# Reversible Data Hiding in Encrypted Image Based on Multi-MSB Embedding Strategy
## 4 Experimental Results and Analysis
### Comparisons with Related Methods and Analysis
The method proposed in [35] considers patch-level sparse representation when embedding secret data. In addition, the learned dictionary is also embedded into the encrypted image. With the powerful representation of sparse coding, the large space can be vacated, so that the more secret bits can be embed in the encrypted image. As we can see from Figure 10, with the increase of embedding data, the PSNR of the decrypted image is obviously decreasing. For example, for the image Lena, when the embedding rate increased from 0.05 bpp to 0.75 bpp, the corresponding PSNR decreased from 54 dB to 30.8 dB. In [36], a lossless, reversible, and combined data-hiding method based on probability homomorphism is proposed. In the lossless scheme, the additional data is embedded into several least significant bit planes of ciphertext pixels by multi-layer wet paper coding, and the ciphertext pixels are replaced by new values. In the reversible scheme, the image histogram is reduced by preprocessing before image encryption, so that the modification of the encrypted image during data embedding will not cause pixel oversaturation in the plaintext domain. Because of the compatibility between lossless and reversible schemes, the two kinds of data embedding operations can be performed simultaneously in the encrypted image. For an image, the higher the embedding rate is, the higher the distortion of the decrypted image. In [31], a separable and error-free reversible data-hiding method for encrypted images based on two-layer pixel error is proposed. A histogram of the error of two adjacent layers of encrypted pixels is used to embed the secret data through histogram shifting to generate a labeled encrypted image. The embedding capacity is determined by the value of parameter \(K\), which is used for determining which prediction errors are used to embed secret data. The higher the value of \(K\), the more secret data can be embedded, but meanwhile, the decrypted image suffers more distortion. Although the PSNRs of reconstructed images of our method cannot reach \(+\infty\), they are all very high. For the reconstructed images Lena, Airplane, and Man, the PSNRs are between 64 dB and 86 dB, 63 dB and 66 dB, and 64 dB and 90 dB respectively, which are much higher than the approach of [PERSON] et al. CPE [38] or methods [31; 35; 36]. In fact, only some edged pixels are changed and most of pixels can be recovered losslessly. The reconstructed image of our method is very close to the original image. Figure 9: \(ER\) comparison with [PERSON] et al. EPE [38] and [PERSON] et al. [39] on 500 images, randomly selected from BOWS-2 database. On the other hand, the proposed method can achieve a higher embedding rate than all the compared methods [31; 35; 36; 38; 39]. Figure 10: Performance comparisons for the tested images Lena, Airplane, and Man with the methods [31; 35; 36; 38; 39]. In summary, the proposed method is able to recover the embedded data and original image without errors and achieves an excellent trade-off between the embedding rate and the visual quality of the reconstructed image with only the encryption key.