Mobile and digital media are getting more and more popular on Internet and cloud services. In social networks, many multi-media such as images, videos, and audios are produced by different aspects of the human activities. Moreover, telemedicine applies telecommunication and information technology to offer clinical health care from a distance. In critical care and emergency situations, health informatics, medical, and imaging data are transmitted from doctors and healthcare professionals to discuss patient issues. Therefore, E-Healthcare data management plays a crucial role in modern hospitals. Over Internet and cloud services, digitized healthcare systems have provided easy access, viewing and sharing of digitized medical images to patients, doctors, medical professionals, health care providers, and institutes of medicine. Medical images may provide for teleconferences among clinicians, interdisciplinary exchanges between radiologists for consultative purposes, and distant learning of medical personnel. For illegal purposes used for insurance, for example, digital medical malignant nodule images may be modified on lung parenchyma in chest CT scan images. Therefore, data hiding schemes (Wang et al., 2017; Huang et al., 2017; Li et al., 2018; Wang et al., 2018) are much simpler and cheaper than an intrusion detection system (Huang and Hwang, 2012) to protect security and privacy of images by image with an unique digital identity.

Reversible data hiding schemes (Li et al., 2016; Huang et al., 2013a; Chen and Guo, 2020; Kim et al., 2009) (RDH) are applied to embed secrets inside an image as a stego-image with minimal distortion. After the secrets are retrieved from a stego-image at the extraction stage, the original images can be reconstructed exactly. The major applications of RDH are authentication, diagnostic image, military imagery, astronomical images, satellite, and artwork preservation. Shi et al. (2016) classified RDH techniques into six categories: histogram shifting, image compressing (e.g., JPEG), semi-fragile authentication, image contrast enhancement, encrypted images, and RDH based on audio and video. In general, there are two types of popular RDH techniques: histogram shifting (HS) (Thodi and Rodriguez, 2007; Hong et al., 2008) and difference expansion (DE). In 2006, Ni et al. (2006) proposed the first HS-based RDH by modifying the generated histogram. Some extensions of Ni et al.’s HS-based RDH methods proposed such as block-based HS (Fallahpour and Sedaaghi, 2007), difference-histogram (Lee et al., 2006), high-frequency IWT coefficients (Xuan et al., 2007; Huang et al., 2017). In 2002, Tian (2002) proposed a high capacity DE method. Furthermore, DE has been developed in three species: integer-to-integer transformation (Qiu et al., 2016), prediction-error expansion (PEE) (Dragoi and Coltuc, 2015), and adaptive embedding (Hong et al., 2015). There are three approaches in image compressing: RDH with quantized DCT coefficients modification (Huang et al., 2016), RDH with quantization table modification (Wang et al., 2013), RDH with Huffman table modification (Wu and Deng, 2011). In 2003, Vleeschouwer et al. (2003) presented the first robust RDH based on the correlations among the neighbouring pixels. In general, the approaches of contrast enhancement RDH applied some functionalities such as histogram bin expansion operations to improve the visual quality. There are four RDH approaches with contrast enhancement: method by histogram bin expansion (Wu et al., 2015a), method with contrast enhancement for medical images (Wu et al., 2015b), method with the controlled contrast enhancement (Gao and Shi, 2015), and automatic contrast enhancement method (Kim et al., 2015). Due to protection of the privacy of data and enabling the cloud server to easily manage the data, more and more researchers study reversible data hiding in encrypted images. The techniques of encrypted images are divided into three types: vacating room before encryption (Cao et al., 2016), vacating room after encryption (Zhang, 2011), and reversible image transformation (Zhang et al., 2016).

Considering resource sharing data in Cloud computing environments, stego-images may be disturbed by various techniques such as a chaotic Hénon function to obtain encrypted images (Huang et al., 2013b). Abbasy and Shanmugam (2011) presented biological aspects of the DNA to increase the level of data confidentiality among clients. Some other authors (Zhang, 2012; Surekha and Swamy, 2013) converted stego-images into encryption data transferred to public Cloud environments. Based on prediction error expansion, a predictive value is calculated by predictors. Then the secret bit-stream will be embedded into the cover image according to the expansion of the difference between a pixel and its predictive values.

