# A Neural-Network-Based Watermarking Method Approximating JPEG Quantization
## 6 Conclusions  
The JT-Net in ReDMark [11] is a network that simulates JPEG compression. This network substitutes the quantization process with a process that adds noise proportional to the value of the quantization table. In previous work [15], a quantized activation function (QAF) quantized by constant intensity (constant QAF-Net) was proposed. In this paper, we proposed the quantization table-based QAF network (QT-QAF-Net), which can  
Figure 14: Histogram of PSNR for embedding intensity \(\alpha=1.0\) for QT-QAF-Net: (**a**) intensity \(\alpha=1.0\) for JT-Net and \(\alpha=0.55\) for constant QAF-Net and (**b**) intensity \(\alpha=0.95\) for JT-Net and intensity for constant QAF-Net \(\alpha=0.50\).  
Figure 15: BER for the JPEG compression level \(Q\).  
approximate the quantization process of the JPEG compression according to the standard. By approximating the quantization of the JPEG compression using the QAF, we expected to improve the robustness against the JPEG compression. The results of computer simulations showed that the QAF represented quantization with sufficient accuracy. Also, we found that the network trained with the QAF was more robust against the JPEG compression than those trained with the JT-Net. Because the embedding and extraction networks were more robust against the JPEG compression when trained with the QAF, we conclude that our method is more suitable for simulating JPEG compression than conventional methods applying additive noise.  
Further studies with QAF are expected. For example, since QAF is differentiable over the whole interval, it may produce better adversarial images compared to JPEGdiff [12]. Furthermore, there is a study on the estimation of the sign bit of DCT coefficients [22]. The non-linearity of the quantized DCT coefficients makes estimation difficult. The solution could be simplified by using QAF.  
Conceptualization, M.K.; methodology, M.K. and S.Y.; software, S.Y.; investigation, S.Y.; resources, M.K.; data curation, M.K. and S.Y.; writing--original draft preparation, S.Y.; writing--review and editing, M.K.; visualization, S.Y.; supervision, M.K.; project administration, M.K.; funding acquisition, M.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by JSPS KAKENHI Grant Number 20K11973 and Support Center for Advanced Telecommunications Technology (SCAT) research grant.  
Not applicable.  
Publicly available datasets were analyzed in this study. These data can be found here: CIFAR-10 dataset [[https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)]([https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)) (accessed on 3 June 2024) and Computer Vision Group. University of Granada [[https://ccia.ugr.es/cvg/CG/base.htm](https://ccia.ugr.es/cvg/CG/base.htm)]([https://ccia.ugr.es/cvg/CG/base.htm](https://ccia.ugr.es/cvg/CG/base.htm)) (accessed on 3 June 2024).  
The computations were performed using the supercomputer facilities at the Research Institute for Information Technology of Kyushu University.  
The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.