This article presents a refined notion of incompatible JPEG images for a quality factor of 100. It can be used to 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 distinct 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 256x256 images. A Selection-Channel-Aware version of the test is even more powerful and outperforms e-SRNet while using only 1% of the blocks.

翻译：本文针对质量因子为100的JPEG图像提出了一个精炼的不兼容图像概念，该概念可用于检测在DCT系数中嵌入信息的隐写方案。我们证明，在JPEG处理流程中，DCT变换与量化函数的组合可能将像素域中多个不同的块映射到DCT域中的同一块。然而，并非所有DCT块都能通过此映射获得：我们将这类无法获得的块称为不兼容块。特别地，当DCT系数被人为修改以嵌入信息时，就可能产生不兼容现象。我们证明，区分兼容块与不兼容块的问题是一个有解或无解的逆问题，并提出了两种不同的解决方法。第一种方法基于启发式算法，能在解存在时快速找到解。第二种方法被构建为整数线性规划问题，可在合理时间内针对特定DCT变换检测不兼容块。我们证明，一个块变为不兼容的概率仅取决于修改次数。最后，利用启发式算法，我们可以根据每幅图像中兼容块的数量推导出似然比检验来进行隐写分析。通过模拟该检验的结果，我们证明在仅使用256x256图像中10%的块时，该方法在0.001至0.01 bpp的所有嵌入率下均优于深度学习检测器e-SRNet。而考虑选择通道感知的改进版本更加强大，仅需使用1%的块即可超越e-SRNet的性能。