Most of image data hiding techniques (Huang et al., 2012; Wu et al., 2009; Zhang S. et al., 2016; Jana et al., 2016) are developed in 2D images. However, many medical images are produced and processed (Tseng and Huang, 2010) as stacks of slices such as CT, MRI, and PET. These slices can be used to generate 3D image volumetric information. Thus, it is important to apply data hiding in 3D images efficiently. Recently, for digital media it is getting more and more important to apply data hiding to the quality of compressed video. Shanableh (2012) applied data hiding schemes to embed secrets into a compressed video bit stream for copyright protection.

In this paper, two-tier structures, histogram-shifting of median and prediction error, are utilized to embed secret messages. The rest of this paper is presented as follows. The second section demonstrates our method. The fourth section shows the outcome of the experiments. Conclusions are presented in the last section.

In this paper, we apply a block median preservation technique (Luo et al., 2011), a prediction-based reversible hiding method (Chang et al., 2012), and a histogram-based overflow/underflow process (Huang et al., 2013b) to embed n bits of secret messages for each block in gray level images. Adopting overlapping blocks partition and a histogram-based overflow/underflow process, the capacity can be improved. Two-tier data hiding will be adopted to embed messages. The detail of a two-tier data hiding scheme is described as follows.

In this paper, we demonstrate two-tier medical images data hiding based on histogram shifting of prediction errors to experiment on medical images with DICOM. The peak signal-to-noise ratio (PSNR) is applied to measure the quality. (22) PSNR=10×log102552MSE(dB), (23) MSE=1W×H ∑i=1W ∑j=1H(I(i,j)−I′(i,j)2), where W and H are the width and the height of the test image. I(i,j) and I′(i,j) are two pixel values of the cover image and stego-image at the location (i,j) . We test on 16-bit depth CT medical image shown in Fig. 4. In Table 1, we set the embedding level to 1. Different kinds of threshold result in capacity and PSNR. Obviously, the more threshold T, the more capacity. The more threshold, the smaller PSNR. On the contrary, we set the threshold to 21 and various embedding levels in Table 2. The greater the embedding level E, the more capacity, and the smaller PSNR. In Table 3, we set an embedding level and threshold to 21. The largest of bpp is 2.641178445 and the PSNR is 63.24405029.

In this paper, we also used Lena and airplane with 8-bit depth 512×512 image shown in Fig. 6. Let the threshold be 1 and the embedding level be 1–4. When bpp is 1.299938202 in the Lena image, the PSNR will be 26.39720695. Because of overflow/underflow processing, the stego-image of Lena will be shifted and the pixels will have poor PSNR. Owing to histogram shifting of the whole image, the most of the image shape will be preserved as shown in Fig. 5 and Table 4. In Fig. 7, we compare a 16-bit grayscale medical image and 8 bit images. We compare the method of median and prediction shown in Table 5. Our method has more capacity at the same PSNR.

The embedding algorithm is used to embed the secret data into the cover image as a stego-image. Stego-images are transmitted over the Internet. If stego-images are altered or destroyed due to certain attacks, our method has the basic characteristics of data hiding to protect secret data. Because the secret data is hidden in the cover image, it is difficult for the human visual system to detect any unperceivable secret data.

In our method, there are two layers of block median retention technology and a predictive reversible hiding method to hide secret data. Therefore, our method is a technique that resists the attack of this technique without parameters such as threshold, EL and overflow/underflow methods. We also applied 2 × 2 overlapping blocks to partition the image. If a hacker changes the secure covert image over the network, the secure covert image cannot be extracted correctly.

We have proposed the data hiding of two-tier medical images based on histogram shifting of prediction error. The median histogram shifting technique and prediction error schemes as the two-tier hiding have high capacity and PSNR in 16-bit medical images. The overlapping block partitions have also been adopted in this scheme, and it has performed well. At the Tier-1 data hider, the median histogram shifting technique is based on a multi-level histogram shifting mechanism. Due to adopting two types of embedding strategies, the block medians are able to be preserved. Therefore, the stego-image utilizes these block medians to convert the stego image to the original image successfully. At the Tier-2 data hider, the prediction error scheme applies a pre-determined threshold and the absolute difference of the neighbouring pixels to decide whether the current pixel is embeddable.