## 1 Introduction
Through the cloud technology, IoT applications, blockchain, AI artificial intelligence technology, and algorithms [1; 2; 3; 4; 5; 6; 7], RDH can be used as a tool to do many things with reversible image operations. After operating the image to the desired target, we can explore all the feature values to be restored to the original image from the target image. These feature values are some derived auxiliary parameters, and then these auxiliary parameters are embedded in the target image through reversible data embedding technology. The three main methods are difference expansion (DE) [11], histogram shifting (HS) [12; 13; 14], and prediction error expansion (PEE) [15; 16; 17]. The histogram shifting (HS) [12] proposed by [PERSON] et al. in 2006 changes the histogram of the image in hiding the embedding secret message, and the histogram is based on the count of the number of all pixel values in the gray-scale image and is drawn into a graph. The pixel value that appears most is the peak point, and the pixel value that does not appear is the zero point. The pixel values in between will move one unit to the zero point to create space. At this time, the peak point can hide the embedding secret message with secret data 1 bit. For the HS method, because the pixel value can only be adjusted at most 1 bit each time, it can have higher image quality, but the embedding capacity will be relatively low. Other scholars have successively proposed related technologies based on the HS method, including generalized histogram shifting [18], two dimensional histogram shifting (TDHS) [19], and adaptive embedding [20]. Another mainstream method of RDH that [PERSON] and [PERSON] first proposed is the prediction error expansion (PEE) [15], which is based on the difference between the pixel values to perform the action of embedding, so embedding capacity is twice higher compared with the general DE. Additionally, PEE has a more complex predictor than DE, so it produces a prediction error that is smaller than the pixel differences of DE. In order to reduce the excessive distortion after embedding the secret message, [PERSON] et al. proposed an improved method [21] to reduce the size of the location map. In 2014, [PERSON] et al. proposed an improved PVO-based reversible data hiding (IPVO) method [22] based on pixel-value ordering (PVO) and prediction-error expansion (PEE). The IPVO method makes full use of image redundancy to hide information at the prediction errors of 0 or \(1/-1\) to achieve excellent embedding performance. In 2020, [PERSON] and [PERSON] successively proposed a pairwise IPVO method [23] to hide data in a smoother block and used the bin reservation strategy [24] to further combine PEE technology to increase the capacity embedded in the carrier. However, the method has lower image quality under low hidden payload. In 2020, [PERSON] et al. proposed an improved prediction-error expansion (I-PEE) scheme [25] to achieve higher embedding capacity and good image quality. In the spatial domain, exquisite pictures are usually transmitted or stored in a JPEG compression format. In view of this, in 2017, [PERSON] et al. proposed a robust significant bit-difference expansion (SBDE) method [26], which uses the higher significant bits (HiSB) in the pixel value as the cover image represented by (\(I_{HiSB}\)). The reason is that general image processing or attacks will make changes in the lower significant bits (LoSB). Therefore, hiding the data in \(I_{HiSB}\) can better maintain the integrity of the data content and increase the robustness of the hiding method. In 2020, [PERSON] and [PERSON] [27] also proposed the two-layer embedding (TLE) method that hides two secret data in the original pixels. [PERSON] and [PERSON]'s TLE strategy based on the HS method of PEE uses the sorted predictors and repeatedly embedding, keeping the pixel value unchanged to increase the embedding capacity. The TLE method effectively solves the problem of low capacity of the SBDE method, but there is still room for improvement.