Reversible Data Hiding Based on Two-level HDWT Coefficient Histograms

In recent years, reversible data hiding has attracted much more attention than before. Reversibility signifies that the original media can be recovered without any loss from the marked media after extracting the embedded message. This paper presents a new method that adopts two-level wavelet transform and exploits the feature of large wavelet coefficient variance to achieve the goal of high capacity with imperceptibility. Our method differs from those of previous ones in which the wavelet coefficients histogram not gray-level histogram is manipulated. Besides, clever shifting rules are introduced into histogram to avoid the decimal problem in pixel values after recovery to achieve reversibility. With small alteration of the wavelet coefficients in the embedding process, and therefore low visual distortion is obtained in the marked image. In addition, an important feature of our design is that the use of threshold is much different from previous studies. The results indicate that our design is superior to many other state-of-the-art reversible data hiding schemes.

💡 Research Summary

The paper introduces a reversible data hiding scheme that operates in the transform domain by exploiting the statistical properties of two‑level Haar discrete wavelet transform (HDWT) coefficients. After applying a two‑level HDWT to the cover image, the authors focus on the middle‑ and high‑frequency sub‑bands (LH, HL, HH). They compute three difference images between a reference sub‑band (LH) and the other two sub‑bands, and construct histograms of these difference values. By selecting a threshold T, the histograms are shifted left or right by eight units to create empty bins. Secret bits are embedded into these empty bins using a set of shifting rules that avoid decimal artifacts and prevent overflow/underflow. When all bins are filled, a centralization step moves the histogram by four units toward zero, reducing the variance of the modified coefficients and improving visual quality. A flag‑bit indicates whether any bin overlaps after shifting, and the values of T and the centralization flag f, together with the flag‑bits, are compressed with LZMA and stored in the remaining empty bins, resulting in less than 2.74 % overhead. During extraction, the marked image is decomposed again, the histograms are restored based on the stored metadata, and the original coefficients are recovered, guaranteeing lossless reconstruction. Experimental results on standard test images demonstrate that the proposed method achieves higher embedding capacity (up to 210 kbit) and superior image quality (PSNR > 48 dB, SSIM > 0.99) compared with state‑of‑the‑art reversible schemes such as those by Ni, Tian, and Fridrich. The approach is particularly suitable for applications requiring exact recovery of high‑fidelity images, such as medical imaging, forensic evidence, and military reconnaissance.