combination of the DCT transform with the quantization function can map several blocks in the pixel domain to the same block in the DCT domain. However, not every DCT block can be obtained: we call those blocks incompatible. In particular, incompatibility can happen when DCT coefficients are manually modified to embed a message. We show that the problem of distinguishing compatible blocks from incompatible ones is an inverse problem with or without solution and we propose two different methods to solve it. The first one is heuristic-based, fast to find a solution if it exists. The second is formulated as an Integer Linear Programming problem and can detect incompatible blocks only for a specific DCT transform in a reasonable amount of time. We show that the probability for a block to become incompatible only relies on the number of modifications. Finally, using the heuristic algorithm we can derive a Likelihood Ratio Test depending on the number of compatible blocks per image to perform steganalysis. We simulate the result of this test and show that it outperforms a deep learning detector e-SRNet for every payload between 0.001 and 0.01 bpp by using only 10% of the blocks from $\bf 256\times 256$ images. A Selection-Channel-Aware version of the test is even more powerful and outperforms e-SRNet while using only 1% of the blocks.

中文翻译：

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查找不兼容的模块以进行可靠的 JPEG 隐写分析


本文提出了品质因数为 100 的不兼容 JPEG 图像的改进概念。它可以检测嵌入 DCT 系数中的隐写方案的存在。我们表明，在 JPEG 管道中，DCT 变换与量化函数的组合可以将像素域中的多个块映射到 DCT 域中的同一块。然而，并不是每个 DCT 块都可以获得：我们称这些块不兼容。特别是，当手动修改 DCT 系数以嵌入消息时，可能会发生不兼容。我们表明，区分兼容区块和不兼容区块的问题是一个有或没有解决方案的逆问题，我们提出了两种不同的方法来解决这个问题。第一个是基于启发式的，如果存在解决方案，则可以快速找到解决方案。第二个被表述为整数线性规划问题，只能在合理的时间内检测特定 DCT 变换的不兼容块。我们表明，一个区块变得不兼容的概率只取决于修改的数量。最后，使用启发式算法，我们可以根据每张图像的兼容块的数量得出似然比检验，以执行隐写分析。我们模拟了该测试的结果，并表明它仅使用 $\bf 256\times 256$ 图像中 10% 的块，对于 0.001 到 0.01 bpp 之间的每个有效载荷，它的性能都优于深度学习检测器 e-SRNet。该测试的 Selection-Channel-Aware 版本功能更强大，在仅使用 1% 的块时优于 e-SRNet。