*1.1. Background*

With the rapid development of information technology, the internet has been ubiquitous in the world. Thanks to the development of optical communication systems (see [1] for more discussions), people can easily communicate with each other and share multimedia messages, including texts, sound, images, videos, etc. Obviously, the internet provides much more impact on human society than any other medium, while at the same time, issues regarding information security have received considerable and critical attention.

*Data hiding* is an available technique to deal with secure communication so that the secure data is imperceptibly embedded without drawing attention [2]. The multimedia is used as a cover carrier to hide secret data which will be transmitted in the internet. Reversible data hiding (RDH) not only guarantees the safe transmission of data content but also recovers the hidden data as well as the cover images [3,4]. However, most of these RDH algorithms bring permanent distortions to the original carrier during the embedding

**Citation:** Hung, C.-C.; Lin, C.-C.; Wu, H.-C.; Lin, C.-W. A Study on Reversible Data Hiding Technique Based on Three-Dimensional Prediction-Error Histogram Modification and a Multilayer Perceptron. *Appl. Sci.* **2022**, *12*, 2502. https://doi.org/10.3390/app12052502

Academic Editors: Leandros Maglaras, Helge Janicke and Mohamed Amine Ferrag

Received: 13 January 2022 Accepted: 23 February 2022 Published: 28 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

process, and these distortions are unacceptable in certain applications [5]. In order to achieve information hiding and distortion-free recovery of the original carrier, distortionfree reversible data hiding is considered [4]. This technique enables the receiver to both extract the embedded data correctly and acquire the original carrier without distortion. Generally, RDH is a fragile hiding technology, which is different from digital watermarking. When implementing the RDH mothod, the distortion that occurs during the transmission of the carrier should be avoided. According to the embedding method, the existing image RDH algorithm can be divided into spatial domain, transform domain, and encryption domain RDH scheme [6]. In this paper, we focus on RDH of spatial domain. Its embedding and extraction frameworks are shown in Figure 1. In the embedding side, the sender embeds secret data into the cover image by a reversible embedding algorithm. In the extraction side, the receiver extracts the secret data embedded in the stego-image by a reversible extraction algorithm and achieves distortion-free recovery image exactly the same as the original image. The performance of RDH algorithm depends on two conflicting factors as trade-offs: the embedding distortion between the cover image and the stegoimage and the embedding capacity (EC). For the former factor, PSNR (peak-to-noise-ratio) is widely used (refer to [7] for more discussion). A higher PSNR value means that the stego-image is more similar to the original one. For the latter factor, EC stands for the number of bits which can be embedded into the cover image. Therefore, we favor an RDH algorithm which brings higher EC and lower PSNR, while a trade-off of them is usually considered to fit specific applications [6].

**Figure 1.** The embedding and extraction frameworks of the spatial domain RDH.
